diff --git a/.github/workflows/CI_sequential 2.yml b/.github/workflows/CI_sequential 2.yml index 428b281a0..7b3b86cbe 100644 --- a/.github/workflows/CI_sequential 2.yml +++ b/.github/workflows/CI_sequential 2.yml @@ -840,3 +840,20 @@ jobs: ./horses3d.ns Cylinder_pAdaptationRL_GaussLobatto.control if: '!cancelled()' +# +# 38) Lamb vector computation and stats +# -------------------------------------------- + + - name: Build LambVector + working-directory: ./Solver/test/NavierStokes/LambVector/SETUP + run: | + source /opt/intel/oneapi/setvars.sh || true + make MODE=${{matrix.mode}} COMPILER=${{matrix.compiler}} COMM=${{matrix.comm}} ENABLE_THREADS=${{matrix.enable_threads}} WITH_MKL=${{matrix.mkl}} WITH_HDF5=${{matrix.hdf5}} + if: '!cancelled()' + + - name: Run LambVector + working-directory: ./Solver/test/NavierStokes/LambVector + run: | + source /opt/intel/oneapi/setvars.sh || true + ./horses3d.ns TaylorGreen.control + if: '!cancelled()' \ No newline at end of file diff --git a/Solver/configure b/Solver/configure index da42879a6..0ce26763c 100755 --- a/Solver/configure +++ b/Solver/configure @@ -84,6 +84,7 @@ TEST_CASES="./Euler/BoxAroundCircle \ ./NavierStokes/Cylinder_pAdaptationRL_GaussLobatto \ ./NavierStokes/ABLBoundaryMapping \ ./NavierStokes/ActuatorLineController \ + ./NavierStokes/LambVector \ ./IncompressibleNS/Convergence \ ./IncompressibleNS/Kovasznay \ ./IncompressibleNS/TaylorGreen \ diff --git a/Solver/test/NavierStokes/LambVector/MMS_Q_degree5 b/Solver/test/NavierStokes/LambVector/MMS_Q_degree5 new file mode 100644 index 000000000..272002810 Binary files /dev/null and b/Solver/test/NavierStokes/LambVector/MMS_Q_degree5 differ diff --git a/Solver/test/NavierStokes/LambVector/NavierStokes_MMSLambVector.ipynb b/Solver/test/NavierStokes/LambVector/NavierStokes_MMSLambVector.ipynb new file mode 100644 index 000000000..21f07cf9f --- /dev/null +++ b/Solver/test/NavierStokes/LambVector/NavierStokes_MMSLambVector.ipynb @@ -0,0 +1,3381 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "95b1c46a", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from sympy import *\n", + "init_printing()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "bb7e858f", + "metadata": {}, + "outputs": [], + "source": [ + "# Define symbols\n", + "x, y, z, t = symbols('x y z t', real=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "6f8e8f16", + "metadata": {}, + "outputs": [], + "source": [ + "# Define gradient and divergence operators\n", + "def gradient(f):\n", + " if isinstance(f, NDimArray):\n", + " return Matrix([[diff(f[0], x), diff(f[0], y), diff(f[0], z)],\n", + " [diff(f[1], x), diff(f[1], y), diff(f[1], z)],\n", + " [diff(f[2], x), diff(f[2], y), diff(f[2], z)]])\n", + " else:\n", + " return Array([diff(f, x), diff(f, y), diff(f, z)])\n", + "# gradient = lambda f: Array([diff(f, x), diff(f, y), diff(f, z)])\n", + "# gradientVector = lambda f: Matrix([[diff(f[0], x), diff(f[0], y), diff(f[0], z)],\n", + "# [diff(f[1], x), diff(f[1], y), diff(f[1], z)],\n", + "# [diff(f[2], x), diff(f[2], y), diff(f[2], z)]])\n", + "def divergence(f):\n", + " if isinstance(f, NDimArray):\n", + " return diff(f[0], x) + diff(f[1], y) + diff(f[2], z)\n", + " elif isinstance(f, MatrixBase):\n", + " return Array([diff(f[0,0], x) + diff(f[1,0], y) + diff(f[2,0], z),\n", + " diff(f[0,1], x) + diff(f[1,1], y) + diff(f[2,1], z),\n", + " diff(f[0,2], x) + diff(f[1,2], y) + diff(f[2,2], z)])\n", + " else:\n", + " print(\"Type: \", type(f))\n", + " raise ValueError(\"Unknown type in divergence\")\n", + "# divergenceTensor = lambda f: Array([diff(f[0,0], x) + diff(f[1,0], y) + diff(f[2,0], z),\n", + "# diff(f[0,1], x) + diff(f[1,1], y) + diff(f[2,1], z),\n", + "# diff(f[0,2], x) + diff(f[1,2], y) + diff(f[2,2], z)])" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "e8961fcd", + "metadata": {}, + "outputs": [], + "source": [ + "# Define symbols\n", + "mu, Lambda = symbols('mu lambda', real=True)\n", + "gamma, Pr, Mach = symbols('gamma Pr M', real=True)\n", + "Re = symbols('Re', real=True)\n", + "kappa = symbols('kappa', real=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "14595c2f", + "metadata": {}, + "outputs": [], + "source": [ + "# Density\n", + "rho_func = Function('rho')\n", + "rho = rho_func(x,y,z,t)\n", + "# Velocity\n", + "u_func = Function('u')\n", + "v_func = Function('v')\n", + "w_func = Function('w')\n", + "u = u_func(x,y,z,t)\n", + "v = v_func(x,y,z,t)\n", + "w = w_func(x,y,z,t)\n", + "vel = Array([u, v, w])\n", + "# Pressure\n", + "# p_func = Function('p')\n", + "# p = p_func(x,y,z,t)\n", + "# Energy\n", + "E_func = Function('E')\n", + "E = E_func(x,y,z,t)\n", + "# Temperature\n", + "T_func= Function('T')\n", + "T = T_func(x,y,z,t)\n", + "# Manufactured solution source term\n", + "srho_func = Function('s_rho')\n", + "srho = srho_func(x,y,z,t)\n", + "srhou_func = Function('s_rhou')\n", + "srhov_func = Function('s_rhov')\n", + "srhow_func = Function('s_rhow')\n", + "srhoE_func = Function('s_rhoe')\n", + "srhou = srhou_func(x,y,z,t)\n", + "srhov = srhov_func(x,y,z,t)\n", + "srhow = srhow_func(x,y,z,t)\n", + "srhoE = srhoE_func(x,y,z,t)\n", + "s_vel = Array([srhou, srhov, srhow])" + ] + }, + { + "cell_type": "markdown", + "id": "24719efb", + "metadata": {}, + "source": [ + "## Navier-Stokes equations" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "637c5879", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)} & \\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} & \\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)}\\\\\\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)} & \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)} & \\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)}\\\\\\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)} & \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)} & \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡∂ ∂ ∂ ⎤\n", + "⎢──(u(x, y, z, t)) ──(u(x, y, z, t)) ──(u(x, y, z, t))⎥\n", + "⎢∂x ∂y ∂z ⎥\n", + "⎢ ⎥\n", + "⎢∂ ∂ ∂ ⎥\n", + "⎢──(v(x, y, z, t)) ──(v(x, y, z, t)) ──(v(x, y, z, t))⎥\n", + "⎢∂x ∂y ∂z ⎥\n", + "⎢ ⎥\n", + "⎢∂ ∂ ∂ ⎥\n", + "⎢──(w(x, y, z, t)) ──(w(x, y, z, t)) ──(w(x, y, z, t))⎥\n", + "⎣∂x ∂y ∂z ⎦" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "gradVel = gradient(vel)\n", + "gradVel" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "2fe5b665", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/latex": [ + "$\\displaystyle \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}$" + ], + "text/plain": [ + "∂ ∂ ∂ \n", + "──(u(x, y, z, t)) + ──(v(x, y, z, t)) + ──(w(x, y, z, t))\n", + "∂x ∂y ∂z " + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "divVel = divergence(vel)\n", + "divVel" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "1b5b9d6a", + "metadata": {}, + "outputs": [], + "source": [ + "gradu = gradVel[0,:]\n", + "gradv = gradVel[1,:]\n", + "gradw = gradVel[2,:]" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "4f2cf893", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}M^{2} \\gamma \\left(\\gamma - 1\\right) \\left(\\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} E{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - \\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)} - v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)} - w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)}\\right) & M^{2} \\gamma \\left(\\gamma - 1\\right) \\left(\\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} E{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - \\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} - v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)} - w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)}\\right) & M^{2} \\gamma \\left(\\gamma - 1\\right) \\left(\\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} E{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - \\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} - v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} - w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}\\right)\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡ ⎛ ∂ ∂ ↪\n", + "⎢ ⎜E(x, y, z, t)⋅──(ρ(x, y, z, t)) + ρ(x, y, z, t)⋅──(E(x, y, z, t ↪\n", + "⎢ 2 ⎜ ∂x ∂x ↪\n", + "⎢M ⋅γ⋅(γ - 1)⋅⎜─────────────────────────────────────────────────────────────── ↪\n", + "⎣ ⎝ ρ(x, y, z, t) ↪\n", + "\n", + "↪ ∂ ↪\n", + "↪ )) E(x, y, z, t)⋅──(ρ(x, y, z, t)) ↪\n", + "↪ ∂x ∂ ↪\n", + "↪ ── - ─────────────────────────────── - u(x, y, z, t)⋅──(u(x, y, z, t)) - v(x ↪\n", + "↪ ρ(x, y, z, t) ∂x ↪\n", + "\n", + "↪ ⎞ ↪\n", + "↪ ⎟ ↪\n", + "↪ ∂ ∂ ⎟ 2 ↪\n", + "↪ , y, z, t)⋅──(v(x, y, z, t)) - w(x, y, z, t)⋅──(w(x, y, z, t))⎟ M ⋅γ⋅(γ - 1 ↪\n", + "↪ ∂x ∂x ⎠ ↪\n", + "\n", + "↪ ⎛ ∂ ∂ ↪\n", + "↪ ⎜E(x, y, z, t)⋅──(ρ(x, y, z, t)) + ρ(x, y, z, t)⋅──(E(x, y, z, t)) E(x, ↪\n", + "↪ ⎜ ∂y ∂y ↪\n", + "↪ )⋅⎜───────────────────────────────────────────────────────────────── - ───── ↪\n", + "↪ ⎝ ρ(x, y, z, t) ↪\n", + "\n", + "↪ ∂ ↪\n", + "↪ y, z, t)⋅──(ρ(x, y, z, t)) ↪\n", + "↪ ∂y ∂ ↪\n", + "↪ ────────────────────────── - u(x, y, z, t)⋅──(u(x, y, z, t)) - v(x, y, z, t) ↪\n", + "↪ ρ(x, y, z, t) ∂y ↪\n", + "\n", + "↪ ⎞ ⎛ ↪\n", + "↪ ⎟ ⎜E(x, y, ↪\n", + "↪ ∂ ∂ ⎟ 2 ⎜ ↪\n", + "↪ ⋅──(v(x, y, z, t)) - w(x, y, z, t)⋅──(w(x, y, z, t))⎟ M ⋅γ⋅(γ - 1)⋅⎜─────── ↪\n", + "↪ ∂y ∂y ⎠ ⎝ ↪\n", + "\n", + "↪ ∂ ∂ ∂ ↪\n", + "↪ z, t)⋅──(ρ(x, y, z, t)) + ρ(x, y, z, t)⋅──(E(x, y, z, t)) E(x, y, z, t)⋅─ ↪\n", + "↪ ∂z ∂z ∂ ↪\n", + "↪ ────────────────────────────────────────────────────────── - ─────────────── ↪\n", + "↪ ρ(x, y, z, t) ρ(x, y ↪\n", + "\n", + "↪ ↪\n", + "↪ ─(ρ(x, y, z, t)) ↪\n", + "↪ z ∂ ∂ ↪\n", + "↪ ──────────────── - u(x, y, z, t)⋅──(u(x, y, z, t)) - v(x, y, z, t)⋅──(v(x, y ↪\n", + "↪ , z, t) ∂z ∂z ↪\n", + "\n", + "↪ ⎞⎤\n", + "↪ ⎟⎥\n", + "↪ ∂ ⎟⎥\n", + "↪ , z, t)) - w(x, y, z, t)⋅──(w(x, y, z, t))⎟⎥\n", + "↪ ∂z ⎠⎦" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "gradT = Array([(gamma-1)*gamma*Mach**2*( S(1)/rho*diff(rho*E,x) - (rho*E)/rho**2*diff(rho,x)-u*gradu[0]-v*gradv[0]-w*gradw[0]),\n", + " (gamma-1)*gamma*Mach**2*( S(1)/rho*diff(rho*E,y) - (rho*E)/rho**2*diff(rho,y)-u*gradu[1]-v*gradv[1]-w*gradw[1]),\n", + " (gamma-1)*gamma*Mach**2*( S(1)/rho*diff(rho*E,z) - (rho*E)/rho**2*diff(rho,z)-u*gradu[2]-v*gradv[2]-w*gradw[2])])\n", + "gradT" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "b48504b6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0\\\\\\mu \\left(\\frac{4 \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}}{3}\\right) & \\mu \\left(\\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)}\\right) & \\mu \\left(\\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)}\\right)\\\\\\mu \\left(\\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)}\\right) & \\mu \\left(- \\frac{2 \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)}}{3} + \\frac{4 \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}}{3}\\right) & \\mu \\left(\\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)}\\right)\\\\\\mu \\left(\\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)}\\right) & \\mu \\left(\\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)}\\right) & \\mu \\left(- \\frac{2 \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)}}{3} + \\frac{4 \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}}{3}\\right)\\\\M^{2} \\gamma \\kappa \\left(\\gamma - 1\\right) \\left(\\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} E{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - \\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)} - v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)} - w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)}\\right) + \\mu \\left(\\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)}\\right) v{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)}\\right) w{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{4 \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}}{3}\\right) u{\\left(x,y,z,t \\right)} & M^{2} \\gamma \\kappa \\left(\\gamma - 1\\right) \\left(\\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} E{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - \\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} - v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)} - w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)}\\right) + \\mu \\left(\\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)}\\right) u{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)}\\right) w{\\left(x,y,z,t \\right)} + \\mu \\left(- \\frac{2 \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)}}{3} + \\frac{4 \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}}{3}\\right) v{\\left(x,y,z,t \\right)} & M^{2} \\gamma \\kappa \\left(\\gamma - 1\\right) \\left(\\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} E{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - \\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} - v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} - w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}\\right) + \\mu \\left(\\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)}\\right) u{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)}\\right) v{\\left(x,y,z,t \\right)} + \\mu \\left(- \\frac{2 \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)}}{3} + \\frac{4 \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}}{3}\\right) w{\\left(x,y,z,t \\right)}\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + 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↪\n", + "↪ ⎛∂ ∂ ⎞ ↪\n", + "↪ μ⋅⎜──(u(x, y, z, t)) + ──(v(x, y, z, t))⎟ ↪\n", + "↪ ⎝∂y ∂x ⎠ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛∂ ∂ ⎞ ↪\n", + "↪ μ⋅⎜──(u(x, y, z, t)) + ──(w(x, y, z, t))⎟ ↪\n", + "↪ ⎝∂z ∂x ⎠ ↪\n", + "↪ ↪\n", + "↪ ⎞ ↪\n", + "↪ ⎟ ↪\n", + "↪ ∂ ∂ ⎟ ⎛∂ ↪\n", + "↪ (x, y, z, t)⋅──(v(x, y, z, t)) - w(x, y, z, t)⋅──(w(x, y, z, t))⎟ + μ⋅⎜──(u( ↪\n", + "↪ ∂x ∂x ⎠ ⎝∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎞ ↪\n", + "↪ x, y, z, t))⎟ ↪\n", + "↪ ⎟ ↪\n", + "↪ ────────────⎟ ↪\n", + "↪ 3 ⎠ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ⎞ ⎛∂ ∂ ↪\n", + "↪ x, y, z, t)) + ──(v(x, y, z, t))⎟⋅v(x, y, z, t) + μ⋅⎜──(u(x, y, z, t)) + ──( ↪\n", + "↪ ∂x ⎠ ⎝∂z ∂x ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ ∂ ∂ ↪\n", + "↪ ⎜4⋅──(u(x, y, z, t)) 2⋅──(v(x, y, z, t)) ↪\n", + "↪ ⎞ ⎜ ∂x ∂y ↪\n", + "↪ w(x, y, z, t))⎟⋅w(x, y, z, t) + μ⋅⎜─────────────────── - ─────────────────── ↪\n", + "↪ ⎠ ⎝ 3 3 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ⎞ ⎛ ∂ ↪\n", + "↪ 2⋅──(w(x, y, z, t))⎟ ⎜E(x, y, z, t)⋅──(ρ(x, ↪\n", + "↪ ∂z ⎟ 2 ⎜ ∂y ↪\n", + "↪ - ───────────────────⎟⋅u(x, y, z, t) M ⋅γ⋅κ⋅(γ - 1)⋅⎜───────────────────── ↪\n", + "↪ 3 ⎠ ⎝ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ y, z, t)) + ρ(x, y, z, t)⋅──(E(x, y, z, t)) E(x, y, z, t)⋅──(ρ(x, y, z, t ↪\n", + "↪ ∂y ∂y ↪\n", + "↪ ──────────────────────────────────────────── - ───────────────────────────── ↪\n", + "↪ ρ(x, y, z, t) ρ(x, y, z, t) ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ ∂ ↪\n", + "↪ ⎜ 2⋅──(u(x, ↪\n", + "↪ ⎜ ∂x ↪\n", + "↪ μ⋅⎜- ───────── ↪\n", + "↪ ⎝ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ )) ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ ── - u(x, y, z, t)⋅──(u(x, y, z, t)) - v(x, y, z, t)⋅──(v(x, y, z, t)) - w(x ↪\n", + "↪ ∂y ∂y ↪\n", + "\n", + "↪ 0 ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛∂ ∂ ⎞ ↪\n", + "↪ μ⋅⎜──(u(x, y, z, t)) + ──(v(x, y, z, t))⎟ ↪\n", + "↪ ⎝∂y ∂x ⎠ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ⎞ ↪\n", + "↪ y, z, t)) 4⋅──(v(x, y, z, t)) 2⋅──(w(x, y, z, t))⎟ ↪\n", + "↪ ∂y ∂z ⎟ ↪\n", + "↪ ────────── + ─────────────────── - ───────────────────⎟ ↪\n", + "↪ 3 3 3 ⎠ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛∂ ∂ ⎞ ↪\n", + "↪ μ⋅⎜──(v(x, y, z, t)) + ──(w(x, y, z, t))⎟ ↪\n", + "↪ ⎝∂z ∂y ⎠ ↪\n", + "↪ ↪\n", + "↪ ⎞ ↪\n", + "↪ ⎟ ↪\n", + "↪ ∂ ⎟ ⎛∂ ∂ ⎞ ↪\n", + "↪ , y, z, t)⋅──(w(x, y, z, t))⎟ + μ⋅⎜──(u(x, y, z, t)) + ──(v(x, y, z, t))⎟⋅u( ↪\n", + "↪ ∂y ⎠ ⎝∂y ∂x ⎠ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ ↪\n", + "↪ ⎜ ↪\n", + "↪ ⎛∂ ∂ ⎞ ⎜ ↪\n", + "↪ x, y, z, t) + μ⋅⎜──(v(x, y, z, t)) + ──(w(x, y, z, t))⎟⋅w(x, y, z, t) + μ⋅⎜- ↪\n", + "↪ ⎝∂z ∂y ⎠ ⎝ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ∂ ⎞ ↪\n", + "↪ 2⋅──(u(x, y, z, t)) 4⋅──(v(x, y, z, t)) 2⋅──(w(x, y, z, t))⎟ ↪\n", + "↪ ∂x ∂y ∂z ⎟ ↪\n", + "↪ ─────────────────── + ─────────────────── - ───────────────────⎟⋅v(x, y, z, ↪\n", + "↪ 3 3 3 ⎠ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ ∂ ∂ ↪\n", + "↪ ⎜E(x, y, z, t)⋅──(ρ(x, y, z, t)) + ρ(x, y, z, t)⋅──(E(x, ↪\n", + "↪ 2 ⎜ ∂z ∂z ↪\n", + "↪ t) M ⋅γ⋅κ⋅(γ - 1)⋅⎜─────────────────────────────────────────────────────── ↪\n", + "↪ ⎝ ρ(x, y, z, t) ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ↪\n", + "↪ y, z, t)) E(x, y, z, t)⋅──(ρ(x, y, z, t)) ↪\n", + "↪ ∂z ∂ ↪\n", + "↪ ────────── - ─────────────────────────────── - u(x, y, z, t)⋅──(u(x, y, z, t ↪\n", + "↪ ρ(x, y, z, t) ∂z ↪\n", + "\n", + "↪ 0 ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛∂ ∂ ↪\n", + "↪ μ⋅⎜──(u(x, y, z, t)) + ──(w(x, y, ↪\n", + "↪ ⎝∂z ∂x ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛∂ ∂ ↪\n", + "↪ μ⋅⎜──(v(x, y, z, t)) + ──(w(x, y, ↪\n", + "↪ ⎝∂z ∂y ↪\n", + "↪ ↪\n", + "↪ ⎛ ∂ ∂ ↪\n", + "↪ ⎜ 2⋅──(u(x, y, z, t)) 2⋅──(v(x, y, z, t)) ↪\n", + "↪ ⎜ ∂x ∂y ↪\n", + "↪ μ⋅⎜- ─────────────────── - ─────────────────── + ↪\n", + "↪ ⎝ 3 3 ↪\n", + "↪ ↪\n", + "↪ ⎞ ↪\n", + "↪ ⎟ ↪\n", + "↪ ∂ ∂ ⎟ ↪\n", + "↪ )) - v(x, y, z, t)⋅──(v(x, y, z, t)) - w(x, y, z, t)⋅──(w(x, y, z, t))⎟ + μ⋅ ↪\n", + "↪ ∂z ∂z ⎠ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎞ ↪\n", + "↪ z, t))⎟ ↪\n", + "↪ ⎠ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎞ ↪\n", + "↪ z, t))⎟ ↪\n", + "↪ ⎠ ↪\n", + "↪ ↪\n", + "↪ ∂ ⎞ ↪\n", + "↪ 4⋅──(w(x, y, z, t))⎟ ↪\n", + "↪ ∂z ⎟ ↪\n", + "↪ ───────────────────⎟ ↪\n", + "↪ 3 ⎠ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛∂ ∂ ⎞ ⎛∂ ↪\n", + "↪ ⎜──(u(x, y, z, t)) + ──(w(x, y, z, t))⎟⋅u(x, y, z, t) + μ⋅⎜──(v(x, y, z, t)) ↪\n", + "↪ ⎝∂z ∂x ⎠ ⎝∂z ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ ∂ ∂ ↪\n", + "↪ ⎜ 2⋅──(u(x, y, z, t)) 2⋅──(v(x, y ↪\n", + "↪ ∂ ⎞ ⎜ ∂x ∂y ↪\n", + "↪ + ──(w(x, y, z, t))⎟⋅v(x, y, z, t) + μ⋅⎜- ─────────────────── - ─────────── ↪\n", + "↪ ∂y ⎠ ⎝ 3 3 ↪\n", + "\n", + "↪ ⎤\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ∂ ⎞ ⎥\n", + "↪ , z, t)) 4⋅──(w(x, y, z, t))⎟ ⎥\n", + "↪ ∂z ⎟ ⎥\n", + "↪ ──────── + ───────────────────⎟⋅w(x, y, z, t)⎥\n", + "↪ 3 ⎠ ⎦" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Viscous flux\n", + "Fviscous_q_d = MutableDenseNDimArray([[S(0), S(0), S(0)],\n", + " [mu * (2 * gradu[0] - S(2)/3 * divVel), S(0), S(0)],\n", + " [mu * (gradv[0] + gradu[1]), mu * (2 * gradv[1] - S(2)/3 * divVel), S(0)],\n", + " [mu * (gradw[0] + gradu[2]), mu * (gradw[1] + gradv[2]), mu * (2 * gradw[2] - S(2)/3 * divVel)],\n", + " [S(0), S(0), S(0)]])\n", + "Fviscous_q_d[1,1] = Fviscous_q_d[2,0]\n", + "Fviscous_q_d[1,2] = Fviscous_q_d[3,0]\n", + "Fviscous_q_d[2,2] = Fviscous_q_d[3,1]\n", + "Fviscous_q_d[4,0] = Fviscous_q_d[1,0]*u + Fviscous_q_d[2,0]*v + Fviscous_q_d[3,0]*w + kappa * gradT[0]\n", + "Fviscous_q_d[4,1] = Fviscous_q_d[1,1]*u + Fviscous_q_d[2,1]*v + Fviscous_q_d[3,1]*w + kappa * gradT[1]\n", + "Fviscous_q_d[4,2] = Fviscous_q_d[1,2]*u + Fviscous_q_d[2,2]*v + Fviscous_q_d[3,2]*w + kappa * gradT[2]\n", + "Fviscous_q_d" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "084d0d49", + "metadata": {}, + "outputs": [], + "source": [ + "# Pressure\n", + "p = (gamma - 1) * (rho*E - S(1)/2 * (rho*u**2 + rho*v**2 + rho*w**2))" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "c4487996", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} & \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} & \\rho{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)}\\\\\\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)} - \\frac{\\rho{\\left(x,y,z,t \\right)} u^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} v^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} w^{2}{\\left(x,y,z,t \\right)}}{2}\\right) + \\rho{\\left(x,y,z,t \\right)} u^{2}{\\left(x,y,z,t \\right)} & \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} & \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)}\\\\\\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} & \\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)} - \\frac{\\rho{\\left(x,y,z,t \\right)} u^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} v^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} w^{2}{\\left(x,y,z,t \\right)}}{2}\\right) + \\rho{\\left(x,y,z,t \\right)} v^{2}{\\left(x,y,z,t \\right)} & \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)}\\\\\\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} & \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} & \\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)} - \\frac{\\rho{\\left(x,y,z,t \\right)} u^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} v^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} w^{2}{\\left(x,y,z,t \\right)}}{2}\\right) + \\rho{\\left(x,y,z,t \\right)} w^{2}{\\left(x,y,z,t \\right)}\\\\\\left(\\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)} - \\frac{\\rho{\\left(x,y,z,t \\right)} u^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} v^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} w^{2}{\\left(x,y,z,t \\right)}}{2}\\right) + E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)}\\right) u{\\left(x,y,z,t \\right)} & \\left(\\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)} - \\frac{\\rho{\\left(x,y,z,t \\right)} u^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} v^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} w^{2}{\\left(x,y,z,t \\right)}}{2}\\right) + E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)}\\right) v{\\left(x,y,z,t \\right)} & \\left(\\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)} - \\frac{\\rho{\\left(x,y,z,t \\right)} u^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} v^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} w^{2}{\\left(x,y,z,t \\right)}}{2}\\right) + E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)}\\right) w{\\left(x,y,z,t \\right)}\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡ ρ(x ↪\n", + "⎢ ↪\n", + "⎢ ⎛ 2 ↪\n", + "⎢ ⎜ ρ(x, y, z, t)⋅u (x, y, z, t) ↪\n", + "⎢ (γ - 1)⋅⎜E(x, y, z, t)⋅ρ(x, y, z, t) - ──────────────────────────── - ↪\n", + "⎢ ⎝ 2 ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ρ(x, y, z, ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢ ρ(x, y, z, ↪\n", + "⎢ ↪\n", + "⎢ ↪\n", + "⎢⎛ ⎛ 2 ↪\n", + "⎢⎜ ⎜ ρ(x, y, z, t)⋅u (x, y, z, t) ρ(x, y ↪\n", + "⎢⎜(γ - 1)⋅⎜E(x, y, z, t)⋅ρ(x, y, z, t) - ──────────────────────────── - ────── ↪\n", + "⎣⎝ ⎝ 2 ↪\n", + "\n", + "↪ , y, z, t)⋅u(x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ 2 2 ⎞ ↪\n", + "↪ ρ(x, y, z, t)⋅v (x, y, z, t) ρ(x, y, z, t)⋅w (x, y, z, t)⎟ ↪\n", + "↪ ──────────────────────────── - ────────────────────────────⎟ + ρ(x, y, z, t) ↪\n", + "↪ 2 2 ⎠ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ t)⋅u(x, y, z, t)⋅v(x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ t)⋅u(x, y, z, t)⋅w(x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 2 ⎞ ↪\n", + "↪ , z, t)⋅v (x, y, z, t) ρ(x, y, z, t)⋅w (x, y, z, t)⎟ ↪\n", + "↪ ────────────────────── - ────────────────────────────⎟ + E(x, y, z, t)⋅ρ(x, ↪\n", + "↪ 2 2 ⎠ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 ↪\n", + "↪ ⋅u (x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ ↪\n", + "↪ ⎜ ρ(x, ↪\n", + "↪ (γ - 1)⋅⎜E(x, y, z, t)⋅ρ(x, y, z, t) - ───── ↪\n", + "↪ ⎝ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎞ ⎛ ⎛ ↪\n", + "↪ ⎟ ⎜ ⎜ ρ(x, y, z, ↪\n", + "↪ y, z, t)⎟⋅u(x, y, z, t) ⎜(γ - 1)⋅⎜E(x, y, z, t)⋅ρ(x, y, z, t) - ─────────── ↪\n", + "↪ ⎠ ⎝ ⎝ ↪\n", + "\n", + "↪ ρ(x, y, z, t)⋅v(x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ρ(x, y, z, t)⋅u(x, y, z, t)⋅v(x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 2 2 ↪\n", + "↪ y, z, t)⋅u (x, y, z, t) ρ(x, y, z, t)⋅v (x, y, z, t) ρ(x, y, z, t)⋅w (x, ↪\n", + "↪ ─────────────────────── - ──────────────────────────── - ─────────────────── ↪\n", + "↪ 2 2 2 ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ρ(x, y, z, t)⋅v(x, y, z, t)⋅w(x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 2 2 ↪\n", + "↪ t)⋅u (x, y, z, t) ρ(x, y, z, t)⋅v (x, y, z, t) ρ(x, y, z, t)⋅w (x, y, z, ↪\n", + "↪ ───────────────── - ──────────────────────────── - ───────────────────────── ↪\n", + "↪ 2 2 2 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎞ ↪\n", + "↪ y, z, t)⎟ 2 ↪\n", + "↪ ─────────⎟ + ρ(x, y, z, t)⋅v (x, y, z, t) ↪\n", + "↪ ⎠ ↪\n", + "↪ ↪\n", + "↪ ⎛ ↪\n", + "↪ ⎜ ↪\n", + "↪ (γ - 1)⋅⎜E(x, y, z ↪\n", + "↪ ⎝ ↪\n", + "↪ ↪\n", + "↪ ⎞ ⎞ ⎛ ⎛ ↪\n", + "↪ t)⎟ ⎟ ⎜ ⎜ ↪\n", + "↪ ───⎟ + E(x, y, z, t)⋅ρ(x, y, z, t)⎟⋅v(x, y, z, t) ⎜(γ - 1)⋅⎜E(x, y, z, t)⋅ρ ↪\n", + "↪ ⎠ ⎠ ⎝ ⎝ ↪\n", + "\n", + "↪ ρ(x, y, z, t)⋅w(x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ρ(x, y, z, t)⋅u(x, y, z, t)⋅w(x, y ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ρ(x, y, z, t)⋅v(x, y, z, t)⋅w(x, y ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 2 ↪\n", + "↪ ρ(x, y, z, t)⋅u (x, y, z, t) ρ(x, y, z, t)⋅v (x, y, z ↪\n", + "↪ , t)⋅ρ(x, y, z, t) - ──────────────────────────── - ──────────────────────── ↪\n", + "↪ 2 2 ↪\n", + "↪ ↪\n", + "↪ 2 2 ↪\n", + "↪ ρ(x, y, z, t)⋅u (x, y, z, t) ρ(x, y, z, t)⋅v (x, y, z, t) ↪\n", + "↪ (x, y, z, t) - ──────────────────────────── - ──────────────────────────── - ↪\n", + "↪ 2 2 ↪\n", + "\n", + "↪ ⎤\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ , z, t) ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ , z, t) ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ 2 ⎞ ⎥\n", + "↪ , t) ρ(x, y, z, t)⋅w (x, y, z, t)⎟ 2 ⎥\n", + "↪ ──── - ────────────────────────────⎟ + ρ(x, y, z, t)⋅w (x, y, z, t) ⎥\n", + "↪ 2 ⎠ ⎥\n", + "↪ ⎥\n", + "↪ 2 ⎞ ⎞ ⎥\n", + "↪ ρ(x, y, z, t)⋅w (x, y, z, t)⎟ ⎟ ⎥\n", + "↪ ────────────────────────────⎟ + E(x, y, z, t)⋅ρ(x, y, z, t)⎟⋅w(x, y, z, t)⎥\n", + "↪ 2 ⎠ ⎠ ⎦" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Inviscid/Euler flux\n", + "Finviscid_q_d = MutableDenseNDimArray([[rho*u, rho*v, rho*w],\n", + " [rho*u**2+p, S(0), S(0)],\n", + " [rho*u*v, rho*v**2+p, S(0)],\n", + " [rho*u*w, rho*v*w, rho*w**2+p],\n", + " [(rho*E+p)*u, (rho*E+p)*v, (rho*E+p)*w]])\n", + "Finviscid_q_d[1,1] = Finviscid_q_d[2,0]\n", + "Finviscid_q_d[1,2] = Finviscid_q_d[3,0]\n", + "Finviscid_q_d[2,2] = Finviscid_q_d[3,1]\n", + "Finviscid_q_d" + ] + }, + { + "cell_type": "markdown", + "id": "b553c744", + "metadata": {}, + "source": [ + "### Rho equation" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "3f13c65a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/latex": [ + "$\\displaystyle \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)} + u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)} + v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)} + w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial t} \\rho{\\left(x,y,z,t \\right)} = s_{\\rho}{\\left(x,y,z,t \\right)}$" + ], + "text/plain": [ + " ∂ ∂ ↪\n", + "ρ(x, y, z, t)⋅──(u(x, y, z, t)) + ρ(x, y, z, t)⋅──(v(x, y, z, t)) + ρ(x, y, z, ↪\n", + " ∂x ∂y ↪\n", + "\n", + "↪ ∂ ∂ ∂ ↪\n", + "↪ t)⋅──(w(x, y, z, t)) + u(x, y, z, t)⋅──(ρ(x, y, z, t)) + v(x, y, z, t)⋅──(ρ ↪\n", + "↪ ∂z ∂x ∂y ↪\n", + "\n", + "↪ ∂ ∂ ↪\n", + "↪ (x, y, z, t)) + w(x, y, z, t)⋅──(ρ(x, y, z, t)) + ──(ρ(x, y, z, t)) = sᵨ(x, ↪\n", + "↪ ∂z ∂t ↪\n", + "\n", + "↪ \n", + "↪ y, z, t)\n", + "↪ " + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rhodt = diff(rho, t)\n", + "Frho = Finviscid_q_d[0,:] - S(1)/Re * Fviscous_q_d[0,:]\n", + "# divergence(Frho)\n", + "Eqrho = Eq(rhodt + divergence(Frho), srho)\n", + "Eqrho" + ] + }, + { + "cell_type": "markdown", + "id": "087c97e0", + "metadata": {}, + "source": [ + "### Rho*u equations" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "d0162db2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/latex": [ + "$\\displaystyle \\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} E{\\left(x,y,z,t \\right)} - \\frac{u^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)}}{2} - \\frac{v^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)}}{2} - \\frac{w^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)}}{2}\\right) + 2 \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial t} u{\\left(x,y,z,t \\right)} + u^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)} + u{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)} + u{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)} + u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial t} \\rho{\\left(x,y,z,t \\right)} - \\frac{\\mu \\left(\\frac{\\partial^{2}}{\\partial y^{2}} u{\\left(x,y,z,t \\right)} + \\frac{\\partial^{2}}{\\partial y\\partial x} v{\\left(x,y,z,t \\right)}\\right)}{Re} - \\frac{\\mu \\left(\\frac{\\partial^{2}}{\\partial z^{2}} u{\\left(x,y,z,t \\right)} + \\frac{\\partial^{2}}{\\partial z\\partial x} w{\\left(x,y,z,t \\right)}\\right)}{Re} - \\frac{\\mu \\left(\\frac{4 \\frac{\\partial^{2}}{\\partial x^{2}} u{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial^{2}}{\\partial y\\partial x} v{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial^{2}}{\\partial z\\partial x} w{\\left(x,y,z,t \\right)}}{3}\\right)}{Re} = s_{rhou}{\\left(x,y,z,t \\right)}$" + ], + "text/plain": [ + " ↪\n", + " ↪\n", + " ↪\n", + " ↪\n", + " ⎛ ↪\n", + " ⎜ ↪\n", + " ⎜ ∂ ∂ ↪\n", + "(γ - 1)⋅⎜E(x, y, z, t)⋅──(ρ(x, y, z, t)) - ρ(x, y, z, t)⋅u(x, y, z, t)⋅──(u(x, ↪\n", + " ⎝ ∂x ∂x ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ↪\n", + "↪ y, z, t)) - ρ(x, y, z, t)⋅v(x, y, z, t)⋅──(v(x, y, z, t)) - ρ(x, y, z, t)⋅w ↪\n", + "↪ ∂x ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 ↪\n", + "↪ u (x, y, ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ (x, y, z, t)⋅──(w(x, y, z, t)) + ρ(x, y, z, t)⋅──(E(x, y, z, t)) - ───────── ↪\n", + "↪ ∂x ∂x ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ 2 ∂ 2 ↪\n", + "↪ z, t)⋅──(ρ(x, y, z, t)) v (x, y, z, t)⋅──(ρ(x, y, z, t)) w (x, y, z, t)⋅ ↪\n", + "↪ ∂x ∂x ↪\n", + "↪ ─────────────────────── - ──────────────────────────────── - ─────────────── ↪\n", + "↪ 2 2 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ⎞ ↪\n", + "↪ ──(ρ(x, y, z, t))⎟ ↪\n", + "↪ ∂x ⎟ ∂ ↪\n", + "↪ ─────────────────⎟ + 2⋅ρ(x, y, z, t)⋅u(x, y, z, t)⋅──(u(x, y, z, t)) + ρ(x, ↪\n", + "↪ 2 ⎠ ∂x ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ y, z, t)⋅u(x, y, z, t)⋅──(v(x, y, z, t)) + ρ(x, y, z, t)⋅u(x, y, z, t)⋅──(w( ↪\n", + "↪ ∂y ∂z ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ↪\n", + "↪ x, y, z, t)) + ρ(x, y, z, t)⋅v(x, y, z, t)⋅──(u(x, y, z, t)) + ρ(x, y, z, t) ↪\n", + "↪ ∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ 2 ↪\n", + "↪ ⋅w(x, y, z, t)⋅──(u(x, y, z, t)) + ρ(x, y, z, t)⋅──(u(x, y, z, t)) + u (x, y ↪\n", + "↪ ∂z ∂t ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ , z, t)⋅──(ρ(x, y, z, t)) + u(x, y, z, t)⋅v(x, y, z, t)⋅──(ρ(x, y, z, t)) + ↪\n", + "↪ ∂x ∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ u(x, y, z, t)⋅w(x, y, z, t)⋅──(ρ(x, y, z, t)) + u(x, y, z, t)⋅──(ρ(x, y, z, ↪\n", + "↪ ∂z ∂t ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ 2 2 ⎞ ⎛ 2 ↪\n", + "↪ ⎜∂ ∂ ⎟ ⎜∂ ↪\n", + "↪ μ⋅⎜───(u(x, y, z, t)) + ─────(v(x, y, z, t))⎟ μ⋅⎜───(u(x, y, z, t)) ↪\n", + "↪ ⎜ 2 ∂y ∂x ⎟ ⎜ 2 ↪\n", + "↪ ⎝∂y ⎠ ⎝∂z ↪\n", + "↪ t)) - ───────────────────────────────────────────── - ────────────────────── ↪\n", + "↪ Re R ↪\n", + "\n", + "↪ ⎛ 2 ↪\n", + "↪ ⎜ ∂ 2 ↪\n", + "↪ 2 ⎞ ⎜4⋅───(u(x, y, z, t)) ∂ ↪\n", + "↪ ∂ ⎟ ⎜ 2 2⋅─────(v(x, y, z, t)) ↪\n", + "↪ + ─────(w(x, y, z, t))⎟ ⎜ ∂x ∂y ∂x ↪\n", + "↪ ∂z ∂x ⎟ μ⋅⎜──────────────────── - ────────────────────── - ↪\n", + "↪ ⎠ ⎝ 3 3 ↪\n", + "↪ ─────────────────────── - ────────────────────────────────────────────────── ↪\n", + "↪ e Re ↪\n", + "\n", + "↪ ⎞ \n", + "↪ 2 ⎟ \n", + "↪ ∂ ⎟ \n", + "↪ 2⋅─────(w(x, y, z, t))⎟ \n", + "↪ ∂z ∂x ⎟ \n", + "↪ ──────────────────────⎟ \n", + "↪ 3 ⎠ \n", + "↪ ──────────────────────── = sᵣₕₒᵤ(x, y, z, t)\n", + "↪ " + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rhoudt = diff(rho*u,t)\n", + "Frhou = Finviscid_q_d[1,:] - S(1)/Re * Fviscous_q_d[1,:]\n", + "Eqrhou = Eq(rhoudt + divergence(Frhou), srhou)\n", + "Eqrhou" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "dac8954a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/latex": [ + "$\\displaystyle \\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} E{\\left(x,y,z,t \\right)} - \\frac{u^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)}}{2} - \\frac{v^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)}}{2} - \\frac{w^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)}}{2}\\right) + \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)} + 2 \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial t} v{\\left(x,y,z,t \\right)} + u{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)} + v^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)} + v{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)} + v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial t} \\rho{\\left(x,y,z,t \\right)} - \\frac{\\mu \\left(\\frac{\\partial^{2}}{\\partial x^{2}} v{\\left(x,y,z,t \\right)} + \\frac{\\partial^{2}}{\\partial y\\partial x} u{\\left(x,y,z,t \\right)}\\right)}{Re} - \\frac{\\mu \\left(\\frac{\\partial^{2}}{\\partial z^{2}} v{\\left(x,y,z,t \\right)} + \\frac{\\partial^{2}}{\\partial z\\partial y} w{\\left(x,y,z,t \\right)}\\right)}{Re} - \\frac{\\mu \\left(\\frac{4 \\frac{\\partial^{2}}{\\partial y^{2}} v{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial^{2}}{\\partial y\\partial x} u{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial^{2}}{\\partial z\\partial y} w{\\left(x,y,z,t \\right)}}{3}\\right)}{Re} = s_{rhov}{\\left(x,y,z,t \\right)}$" + ], + "text/plain": [ + " ↪\n", + " ↪\n", + " ↪\n", + " ↪\n", + " ⎛ ↪\n", + " ⎜ ↪\n", + " ⎜ ∂ ∂ ↪\n", + "(γ - 1)⋅⎜E(x, y, z, t)⋅──(ρ(x, y, z, t)) - ρ(x, y, z, t)⋅u(x, y, z, t)⋅──(u(x, ↪\n", + " ⎝ ∂y ∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ↪\n", + "↪ y, z, t)) - ρ(x, y, z, t)⋅v(x, y, z, t)⋅──(v(x, y, z, t)) - ρ(x, y, z, t)⋅w ↪\n", + "↪ ∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 ↪\n", + "↪ u (x, y, ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ (x, y, z, t)⋅──(w(x, y, z, t)) + ρ(x, y, z, t)⋅──(E(x, y, z, t)) - ───────── ↪\n", + "↪ ∂y ∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ 2 ∂ 2 ↪\n", + "↪ z, t)⋅──(ρ(x, y, z, t)) v (x, y, z, t)⋅──(ρ(x, y, z, t)) w (x, y, z, t)⋅ ↪\n", + "↪ ∂y ∂y ↪\n", + "↪ ─────────────────────── - ──────────────────────────────── - ─────────────── ↪\n", + "↪ 2 2 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ⎞ ↪\n", + "↪ ──(ρ(x, y, z, t))⎟ ↪\n", + "↪ ∂y ⎟ ∂ ↪\n", + "↪ ─────────────────⎟ + ρ(x, y, z, t)⋅u(x, y, z, t)⋅──(v(x, y, z, t)) + ρ(x, y, ↪\n", + "↪ 2 ⎠ ∂x ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ z, t)⋅v(x, y, z, t)⋅──(u(x, y, z, t)) + 2⋅ρ(x, y, z, t)⋅v(x, y, z, t)⋅──(v( ↪\n", + "↪ ∂x ∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ↪\n", + "↪ x, y, z, t)) + ρ(x, y, z, t)⋅v(x, y, z, t)⋅──(w(x, y, z, t)) + ρ(x, y, z, t) ↪\n", + "↪ ∂z ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ ⋅w(x, y, z, t)⋅──(v(x, y, z, t)) + ρ(x, y, z, t)⋅──(v(x, y, z, t)) + u(x, y, ↪\n", + "↪ ∂z ∂t ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ 2 ∂ ↪\n", + "↪ z, t)⋅v(x, y, z, t)⋅──(ρ(x, y, z, t)) + v (x, y, z, t)⋅──(ρ(x, y, z, t)) + ↪\n", + "↪ ∂x ∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ v(x, y, z, t)⋅w(x, y, z, t)⋅──(ρ(x, y, z, t)) + v(x, y, z, t)⋅──(ρ(x, y, z, ↪\n", + "↪ ∂z ∂t ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ 2 2 ⎞ ⎛ 2 ↪\n", + "↪ ⎜∂ ∂ ⎟ ⎜∂ ↪\n", + "↪ μ⋅⎜───(v(x, y, z, t)) + ─────(u(x, y, z, t))⎟ μ⋅⎜───(v(x, y, z, t)) ↪\n", + "↪ ⎜ 2 ∂y ∂x ⎟ ⎜ 2 ↪\n", + "↪ ⎝∂x ⎠ ⎝∂z ↪\n", + "↪ t)) - ───────────────────────────────────────────── - ────────────────────── ↪\n", + "↪ Re R ↪\n", + "\n", + "↪ ⎛ 2 ↪\n", + "↪ ⎜ ∂ 2 ↪\n", + "↪ 2 ⎞ ⎜4⋅───(v(x, y, z, t)) ∂ ↪\n", + "↪ ∂ ⎟ ⎜ 2 2⋅─────(u(x, y, z, t)) ↪\n", + "↪ + ─────(w(x, y, z, t))⎟ ⎜ ∂y ∂y ∂x ↪\n", + "↪ ∂z ∂y ⎟ μ⋅⎜──────────────────── - ────────────────────── - ↪\n", + "↪ ⎠ ⎝ 3 3 ↪\n", + "↪ ─────────────────────── - ────────────────────────────────────────────────── ↪\n", + "↪ e Re ↪\n", + "\n", + "↪ ⎞ \n", + "↪ 2 ⎟ \n", + "↪ ∂ ⎟ \n", + "↪ 2⋅─────(w(x, y, z, t))⎟ \n", + "↪ ∂z ∂y ⎟ \n", + "↪ ──────────────────────⎟ \n", + "↪ 3 ⎠ \n", + "↪ ──────────────────────── = sᵣₕₒᵥ(x, y, z, t)\n", + "↪ " + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rhovdt = diff(rho*v,t)\n", + "Frhov = Finviscid_q_d[2,:] - S(1)/Re * Fviscous_q_d[2,:]\n", + "Eqrhov = Eq(rhovdt + divergence(Frhov), srhov)\n", + "Eqrhov" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "dc15f9ec", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/latex": [ + "$\\displaystyle \\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} E{\\left(x,y,z,t \\right)} - \\frac{u^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)}}{2} - \\frac{v^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)}}{2} - \\frac{w^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)}}{2}\\right) + \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)} + 2 \\rho{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial t} w{\\left(x,y,z,t \\right)} + u{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)} + v{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)} + w^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)} + w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial t} \\rho{\\left(x,y,z,t \\right)} - \\frac{\\mu \\left(\\frac{\\partial^{2}}{\\partial x^{2}} w{\\left(x,y,z,t \\right)} + \\frac{\\partial^{2}}{\\partial z\\partial x} u{\\left(x,y,z,t \\right)}\\right)}{Re} - \\frac{\\mu \\left(\\frac{\\partial^{2}}{\\partial y^{2}} w{\\left(x,y,z,t \\right)} + \\frac{\\partial^{2}}{\\partial z\\partial y} v{\\left(x,y,z,t \\right)}\\right)}{Re} - \\frac{\\mu \\left(\\frac{4 \\frac{\\partial^{2}}{\\partial z^{2}} w{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial^{2}}{\\partial z\\partial x} u{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial^{2}}{\\partial z\\partial y} v{\\left(x,y,z,t \\right)}}{3}\\right)}{Re} = s_{rhow}{\\left(x,y,z,t \\right)}$" + ], + "text/plain": [ + " ↪\n", + " ↪\n", + " ↪\n", + " ↪\n", + " ⎛ ↪\n", + " ⎜ ↪\n", + " ⎜ ∂ ∂ ↪\n", + "(γ - 1)⋅⎜E(x, y, z, t)⋅──(ρ(x, y, z, t)) - ρ(x, y, z, t)⋅u(x, y, z, t)⋅──(u(x, ↪\n", + " ⎝ ∂z ∂z ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ↪\n", + "↪ y, z, t)) - ρ(x, y, z, t)⋅v(x, y, z, t)⋅──(v(x, y, z, t)) - ρ(x, y, z, t)⋅w ↪\n", + "↪ ∂z ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 ↪\n", + "↪ u (x, y, ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ (x, y, z, t)⋅──(w(x, y, z, t)) + ρ(x, y, z, t)⋅──(E(x, y, z, t)) - ───────── ↪\n", + "↪ ∂z ∂z ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ 2 ∂ 2 ↪\n", + "↪ z, t)⋅──(ρ(x, y, z, t)) v (x, y, z, t)⋅──(ρ(x, y, z, t)) w (x, y, z, t)⋅ ↪\n", + "↪ ∂z ∂z ↪\n", + "↪ ─────────────────────── - ──────────────────────────────── - ─────────────── ↪\n", + "↪ 2 2 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ⎞ ↪\n", + "↪ ──(ρ(x, y, z, t))⎟ ↪\n", + "↪ ∂z ⎟ ∂ ↪\n", + "↪ ─────────────────⎟ + ρ(x, y, z, t)⋅u(x, y, z, t)⋅──(w(x, y, z, t)) + ρ(x, y, ↪\n", + "↪ 2 ⎠ ∂x ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ z, t)⋅v(x, y, z, t)⋅──(w(x, y, z, t)) + ρ(x, y, z, t)⋅w(x, y, z, t)⋅──(u(x, ↪\n", + "↪ ∂y ∂x ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ↪\n", + "↪ y, z, t)) + ρ(x, y, z, t)⋅w(x, y, z, t)⋅──(v(x, y, z, t)) + 2⋅ρ(x, y, z, t) ↪\n", + "↪ ∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ ⋅w(x, y, z, t)⋅──(w(x, y, z, t)) + ρ(x, y, z, t)⋅──(w(x, y, z, t)) + u(x, y, ↪\n", + "↪ ∂z ∂t ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ z, t)⋅w(x, y, z, t)⋅──(ρ(x, y, z, t)) + v(x, y, z, t)⋅w(x, y, z, t)⋅──(ρ(x, ↪\n", + "↪ ∂x ∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 ∂ ∂ ↪\n", + "↪ y, z, t)) + w (x, y, z, t)⋅──(ρ(x, y, z, t)) + w(x, y, z, t)⋅──(ρ(x, y, z, ↪\n", + "↪ ∂z ∂t ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ 2 2 ⎞ ⎛ 2 ↪\n", + "↪ ⎜∂ ∂ ⎟ ⎜∂ ↪\n", + "↪ μ⋅⎜───(w(x, y, z, t)) + ─────(u(x, y, z, t))⎟ μ⋅⎜───(w(x, y, z, t)) ↪\n", + "↪ ⎜ 2 ∂z ∂x ⎟ ⎜ 2 ↪\n", + "↪ ⎝∂x ⎠ ⎝∂y ↪\n", + "↪ t)) - ───────────────────────────────────────────── - ────────────────────── ↪\n", + "↪ Re R ↪\n", + "\n", + "↪ ⎛ 2 ↪\n", + "↪ ⎜ ∂ 2 ↪\n", + "↪ 2 ⎞ ⎜4⋅───(w(x, y, z, t)) ∂ ↪\n", + "↪ ∂ ⎟ ⎜ 2 2⋅─────(u(x, y, z, t)) ↪\n", + "↪ + ─────(v(x, y, z, t))⎟ ⎜ ∂z ∂z ∂x ↪\n", + "↪ ∂z ∂y ⎟ μ⋅⎜──────────────────── - ────────────────────── - ↪\n", + "↪ ⎠ ⎝ 3 3 ↪\n", + "↪ ─────────────────────── - ────────────────────────────────────────────────── ↪\n", + "↪ e Re ↪\n", + "\n", + "↪ ⎞ \n", + "↪ 2 ⎟ \n", + "↪ ∂ ⎟ \n", + "↪ 2⋅─────(v(x, y, z, t))⎟ \n", + "↪ ∂z ∂y ⎟ \n", + "↪ ──────────────────────⎟ \n", + "↪ 3 ⎠ \n", + "↪ ──────────────────────── = s_rhow(x, y, z, t)\n", + "↪ " + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rhowdt = diff(rho*w,t)\n", + "Frhow = Finviscid_q_d[3,:] - S(1)/Re * Fviscous_q_d[3,:]\n", + "Eqrhow = Eq(rhowdt + divergence(Frhow), srhow)\n", + "Eqrhow" + ] + }, + { + "cell_type": "markdown", + "id": "91fdd100", + "metadata": {}, + "source": [ + "### Rho*e equation" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "a2437a25", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/latex": [ + "$\\displaystyle \\left(\\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)} - \\frac{\\rho{\\left(x,y,z,t \\right)} u^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} v^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} w^{2}{\\left(x,y,z,t \\right)}}{2}\\right) + E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)}\\right) \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)} + \\left(\\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)} - \\frac{\\rho{\\left(x,y,z,t \\right)} u^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} v^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} w^{2}{\\left(x,y,z,t \\right)}}{2}\\right) + E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)}\\right) \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)} + \\left(\\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)} - \\frac{\\rho{\\left(x,y,z,t \\right)} u^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} v^{2}{\\left(x,y,z,t \\right)}}{2} - \\frac{\\rho{\\left(x,y,z,t \\right)} w^{2}{\\left(x,y,z,t \\right)}}{2}\\right) + E{\\left(x,y,z,t \\right)} \\rho{\\left(x,y,z,t \\right)}\\right) \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)} + \\left(\\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} E{\\left(x,y,z,t \\right)} - \\frac{u^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)}}{2} - \\frac{v^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)}}{2} - \\frac{w^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)}}{2}\\right) + E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} E{\\left(x,y,z,t \\right)}\\right) u{\\left(x,y,z,t \\right)} + \\left(\\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} E{\\left(x,y,z,t \\right)} - \\frac{u^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)}}{2} - \\frac{v^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)}}{2} - \\frac{w^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)}}{2}\\right) + E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} E{\\left(x,y,z,t \\right)}\\right) v{\\left(x,y,z,t \\right)} + \\left(\\left(\\gamma - 1\\right) \\left(E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} u{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} v{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} - \\rho{\\left(x,y,z,t \\right)} w{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} E{\\left(x,y,z,t \\right)} - \\frac{u^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)}}{2} - \\frac{v^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)}}{2} - \\frac{w^{2}{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)}}{2}\\right) + E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} E{\\left(x,y,z,t \\right)}\\right) w{\\left(x,y,z,t \\right)} + E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial t} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial t} E{\\left(x,y,z,t \\right)} - \\frac{M^{2} \\gamma \\kappa \\left(\\gamma - 1\\right) \\left(- \\frac{\\left(E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} E{\\left(x,y,z,t \\right)}\\right) \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)}}{\\rho^{2}{\\left(x,y,z,t \\right)}} + \\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial x^{2}} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial x^{2}} E{\\left(x,y,z,t \\right)} + 2 \\frac{\\partial}{\\partial x} E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - \\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial x^{2}} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} + \\frac{E{\\left(x,y,z,t \\right)} \\left(\\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)}\\right)^{2}}{\\rho^{2}{\\left(x,y,z,t \\right)}} - u{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial x^{2}} u{\\left(x,y,z,t \\right)} - v{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial x^{2}} v{\\left(x,y,z,t \\right)} - w{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial x^{2}} w{\\left(x,y,z,t \\right)} - \\left(\\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)}\\right)^{2} - \\left(\\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)}\\right)^{2} - \\left(\\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)}\\right)^{2} - \\frac{\\frac{\\partial}{\\partial x} E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial x} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}}\\right) + \\mu \\left(\\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)}\\right) \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)}\\right) \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{\\partial^{2}}{\\partial x^{2}} v{\\left(x,y,z,t \\right)} + \\frac{\\partial^{2}}{\\partial y\\partial x} u{\\left(x,y,z,t \\right)}\\right) v{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{\\partial^{2}}{\\partial x^{2}} w{\\left(x,y,z,t \\right)} + \\frac{\\partial^{2}}{\\partial z\\partial x} u{\\left(x,y,z,t \\right)}\\right) w{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{4 \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}}{3}\\right) \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{4 \\frac{\\partial^{2}}{\\partial x^{2}} u{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial^{2}}{\\partial y\\partial x} v{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial^{2}}{\\partial z\\partial x} w{\\left(x,y,z,t \\right)}}{3}\\right) u{\\left(x,y,z,t \\right)}}{Re} - \\frac{M^{2} \\gamma \\kappa \\left(\\gamma - 1\\right) \\left(- \\frac{\\left(E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} E{\\left(x,y,z,t \\right)}\\right) \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)}}{\\rho^{2}{\\left(x,y,z,t \\right)}} + \\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial y^{2}} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial y^{2}} E{\\left(x,y,z,t \\right)} + 2 \\frac{\\partial}{\\partial y} E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - \\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial y^{2}} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} + \\frac{E{\\left(x,y,z,t \\right)} \\left(\\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)}\\right)^{2}}{\\rho^{2}{\\left(x,y,z,t \\right)}} - u{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial y^{2}} u{\\left(x,y,z,t \\right)} - v{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial y^{2}} v{\\left(x,y,z,t \\right)} - w{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial y^{2}} w{\\left(x,y,z,t \\right)} - \\left(\\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)}\\right)^{2} - \\left(\\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)}\\right)^{2} - \\left(\\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)}\\right)^{2} - \\frac{\\frac{\\partial}{\\partial y} E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial y} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}}\\right) + \\mu \\left(\\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)}\\right) \\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{\\partial^{2}}{\\partial y^{2}} u{\\left(x,y,z,t \\right)} + \\frac{\\partial^{2}}{\\partial y\\partial x} v{\\left(x,y,z,t \\right)}\\right) u{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)}\\right) \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{\\partial^{2}}{\\partial y^{2}} w{\\left(x,y,z,t \\right)} + \\frac{\\partial^{2}}{\\partial z\\partial y} v{\\left(x,y,z,t \\right)}\\right) w{\\left(x,y,z,t \\right)} + \\mu \\left(- \\frac{2 \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)}}{3} + \\frac{4 \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}}{3}\\right) \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{4 \\frac{\\partial^{2}}{\\partial y^{2}} v{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial^{2}}{\\partial y\\partial x} u{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial^{2}}{\\partial z\\partial y} w{\\left(x,y,z,t \\right)}}{3}\\right) v{\\left(x,y,z,t \\right)}}{Re} - \\frac{M^{2} \\gamma \\kappa \\left(\\gamma - 1\\right) \\left(- \\frac{\\left(E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} E{\\left(x,y,z,t \\right)}\\right) \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)}}{\\rho^{2}{\\left(x,y,z,t \\right)}} + \\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial z^{2}} \\rho{\\left(x,y,z,t \\right)} + \\rho{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial z^{2}} E{\\left(x,y,z,t \\right)} + 2 \\frac{\\partial}{\\partial z} E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} - \\frac{E{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial z^{2}} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}} + \\frac{E{\\left(x,y,z,t \\right)} \\left(\\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)}\\right)^{2}}{\\rho^{2}{\\left(x,y,z,t \\right)}} - u{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial z^{2}} u{\\left(x,y,z,t \\right)} - v{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial z^{2}} v{\\left(x,y,z,t \\right)} - w{\\left(x,y,z,t \\right)} \\frac{\\partial^{2}}{\\partial z^{2}} w{\\left(x,y,z,t \\right)} - \\left(\\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)}\\right)^{2} - \\left(\\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)}\\right)^{2} - \\left(\\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}\\right)^{2} - \\frac{\\frac{\\partial}{\\partial z} E{\\left(x,y,z,t \\right)} \\frac{\\partial}{\\partial z} \\rho{\\left(x,y,z,t \\right)}}{\\rho{\\left(x,y,z,t \\right)}}\\right) + \\mu \\left(\\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)}\\right) \\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{\\partial^{2}}{\\partial z^{2}} u{\\left(x,y,z,t \\right)} + \\frac{\\partial^{2}}{\\partial z\\partial x} w{\\left(x,y,z,t \\right)}\\right) u{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)}\\right) \\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{\\partial^{2}}{\\partial z^{2}} v{\\left(x,y,z,t \\right)} + \\frac{\\partial^{2}}{\\partial z\\partial y} w{\\left(x,y,z,t \\right)}\\right) v{\\left(x,y,z,t \\right)} + \\mu \\left(- \\frac{2 \\frac{\\partial}{\\partial x} u{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial}{\\partial y} v{\\left(x,y,z,t \\right)}}{3} + \\frac{4 \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)}}{3}\\right) \\frac{\\partial}{\\partial z} w{\\left(x,y,z,t \\right)} + \\mu \\left(\\frac{4 \\frac{\\partial^{2}}{\\partial z^{2}} w{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial^{2}}{\\partial z\\partial x} u{\\left(x,y,z,t \\right)}}{3} - \\frac{2 \\frac{\\partial^{2}}{\\partial z\\partial y} v{\\left(x,y,z,t \\right)}}{3}\\right) w{\\left(x,y,z,t \\right)}}{Re} = s_{rhoe}{\\left(x,y,z,t \\right)}$" + ], + "text/plain": [ + " ↪\n", + " ↪\n", + " ↪\n", + " ↪\n", + " ↪\n", + " ↪\n", + "⎛ ⎛ 2 ↪\n", + "⎜ ⎜ ρ(x, y, z, t)⋅u (x, y, z, t) ρ(x, y, ↪\n", + "⎜(γ - 1)⋅⎜E(x, y, z, t)⋅ρ(x, y, z, t) - ──────────────────────────── - ─────── ↪\n", + "⎝ ⎝ 2 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 2 ⎞ ↪\n", + "↪ z, t)⋅v (x, y, z, t) ρ(x, y, z, t)⋅w (x, y, z, t)⎟ ↪\n", + "↪ ───────────────────── - ────────────────────────────⎟ + E(x, y, z, t)⋅ρ(x, y ↪\n", + "↪ 2 2 ⎠ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + 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"↪ 2 ⎞ ⎞ ↪\n", + "↪ , z, t) ρ(x, y, z, t)⋅w (x, y, z, t)⎟ ⎟ ∂ ↪\n", + "↪ ─────── - ────────────────────────────⎟ + E(x, y, z, t)⋅ρ(x, y, z, t)⎟⋅──(w( ↪\n", + "↪ 2 ⎠ ⎠ ∂z ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ ⎛ ↪\n", + "↪ ⎜ ⎜ ↪\n", + "↪ ⎜ ⎜ ∂ ↪\n", + "↪ x, y, z, t)) + ⎜(γ - 1)⋅⎜E(x, y, z, t)⋅──(ρ(x, y, z, t)) - ρ(x, y, z, t)⋅u(x ↪\n", + "↪ ⎝ ⎝ ∂x ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ , y, z, t)⋅──(u(x, y, z, t)) - ρ(x, y, z, t)⋅v(x, y, z, t)⋅──(v(x, y, z, t)) ↪\n", + "↪ ∂x ∂x ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ - ρ(x, y, z, t)⋅w(x, y, z, t)⋅──(w(x, y, z, t)) + ρ(x, y, z, t)⋅──(E(x, y, ↪\n", + "↪ ∂x ∂x ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 ∂ 2 ∂ ↪\n", + "↪ u (x, y, z, t)⋅──(ρ(x, y, z, t)) v (x, y, z, t)⋅──(ρ(x, y, z, t)) ↪\n", + "↪ ∂x ∂x ↪\n", + "↪ z, t)) - ──────────────────────────────── - ──────────────────────────────── ↪\n", + "↪ 2 2 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 ∂ ⎞ ↪\n", + "↪ w (x, y, z, t)⋅──(ρ(x, y, z, t))⎟ ↪\n", + "↪ ∂x ⎟ ∂ ↪\n", + "↪ - ────────────────────────────────⎟ + E(x, y, z, t)⋅──(ρ(x, y, z, t)) + ρ(x ↪\n", + "↪ 2 ⎠ ∂x ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎞ ⎛ ⎛ ↪\n", + "↪ ⎟ ⎜ ⎜ ↪\n", + "↪ ∂ ⎟ ⎜ ⎜ ∂ ↪\n", + "↪ , y, z, t)⋅──(E(x, y, z, t))⎟⋅u(x, y, z, t) + ⎜(γ - 1)⋅⎜E(x, y, z, t)⋅──(ρ(x ↪\n", + "↪ ∂x ⎠ ⎝ ⎝ ∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ↪\n", + "↪ , y, z, t)) - ρ(x, y, z, t)⋅u(x, y, z, t)⋅──(u(x, y, z, t)) - ρ(x, y, z, t)⋅ ↪\n", + "↪ ∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ v(x, y, z, t)⋅──(v(x, y, z, t)) - ρ(x, y, z, t)⋅w(x, y, z, t)⋅──(w(x, y, z, ↪\n", + "↪ ∂y ∂y ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 ∂ ↪\n", + "↪ u (x, y, z, t)⋅──(ρ(x, y, z, t)) v ↪\n", + "↪ ∂ ∂y ↪\n", + "↪ t)) + ρ(x, y, z, t)⋅──(E(x, y, z, t)) - ──────────────────────────────── - ─ ↪\n", + "↪ ∂y 2 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 ∂ 2 ∂ ⎞ ↪\n", + "↪ (x, y, z, t)⋅──(ρ(x, y, z, t)) w (x, y, z, t)⋅──(ρ(x, y, z, t))⎟ ↪\n", + "↪ ∂y ∂y ⎟ ↪\n", + "↪ ─────────────────────────────── - ────────────────────────────────⎟ + E(x, y ↪\n", + "↪ 2 2 ⎠ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎞ ↪\n", + "↪ ⎟ ↪\n", + "↪ ∂ ∂ ⎟ ↪\n", + "↪ , z, t)⋅──(ρ(x, y, z, t)) + ρ(x, y, z, t)⋅──(E(x, y, z, t))⎟⋅v(x, y, z, t) + ↪\n", + "↪ ∂y ∂y ⎠ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ ⎛ ↪\n", + "↪ ⎜ ⎜ ↪\n", + "↪ ⎜ ⎜ ∂ ∂ ↪\n", + "↪ ⎜(γ - 1)⋅⎜E(x, y, z, t)⋅──(ρ(x, y, z, t)) - ρ(x, y, z, t)⋅u(x, y, z, t)⋅──( ↪\n", + "↪ ⎝ ⎝ ∂z ∂z ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ↪\n", + "↪ u(x, y, z, t)) - ρ(x, y, z, t)⋅v(x, y, z, t)⋅──(v(x, y, z, t)) - ρ(x, y, z, ↪\n", + "↪ ∂z ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 ↪\n", + "↪ u (x, ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ t)⋅w(x, y, z, t)⋅──(w(x, y, z, t)) + ρ(x, y, z, t)⋅──(E(x, y, z, t)) - ───── ↪\n", + "↪ ∂z ∂z ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ 2 ∂ 2 ↪\n", + "↪ y, z, t)⋅──(ρ(x, y, z, t)) v (x, y, z, t)⋅──(ρ(x, y, z, t)) w (x, y, z, ↪\n", + "↪ ∂z ∂z ↪\n", + "↪ ─────────────────────────── - ──────────────────────────────── - ─────────── ↪\n", + "↪ 2 2 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ⎞ ↪\n", + "↪ t)⋅──(ρ(x, y, z, t))⎟ ↪\n", + "↪ ∂z ⎟ ∂ ∂ ↪\n", + "↪ ─────────────────────⎟ + E(x, y, z, t)⋅──(ρ(x, y, z, t)) + ρ(x, y, z, t)⋅──( ↪\n", + "↪ 2 ⎠ ∂z ∂z ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎞ ↪\n", + "↪ ⎟ ↪\n", + "↪ ⎟ ∂ ↪\n", + "↪ E(x, y, z, t))⎟⋅w(x, y, z, t) + E(x, y, z, t)⋅──(ρ(x, y, z, t)) + ρ(x, y, z, ↪\n", + "↪ ⎠ ∂t ↪\n", + "\n", + "↪ ⎛ ↪\n", + "↪ ⎜ ↪\n", + "↪ ⎜ ⎛ ∂ ↪\n", + "↪ ⎜ ⎜E(x, y, z, t)⋅──(ρ(x, y, z, t)) + ↪\n", + "↪ 2 ⎜ ⎝ ∂x ↪\n", + "↪ M ⋅γ⋅κ⋅(γ - 1)⋅⎜- ────────────────────────────────── ↪\n", + "↪ ⎜ ↪\n", + "↪ ∂ ⎝ ↪\n", + "↪ t)⋅──(E(x, y, z, t)) - ──────────────────────────────────────────────────── ↪\n", + "↪ ∂t ↪\n", + "\n", + "↪ 2 ↪\n", + "↪ ∂ ↪\n", + "↪ ∂ ⎞ ∂ E(x, y, z, t)⋅───(ρ(x, ↪\n", + "↪ ρ(x, y, z, t)⋅──(E(x, y, z, t))⎟⋅──(ρ(x, y, z, t)) 2 ↪\n", + "↪ ∂x ⎠ ∂x ∂x ↪\n", + "↪ ─────────────────────────────────────────────────── + ────────────────────── ↪\n", + "↪ 2 ↪\n", + "↪ ρ (x, y, z, t) ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ 2 ↪\n", + "↪ ∂ ∂ ∂ ↪\n", + "↪ y, z, t)) + ρ(x, y, z, t)⋅───(E(x, y, z, t)) + 2⋅──(E(x, y, z, t))⋅──(ρ(x, ↪\n", + "↪ 2 ∂x ∂x ↪\n", + "↪ ∂x ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ρ(x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ 2 ↪\n", + "↪ ∂ ↪\n", + "↪ y, z, t)) E(x, y, z, t)⋅───(ρ(x, y, z, t)) ⎛∂ ↪\n", + "↪ 2 E(x, y, z, t)⋅⎜──(ρ(x, y, z, ↪\n", + "↪ ∂x ⎝∂x ↪\n", + "↪ ───────── - ──────────────────────────────── + ───────────────────────────── ↪\n", + "↪ ρ(x, y, z, t) 2 ↪\n", + "↪ ρ (x, y, z, t) ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ 2 ↪\n", + "↪ ⎞ ↪\n", + "↪ t))⎟ 2 2 ↪\n", + "↪ ⎠ ∂ ∂ ↪\n", + "↪ ───── - u(x, y, z, t)⋅───(u(x, y, z, t)) - v(x, y, z, t)⋅───(v(x, y, z, t)) ↪\n", + "↪ 2 2 ↪\n", + "↪ ∂x ∂x ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 2 ↪\n", + "↪ ∂ ⎛∂ ⎞ ⎛∂ ↪\n", + "↪ - w(x, y, z, t)⋅───(w(x, y, z, t)) - ⎜──(u(x, y, z, t))⎟ - ⎜──(v(x, y, z, t ↪\n", + "↪ 2 ⎝∂x ⎠ ⎝∂x ↪\n", + "↪ ∂x ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ ↪\n", + "↪ ⎟ ↪\n", + "↪ ∂ ∂ ⎟ ↪\n", + "↪ 2 2 ──(E(x, y, z, t))⋅──(ρ(x, y, z, t))⎟ ↪\n", + "↪ ⎞ ⎛∂ ⎞ ∂x ∂x ⎟ ⎛∂ ↪\n", + "↪ ))⎟ - ⎜──(w(x, y, z, t))⎟ - ───────────────────────────────────⎟ + μ⋅⎜──(u ↪\n", + "↪ ⎠ ⎝∂x ⎠ ρ(x, y, z, t) ⎟ ⎝∂y ↪\n", + "↪ ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ Re ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ⎞ ∂ ⎛∂ ↪\n", + "↪ (x, y, z, t)) + ──(v(x, y, z, t))⎟⋅──(v(x, y, z, t)) + μ⋅⎜──(u(x, y, z, t)) ↪\n", + "↪ ∂x ⎠ ∂x ⎝∂z ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ 2 2 ↪\n", + "↪ ∂ ⎞ ∂ ⎜∂ ∂ ↪\n", + "↪ + ──(w(x, y, z, t))⎟⋅──(w(x, y, z, t)) + μ⋅⎜───(v(x, y, z, t)) + ─────(u(x, ↪\n", + "↪ ∂x ⎠ ∂x ⎜ 2 ∂y ∂x ↪\n", + "↪ ⎝∂x ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎞ ⎛ 2 2 ⎞ ↪\n", + "↪ ⎟ ⎜∂ ∂ ⎟ ↪\n", + "↪ y, z, t))⎟⋅v(x, y, z, t) + μ⋅⎜───(w(x, y, z, t)) + ─────(u(x, y, z, t))⎟⋅w(x ↪\n", + "↪ ⎟ ⎜ 2 ∂z ∂x ⎟ ↪\n", + "↪ ⎠ ⎝∂x ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ ∂ ∂ ∂ ↪\n", + "↪ ⎜4⋅──(u(x, y, z, t)) 2⋅──(v(x, y, z, t)) 2⋅──(w(x, y, z, ↪\n", + "↪ ⎜ ∂x ∂y ∂z ↪\n", + "↪ , y, z, t) + μ⋅⎜─────────────────── - ─────────────────── - ──────────────── ↪\n", + "↪ ⎝ 3 3 3 ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎛ 2 ↪\n", + "↪ ⎜ ∂ 2 ↪\n", + "↪ ⎞ ⎜4⋅───(u(x, y, z, t)) ∂ ↪\n", + "↪ t))⎟ ⎜ 2 2⋅─────(v(x, y, z, t)) ↪\n", + "↪ ⎟ ∂ ⎜ ∂x ∂y ∂x ↪\n", + "↪ ───⎟⋅──(u(x, y, z, t)) + μ⋅⎜──────────────────── - ────────────────────── - ↪\n", + "↪ ⎠ ∂x ⎝ 3 3 ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ ⎛ ↪\n", + "↪ 2 ⎟ ⎜ ↪\n", + "↪ ∂ ⎟ ⎜ ⎛ ∂ ↪\n", + "↪ 2⋅─────(w(x, y, z, t))⎟ ⎜ ⎜E(x, y, z, t)⋅──( ↪\n", + "↪ ∂z ∂x ⎟ 2 ⎜ ⎝ ∂y ↪\n", + "↪ ──────────────────────⎟⋅u(x, y, z, t) M ⋅γ⋅κ⋅(γ - 1)⋅⎜- ────────────────── ↪\n", + "↪ 3 ⎠ ⎜ ↪\n", + "↪ ⎝ ↪\n", + "↪ ───────────────────────────────────── - ──────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ⎞ ∂ E(x, y ↪\n", + "↪ ρ(x, y, z, t)) + ρ(x, y, z, t)⋅──(E(x, y, z, t))⎟⋅──(ρ(x, y, z, t)) ↪\n", + "↪ ∂y ⎠ ∂y ↪\n", + "↪ ─────────────────────────────────────────────────────────────────── + ────── ↪\n", + "↪ 2 ↪\n", + "↪ ρ (x, y, z, t) ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ 2 2 ↪\n", + "↪ ∂ ∂ ∂ ↪\n", + "↪ , z, t)⋅───(ρ(x, y, z, t)) + ρ(x, y, z, t)⋅───(E(x, y, z, t)) + 2⋅──(E(x, y, ↪\n", + "↪ 2 2 ∂y ↪\n", + "↪ ∂y ∂y ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ρ(x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ 2 ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ z, t))⋅──(ρ(x, y, z, t)) E(x, y, z, t)⋅───(ρ(x, y, z, t)) ↪\n", + "↪ ∂y 2 E(x, y, z, t) ↪\n", + "↪ ∂y ↪\n", + "↪ ───────────────────────── - ──────────────────────────────── + ───────────── ↪\n", + "↪ ρ(x, y, z, t) 2 ↪\n", + "↪ ρ ( ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ 2 ↪\n", + "↪ ⎛∂ ⎞ ↪\n", + "↪ ⋅⎜──(ρ(x, y, z, t))⎟ 2 2 ↪\n", + "↪ ⎝∂y ⎠ ∂ ∂ ↪\n", + "↪ ───────────────────── - u(x, y, z, t)⋅───(u(x, y, z, t)) - v(x, y, z, t)⋅─── ↪\n", + "↪ 2 2 ↪\n", + "↪ x, y, z, t) ∂y ∂y ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 2 ↪\n", + "↪ ∂ ⎛∂ ⎞ ↪\n", + "↪ (v(x, y, z, t)) - w(x, y, z, t)⋅───(w(x, y, z, t)) - ⎜──(u(x, y, z, t))⎟ - ↪\n", + "↪ 2 ⎝∂y ⎠ ↪\n", + "↪ ∂y ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ 2 2 ──(E(x, y, z, t))⋅──(ρ(x, y, z ↪\n", + "↪ ⎛∂ ⎞ ⎛∂ ⎞ ∂y ∂y ↪\n", + "↪ ⎜──(v(x, y, z, t))⎟ - ⎜──(w(x, y, z, t))⎟ - ────────────────────────────── ↪\n", + "↪ ⎝∂y ⎠ ⎝∂y ⎠ ρ(x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ Re ↪\n", + "\n", + "↪ ⎞ ↪\n", + "↪ ⎟ ↪\n", + "↪ ⎟ ↪\n", + "↪ , t))⎟ ⎛ 2 ↪\n", + "↪ ⎟ ⎛∂ ∂ ⎞ ∂ ⎜∂ ↪\n", + "↪ ─────⎟ + μ⋅⎜──(u(x, y, z, t)) + ──(v(x, y, z, t))⎟⋅──(u(x, y, z, t)) + μ⋅⎜── ↪\n", + "↪ ⎟ ⎝∂y ∂x ⎠ ∂y ⎜ ↪\n", + "↪ ⎠ ⎝∂y ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 ⎞ ↪\n", + "↪ ∂ ⎟ ⎛∂ ↪\n", + "↪ ─(u(x, y, z, t)) + ─────(v(x, y, z, t))⎟⋅u(x, y, z, t) + μ⋅⎜──(v(x, y, z, t) ↪\n", + "↪ 2 ∂y ∂x ⎟ ⎝∂z ↪\n", + "↪ ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ 2 2 ↪\n", + "↪ ∂ ⎞ ∂ ⎜∂ ∂ ↪\n", + "↪ ) + ──(w(x, y, z, t))⎟⋅──(w(x, y, z, t)) + μ⋅⎜───(w(x, y, z, t)) + ─────(v(x ↪\n", + "↪ ∂y ⎠ ∂y ⎜ 2 ∂z ∂y ↪\n", + "↪ ⎝∂y ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ ∂ ∂ ↪\n", + "↪ ⎞ ⎜ 2⋅──(u(x, y, z, t)) 4⋅──(v(x, y, z, t)) ↪\n", + "↪ ⎟ ⎜ ∂x ∂y ↪\n", + "↪ , y, z, t))⎟⋅w(x, y, z, t) + μ⋅⎜- ─────────────────── + ─────────────────── ↪\n", + "↪ ⎟ ⎝ 3 3 ↪\n", + "↪ ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎛ 2 ↪\n", + "↪ ⎜ ∂ 2 ↪\n", + "↪ ∂ ⎞ ⎜4⋅───(v(x, y, z, t)) ∂ ↪\n", + "↪ 2⋅──(w(x, y, z, t))⎟ ⎜ 2 2⋅───── ↪\n", + "↪ ∂z ⎟ ∂ ⎜ ∂y ∂y ∂x ↪\n", + "↪ - ───────────────────⎟⋅──(v(x, y, z, t)) + μ⋅⎜──────────────────── - ─────── ↪\n", + "↪ 3 ⎠ ∂y ⎝ 3 ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ ⎛ ↪\n", + "↪ 2 ⎟ ⎜ ↪\n", + "↪ ∂ ⎟ ⎜ ↪\n", + "↪ (u(x, y, z, t)) 2⋅─────(w(x, y, z, t))⎟ ⎜ ↪\n", + "↪ ∂z ∂y ⎟ 2 ⎜ ↪\n", + "↪ ─────────────── - ──────────────────────⎟⋅v(x, y, z, t) M ⋅γ⋅κ⋅(γ - 1)⋅⎜- ↪\n", + "↪ 3 3 ⎠ ⎜ ↪\n", + "↪ ⎝ ↪\n", + "↪ ─────────────────────────────────────────────────────── - ────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ ∂ ∂ ⎞ ∂ ↪\n", + "↪ ⎜E(x, y, z, t)⋅──(ρ(x, y, z, t)) + ρ(x, y, z, t)⋅──(E(x, y, z, t))⎟⋅──(ρ(x, ↪\n", + "↪ ⎝ ∂z ∂z ⎠ ∂z ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 2 ↪\n", + "↪ ρ (x, y, z, t) ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ 2 2 ↪\n", + "↪ ∂ ∂ ↪\n", + "↪ E(x, y, z, t)⋅───(ρ(x, y, z, t)) + ρ(x, y, z, t)⋅───(E(x, y, z, ↪\n", + "↪ y, z, t)) 2 2 ↪\n", + "↪ ∂z ∂z ↪\n", + "↪ ───────── + ──────────────────────────────────────────────────────────────── ↪\n", + "↪ ρ(x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ 2 ↪\n", + "↪ ∂ ∂ ∂ ↪\n", + "↪ t)) + 2⋅──(E(x, y, z, t))⋅──(ρ(x, y, z, t)) E(x, y, z, t)⋅───(ρ(x, y, z, t ↪\n", + "↪ ∂z ∂z 2 ↪\n", + "↪ ∂z ↪\n", + "↪ ─────────────────────────────────────────── - ────────────────────────────── ↪\n", + "↪ ρ(x, y, z, t) ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ 2 ↪\n", + "↪ )) ⎛∂ ⎞ ↪\n", + "↪ E(x, y, z, t)⋅⎜──(ρ(x, y, z, t))⎟ 2 ↪\n", + "↪ ⎝∂z ⎠ ∂ ↪\n", + "↪ ── + ────────────────────────────────── - u(x, y, z, t)⋅───(u(x, y, z, t)) - ↪\n", + "↪ 2 2 ↪\n", + "↪ ρ (x, y, z, t) ∂z ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 2 ↪\n", + "↪ ∂ ∂ ⎛∂ ↪\n", + "↪ v(x, y, z, t)⋅───(v(x, y, z, t)) - w(x, y, z, t)⋅───(w(x, y, z, t)) - ⎜──(u ↪\n", + "↪ 2 2 ⎝∂z ↪\n", + "↪ ∂z ∂z ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ∂ ↪\n", + "↪ 2 2 2 ──(E(x, y, z ↪\n", + "↪ ⎞ ⎛∂ ⎞ ⎛∂ ⎞ ∂z ↪\n", + "↪ (x, y, z, t))⎟ - ⎜──(v(x, y, z, t))⎟ - ⎜──(w(x, y, z, t))⎟ - ──────────── ↪\n", + "↪ ⎠ ⎝∂z ⎠ ⎝∂z ⎠ ρ ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ Re ↪\n", + "\n", + "↪ ⎞ ↪\n", + "↪ ⎟ ↪\n", + "↪ ∂ ⎟ ↪\n", + "↪ , t))⋅──(ρ(x, y, z, t))⎟ ↪\n", + "↪ ∂z ⎟ ⎛∂ ∂ ⎞ ∂ ↪\n", + "↪ ───────────────────────⎟ + μ⋅⎜──(u(x, y, z, t)) + ──(w(x, y, z, t))⎟⋅──(u(x, ↪\n", + "↪ (x, y, z, t) ⎟ ⎝∂z ∂x ⎠ ∂z ↪\n", + "↪ ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ 2 2 ⎞ ↪\n", + "↪ ⎜∂ ∂ ⎟ ↪\n", + "↪ y, z, t)) + μ⋅⎜───(u(x, y, z, t)) + ─────(w(x, y, z, t))⎟⋅u(x, y, z, t) + μ ↪\n", + "↪ ⎜ 2 ∂z ∂x ⎟ ↪\n", + "↪ ⎝∂z ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ 2 ↪\n", + "↪ ⎛∂ ∂ ⎞ ∂ ⎜∂ ↪\n", + "↪ ⋅⎜──(v(x, y, z, t)) + ──(w(x, y, z, t))⎟⋅──(v(x, y, z, t)) + μ⋅⎜───(v(x, y, ↪\n", + "↪ ⎝∂z ∂y ⎠ ∂z ⎜ 2 ↪\n", + "↪ ⎝∂z ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ ∂ ↪\n", + "↪ 2 ⎞ ⎜ 2⋅──(u(x, y, z, t)) 2⋅ ↪\n", + "↪ ∂ ⎟ ⎜ ∂x ↪\n", + "↪ z, t)) + ─────(w(x, y, z, t))⎟⋅v(x, y, z, t) + μ⋅⎜- ─────────────────── - ── ↪\n", + "↪ ∂z ∂y ⎟ ⎝ 3 ↪\n", + "↪ ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎛ 2 ↪\n", + "↪ ⎜ ∂ ↪\n", + "↪ ∂ ∂ ⎞ ⎜4⋅───(w(x, y ↪\n", + "↪ ──(v(x, y, z, t)) 4⋅──(w(x, y, z, t))⎟ ⎜ 2 ↪\n", + "↪ ∂y ∂z ⎟ ∂ ⎜ ∂z ↪\n", + "↪ ───────────────── + ───────────────────⎟⋅──(w(x, y, z, t)) + μ⋅⎜──────────── ↪\n", + "↪ 3 3 ⎠ ∂z ⎝ 3 ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ ↪\n", + "↪ 2 2 ⎟ ↪\n", + "↪ , z, t)) ∂ ∂ ⎟ ↪\n", + "↪ 2⋅─────(u(x, y, z, t)) 2⋅─────(v(x, y, z, t))⎟ ↪\n", + "↪ ∂z ∂x ∂z ∂y ⎟ ↪\n", + "↪ ──────── - ────────────────────── - ──────────────────────⎟⋅w(x, y, z, t) ↪\n", + "↪ 3 3 ⎠ ↪\n", + "↪ ↪\n", + "↪ ───────────────────────────────────────────────────────────────────────── = ↪\n", + "↪ ↪\n", + "\n", + "↪ \n", + "↪ \n", + "↪ \n", + "↪ \n", + "↪ \n", + "↪ \n", + "↪ \n", + "↪ \n", + "↪ sᵣₕₒₑ(x, y, z, t)\n", + "↪ " + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rhoEdt = diff(rho*E,t)\n", + "FrhoE = Finviscid_q_d[4,:] - S(1)/Re * Fviscous_q_d[4,:]\n", + "EqrhoE = Eq(rhoEdt + divergence(FrhoE), srhoE)\n", + "EqrhoE" + ] + }, + { + "cell_type": "markdown", + "id": "f31e6974", + "metadata": {}, + "source": [ + "# Manufactured solution" + ] + }, + { + "cell_type": "markdown", + "id": "c6c4e27b", + "metadata": {}, + "source": [ + "## Write the prescribed solution" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "a3a2ba66", + "metadata": {}, + "outputs": [], + "source": [ + "# Define manufactured solutions for each variable\n", + "rho_ms = S(3) + sin(x+y+z)*exp(t)#(cos(x)+cos(y)+cos(z))*exp(-t**2)\n", + "u_ms = cos(x+y+z)*exp(-t)#-cos(x)*sin(y)*sin(z)*exp(-t)\n", + "v_ms = sin(x+y+z)*exp(-t)#sin(x)*cos(y)*sin(z)*exp(-t)\n", + "w_ms = cos(x+y+z)*exp(-t)#-sin(x)*sin(y)*cos(z)*exp(-t)\n", + "# E_ms = sin(x+y+z)*exp(2*t)#(cos(x)+cos(y)+cos(z))*exp(-2*t)\n", + "E_ms = rho_ms * (u_ms**2+v_ms**2+w_ms**2) / S(2) + S(1)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "4a1803de", + "metadata": {}, + "outputs": [], + "source": [ + "# Replace \n", + "Eqrho_2 = Eqrho.subs([(rho,rho_ms), (u,u_ms), (v,v_ms), (w,w_ms), (E,E_ms)])\n", + "Eqrhou_2 = Eqrhou.subs([(rho,rho_ms), (u,u_ms), (v,v_ms), (w,w_ms), (E,E_ms)])\n", + "Eqrhov_2 = Eqrhov.subs([(rho,rho_ms), (u,u_ms), (v,v_ms), (w,w_ms), (E,E_ms)])\n", + "Eqrhow_2 = Eqrhow.subs([(rho,rho_ms), (u,u_ms), (v,v_ms), (w,w_ms), (E,E_ms)])\n", + "EqrhoE_2 = EqrhoE.subs([(rho,rho_ms), (u,u_ms), (v,v_ms), (w,w_ms), (E,E_ms)])" + ] + }, + { + "cell_type": "markdown", + "id": "644010a9", + "metadata": {}, + "source": [ + "## Solve for the source term" + ] + }, + { + "cell_type": "markdown", + "id": "b81af952", + "metadata": {}, + "source": [ + "### Solve $s_{\\rho}$" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "d033b246", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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vEp5rxPqLqg5g7wOaG9pXuHbz+l6KsrXu7UrNfAR68JOqfSSoH+cn84NtITEUMunMY2jv9jQy5+jWx1VQLJwfbOuURyTB/aR3e4ZFrpGU6BMOjwIrtqnbrqw1hSbNi9YSISLzReRaETkMe3nNSsC4vK8T4TlstHH9dhVU9ePYaN0DwKZYkDg0GA0sHRF5CXtBz5aq+jlgZ+ACEbmrCnvU1uz7NfBx4MhuiQj2XQ+QcqQ9T1T1OKyhuRuYkCQIV6TPpLiOeyCDhqEGOvaYmYw6aQ1yjZm3BNuPJbhs67OOj7Hnw9g04Sck5uVrKXXm+uiRBrWpc7CnZz+iqu+NKW89ff9ksC0sf0yLx85kuG8URmvd69YSP1X7hrclOdAH/rJiUP5oaF/V2k1DobbWsV2pm49Avfwkx/u/UmIopNKZx9AeaWLOkbCPq4hYWMc8IgnuJz3Sb7lGdEDlVmADVY3OXGlbJiJvAPcCG6nqfnEXUdWxauundUVVd29z/dbLTpNOpcpEMIo3B1glcOCofWOx0bZnWfwSyROx2T6nFGlbF27ElmS7ABu9O6EKI1R1eeA6YEdgkoicn+Cw1mjq9YUZ1gFVPRH77f6Ijdq3fWlg1fpMius4Oxk1DBXpuGpNutZ6I+eYeT7WoX2iqm4Uc601Q3/+KNieoKofCNUZiT1xMwL4YWh/Jp25PnqjSW1q0HZejk3JX+IFiKo6EdgNe7psZlA/1/wxLR47M+O+kRJV3UBVR8fsH6GqJ2Oauzm4Ka7cN/C2JE+Gs79sjMX0h1o7aqDdxBRha53blRr7CNTAT3K+/ysshgZlqXXmMbQ3mpRztEjax1VQ3K5dHpEE95Pe6MdcIyrE24CXgY0wA5OWHYuNQs1Q1dlB+QhsitdHgVEisnZCm34KvKmqN2JPMQ5go4xbYcFgdsLz9MIMYH/s5v+x1k5V3Qy4BvtBJ4rIcwAicpWq3gHsrarjROT3JdgY5SbgcGw61DEydF3EsrgMm3Z3G7Cuxr8g6Lsi8lbo712xp/KuLt68JVHVzwPfDq7/e+AoHfripSdF5JLg/3XQZ1Jcx9nIomGoTsd10KRrLTu5xUwReVBVjwS+j73k+GrsaY6VgS2BV4AJQd2bVfU04N+A+1X1KuA17EmijbHE7PTQ6XvRmesjO41qU4GvYWv4flNVd8Ds/hA2Ff8d4LDIE2Z55o9p8diZDfeN9OwOnK6qc7DlLF7EXr65I7AutmTEYZFjKvMNb0tyZTj7yxbATBF5N7K/yrielrxtrWW7UnMfgXr4SW73fwXHUMiuM4+h2WlSzpGljyvXWFjjPCIJ7ifZ6btcY4kZKiKyAJu+NCFasUvZddgXNwPYBHs50IHYO1dmAwensOl47AU6W2AvGjoYGAUch01T+3uKc2VlBvACcFBrRzBCOQtbn243EYmu7zcl2EYbvLJorTl3O5GnGMpCbf27HYI/twYk5t8RYQcKRjH3Aa4RkWdKNdhYJ9iOxF5oFWfzpFD9OugzKa7jlGTRcHBclTqugyZdaxkoImaKyIXAWCzhG48lG3thT6ucG6l7HPYit0ex3+4oLC84AUsU3w5V70Vnro8MNLFNFVtKYBtseYG1ME3thCW840Tkykj9PPPHtHjszIb7RnpmAz/AOhL2w+Ly/sA8QIF/FJEHwwdU7BveluTHcPaXCcR8pqq1m4YCbK1du9IAH4FheP9XYAyF7DrzGJqBBuYckLKPq4i4XdM8IgnuJxno11xjYOHChUvsUNWVgRkiMj5auVPZcENVpwDTgC2kovXn0qCqv8Re+rOtiNxetT1JUdWvAGcDO1T4VMywxXVcDq5j11pZNFVrro9yaKo++hn3jXJw3xgeuL+UQzd/UdVVgekiMrF045yuuJ+UQxPbFddGOTRRG85i3E/KYTjkGtF3qCAiLwIzVfWf05QNQ74HPI1Nlas1ai8f2hM4v2EOtDQ2mjvDG5rCcB0XjOt4Ea61gmm41lwfBdNwffQz7hsF474xrHB/KZiE/nI4tm68U0/cTwqmwe2Ka6NgGqwNZzHuJwUzXHKNIQMqAacBe6rqqJRlwwYReRObMnSHqi5TtT1RVHVtVT1eVS8ELgYewNYdbBJjsCUQJldsx7DFdVwKY3Adu9bKYQwN1ZrroxTG0FB99DPuG6UwBveNYYH7SymMoYO/qOp6wEsickuZRjnJcT8phTE0sF1xbZTCGBqoDWcx7ielMIZhkGsMWfKrhaouB3xQRB5JU+aUg6oeDlwAzAd+AxwtIn+p1CjHSYnr2CkL15rTCdeH48TjvuE4yekHf1HVLUXkjqrtcJpLP/iJkw3XhuN0px/8pCm5RtsBFcdxHMdxHMdxHMdxHMdxHMdxHMf4f6ukXRRT2lacAAAAAElFTkSuQmCC", + "text/latex": [ + "$\\displaystyle \\left(\\left(e^{t} \\sin{\\left(x + y + z \\right)} - 2 \\sin^{2}{\\left(x + y + z \\right)} + \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - 6 e^{- t} \\sin{\\left(x + y + z \\right)} + 3 e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{t} + e^{t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + 2 e^{t} \\cos^{2}{\\left(x + y + z \\right)}\\right) e^{- t}$" + ], + "text/plain": [ + "⎛⎛ t 2 - ↪\n", + "⎝⎝ℯ ⋅sin(x + y + z) - 2⋅sin (x + y + z) + sin(x + y + z)⋅cos(x + y + z) - 6⋅ℯ ↪\n", + "\n", + "↪ t -t ⎞ t t ↪\n", + "↪ ⋅sin(x + y + z) + 3⋅ℯ ⋅cos(x + y + z)⎠⋅ℯ + ℯ ⋅sin(x + y + z)⋅cos(x + y + ↪\n", + "\n", + "↪ t 2 ⎞ -t\n", + "↪ z) + 2⋅ℯ ⋅cos (x + y + z)⎠⋅ℯ " + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "res_srho = solve(Eqrho_2, srho)[0]\n", + "res_srho" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "094284ad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "((exp(t)*sin(x + y + z) - 2*sin(x + y + z)**2 + sin(x + y + z)*cos(x + y + z) - 6*exp(-t)*sin(x + y + z) + 3*exp(-t)*cos(x + y + z))*exp(t) + exp(t)*sin(x + y + z)*cos(x + y + z) + 2*exp(t)*cos(x + y + z)**2)*exp(-t)\n" + ] + } + ], + "source": [ + "print(res_srho)" + ] + }, + { + "cell_type": "markdown", + "id": "6e845f8f", + "metadata": {}, + "source": [ + "### Solve $s_{\\rho \\mathbf{u}}$" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "382fe471", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/latex": [ + "$\\displaystyle \\frac{\\left(Re \\left(\\gamma e^{t} \\sin^{2}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + 2 \\gamma e^{t} \\cos^{3}{\\left(x + y + z \\right)} - e^{t} \\sin^{2}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + \\frac{e^{t} \\sin{\\left(2 x + 2 y + 2 z \\right)} \\cos{\\left(x + y + z \\right)}}{2}\\right) + \\frac{Re \\left(\\gamma e^{t} \\sin^{3}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + 2 \\gamma e^{t} \\sin{\\left(x + y + z \\right)} \\cos^{3}{\\left(x + y + z \\right)} + 6 \\gamma e^{- t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - e^{t} \\sin^{3}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\cos^{3}{\\left(x + y + z \\right)} + 2 e^{t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - 6 e^{- t} \\sin^{2}{\\left(x + y + z \\right)} - 30 e^{- t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + 6 e^{- t} \\cos^{2}{\\left(x + y + z \\right)}\\right) e^{t}}{2} + Re \\left(\\frac{\\gamma \\left(\\left(\\cos{\\left(2 x + 2 y + 2 z \\right)} + 3\\right) e^{t} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 12 \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\sin{\\left(x + y + z \\right)}}{4} + \\frac{3 \\gamma \\left(\\left(\\cos{\\left(2 x + 2 y + 2 z \\right)} + 3\\right) e^{t} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 12 \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- 2 t}}{4} + \\gamma e^{t} \\cos{\\left(x + y + z \\right)} - \\gamma e^{- t} \\sin^{2}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + \\gamma e^{- t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - \\frac{\\left(\\left(\\cos{\\left(2 x + 2 y + 2 z \\right)} + 3\\right) e^{t} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 12 \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\sin{\\left(x + y + z \\right)}}{4} - \\frac{3 \\left(\\left(\\cos{\\left(2 x + 2 y + 2 z \\right)} + 3\\right) e^{t} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 12 \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- 2 t}}{4} - e^{t} \\cos{\\left(x + y + z \\right)} - \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - e^{- t} \\sin^{3}{\\left(x + y + z \\right)} + e^{- t} \\sin^{2}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - 3 e^{- t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} + \\frac{e^{- t} \\sin{\\left(2 x + 2 y + 2 z \\right)} \\cos{\\left(x + y + z \\right)}}{2} - 3 e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{2 t} - \\frac{\\mu \\left(- e^{- t} \\sin{\\left(x + y + z \\right)} - 11 e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{2 t}}{3}\\right) e^{- 2 t}}{Re}$" + ], + "text/plain": [ + "⎛ ⎛ ↪\n", + "⎜ ⎜ t 2 t 3 t 2 ↪\n", + "⎜Re⋅⎜γ⋅ℯ ⋅sin (x + y + z)⋅cos(x + y + z) + 2⋅γ⋅ℯ ⋅cos (x + y + z) - ℯ ⋅sin (x ↪\n", + "⎝ ⎝ ↪\n", + "────────────────────────────────────────────────────────────────────────────── ↪\n", + " ↪\n", + "\n", + "↪ t ⎞ ⎛ t ↪\n", + "↪ ℯ ⋅sin(2⋅x + 2⋅y + 2⋅z)⋅cos(x + y + z)⎟ Re⋅⎝γ⋅ℯ ↪\n", + "↪ + y + z)⋅cos(x + y + z) + ──────────────────────────────────────⎟ + ──────── ↪\n", + "↪ 2 ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ 3 t 3 ↪\n", + "↪ ⋅sin (x + y + z)⋅cos(x + y + z) + 2⋅γ⋅ℯ ⋅sin(x + y + z)⋅cos (x + y + z) + 6⋅ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ -t t 3 ↪\n", + "↪ γ⋅ℯ ⋅sin(x + y + z)⋅cos(x + y + z) - ℯ ⋅sin (x + y + z)⋅cos(x + y + z) - 2⋅ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ t 3 t ↪\n", + "↪ ℯ ⋅sin(x + y + z)⋅cos (x + y + z) + 2⋅ℯ ⋅sin(x + y + z)⋅cos(x + y + z) - 6⋅ℯ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 2 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ -t 2 -t -t 2 ↪\n", + "↪ ⋅sin (x + y + z) - 30⋅ℯ ⋅sin(x + y + z)⋅cos(x + y + z) + 6⋅ℯ ⋅cos (x + y ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ t ⎛ ⎛ t t ↪\n", + "↪ + z)⎠⋅ℯ ⎜γ⋅⎝(cos(2⋅x + 2⋅y + 2⋅z) + 3)⋅ℯ ⋅cos(x + y + z) - 2⋅ℯ ⋅sin(x ↪\n", + "↪ ───────── + Re⋅⎜──────────────────────────────────────────────────────────── ↪\n", + "↪ ⎝ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ -t ↪\n", + "↪ + y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) - 12⋅sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ ⋅sin(x ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎛ t t ↪\n", + "↪ + y + z) 3⋅γ⋅⎝(cos(2⋅x + 2⋅y + 2⋅z) + 3)⋅ℯ ⋅cos(x + y + z) - 2⋅ℯ ⋅sin(x + ↪\n", + "↪ ───────── + ──────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ -2⋅t ↪\n", + "↪ y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) - 12⋅sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ ↪\n", + "↪ ────────────────────────────────────────────────────────────────────── + γ⋅ℯ ↪\n", + "↪ 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ Re ↪\n", + "\n", + "↪ ↪\n", + "↪ t -t 2 -t ↪\n", + "↪ ⋅cos(x + y + z) - γ⋅ℯ ⋅sin (x + y + z)⋅cos(x + y + z) + γ⋅ℯ ⋅sin(x + y + ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎛ t ↪\n", + "↪ ⎝(cos(2⋅x + 2⋅y + 2⋅z) + 3)⋅ℯ ⋅cos(x + y + z) - 2⋅ ↪\n", + "↪ z)⋅sin(2⋅x + 2⋅y + 2⋅z) - ────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ t ⎞ ↪\n", + "↪ ℯ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) - 12⋅sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ -t ⎛ t t ↪\n", + "↪ ⋅sin(x + y + z) 3⋅⎝(cos(2⋅x + 2⋅y + 2⋅z) + 3)⋅ℯ ⋅cos(x + y + z) - 2⋅ℯ ⋅s ↪\n", + "↪ ───────────────── - ──────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ -2⋅t ↪\n", + "↪ in(x + y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) - 12⋅sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ t -t 3 ↪\n", + "↪ - ℯ ⋅cos(x + y + z) - sin(x + y + z)⋅cos(x + y + z) - ℯ ⋅sin (x + y + z) + ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ -t 2 -t ↪\n", + "↪ ℯ ⋅sin (x + y + z)⋅cos(x + y + z) - 3⋅ℯ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅y + 2 ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ -t ⎞ ↪\n", + "↪ ℯ ⋅sin(2⋅x + 2⋅y + 2⋅z)⋅cos(x + y + z) -t ⎟ 2⋅t ↪\n", + "↪ ⋅z) + ─────────────────────────────────────── - 3⋅ℯ ⋅cos(x + y + z)⎟⋅ℯ - ↪\n", + "↪ 2 ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎛ -t -t ⎞ 2⋅t⎞ \n", + "↪ μ⋅⎝- ℯ ⋅sin(x + y + z) - 11⋅ℯ ⋅cos(x + y + z)⎠⋅ℯ ⎟ -2⋅t\n", + "↪ ─────────────────────────────────────────────────────⎟⋅ℯ \n", + "↪ 3 ⎠ \n", + "↪ ─────────────────────────────────────────────────────────────\n", + "↪ " + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "res_srhou = solve(Eqrhou_2, srhou)[0]\n", + "res_srhou" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "e118e36c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(Re*(gamma*exp(t)*sin(x + y + z)**2*cos(x + y + z) + 2*gamma*exp(t)*cos(x + y + z)**3 - exp(t)*sin(x + y + z)**2*cos(x + y + z) + exp(t)*sin(2*x + 2*y + 2*z)*cos(x + y + z)/2) + Re*(gamma*exp(t)*sin(x + y + z)**3*cos(x + y + z) + 2*gamma*exp(t)*sin(x + y + z)*cos(x + y + z)**3 + 6*gamma*exp(-t)*sin(x + y + z)*cos(x + y + z) - exp(t)*sin(x + y + z)**3*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*cos(x + y + z)**3 + 2*exp(t)*sin(x + y + z)*cos(x + y + z) - 6*exp(-t)*sin(x + y + z)**2 - 30*exp(-t)*sin(x + y + z)*cos(x + y + z) + 6*exp(-t)*cos(x + y + z)**2)*exp(t)/2 + Re*(gamma*((cos(2*x + 2*y + 2*z) + 3)*exp(t)*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 12*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z)/4 + 3*gamma*((cos(2*x + 2*y + 2*z) + 3)*exp(t)*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 12*sin(x + y + z)*cos(x + y + z))*exp(-2*t)/4 + gamma*exp(t)*cos(x + y + z) - gamma*exp(-t)*sin(x + y + z)**2*cos(x + y + z) + gamma*exp(-t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - ((cos(2*x + 2*y + 2*z) + 3)*exp(t)*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 12*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z)/4 - 3*((cos(2*x + 2*y + 2*z) + 3)*exp(t)*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 12*sin(x + y + z)*cos(x + y + z))*exp(-2*t)/4 - exp(t)*cos(x + y + z) - sin(x + y + z)*cos(x + y + z) - exp(-t)*sin(x + y + z)**3 + exp(-t)*sin(x + y + z)**2*cos(x + y + z) - 3*exp(-t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) + exp(-t)*sin(2*x + 2*y + 2*z)*cos(x + y + z)/2 - 3*exp(-t)*cos(x + y + z))*exp(2*t) - mu*(-exp(-t)*sin(x + y + z) - 11*exp(-t)*cos(x + y + z))*exp(2*t)/3)*exp(-2*t)/Re\n" + ] + } + ], + "source": [ + "print(res_srhou)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "6bf61084", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/latex": [ + "$\\displaystyle \\frac{\\left(Re \\left(\\gamma e^{t} \\sin^{2}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + 2 \\gamma e^{t} \\cos^{3}{\\left(x + y + z \\right)} + e^{t} \\sin{\\left(2 x + 2 y + 2 z \\right)} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\cos^{3}{\\left(x + y + z \\right)}\\right) + \\frac{Re \\left(\\gamma e^{t} \\sin^{3}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + 2 \\gamma e^{t} \\sin{\\left(x + y + z \\right)} \\cos^{3}{\\left(x + y + z \\right)} + 6 \\gamma e^{- t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - e^{t} \\sin^{3}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + 2 e^{t} \\sin^{2}{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\cos^{3}{\\left(x + y + z \\right)} - 12 e^{- t} \\sin^{2}{\\left(x + y + z \\right)} + 6 e^{- t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + 12 e^{- t} \\cos^{2}{\\left(x + y + z \\right)}\\right) e^{t}}{2} + Re \\left(\\frac{\\gamma \\left(\\left(\\cos{\\left(2 x + 2 y + 2 z \\right)} + 3\\right) e^{t} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 12 \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\sin{\\left(x + y + z \\right)}}{4} + \\frac{3 \\gamma \\left(\\left(\\cos{\\left(2 x + 2 y + 2 z \\right)} + 3\\right) e^{t} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 12 \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- 2 t}}{4} + \\gamma e^{t} \\cos{\\left(x + y + z \\right)} - \\gamma e^{- t} \\sin^{2}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + \\gamma e^{- t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - \\frac{\\left(\\left(\\cos{\\left(2 x + 2 y + 2 z \\right)} + 3\\right) e^{t} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 12 \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\sin{\\left(x + y + z \\right)}}{4} - \\frac{3 \\left(\\left(\\cos{\\left(2 x + 2 y + 2 z \\right)} + 3\\right) e^{t} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 12 \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- 2 t}}{4} - e^{t} \\cos{\\left(x + y + z \\right)} - \\sin^{2}{\\left(x + y + z \\right)} - 2 e^{- t} \\sin^{3}{\\left(x + y + z \\right)} + 3 e^{- t} \\sin^{2}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - e^{- t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 3 e^{- t} \\sin{\\left(x + y + z \\right)} + e^{- t} \\sin{\\left(2 x + 2 y + 2 z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{2 t} - \\frac{\\mu \\left(- 10 e^{- t} \\sin{\\left(x + y + z \\right)} - 2 e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{2 t}}{3}\\right) e^{- 2 t}}{Re}$" + ], + "text/plain": [ + "⎛ ↪\n", + "⎜ ⎛ t 2 t 3 t ↪\n", + "⎜Re⋅⎝γ⋅ℯ ⋅sin (x + y + z)⋅cos(x + y + z) + 2⋅γ⋅ℯ ⋅cos (x + y + z) + ℯ ⋅sin(2⋅x ↪\n", + "⎝ ↪\n", + "────────────────────────────────────────────────────────────────────────────── ↪\n", + " ↪\n", + "\n", + "↪ ⎛ t 3 ↪\n", + "↪ t 3 ⎞ Re⋅⎝γ⋅ℯ ⋅sin (x + y + ↪\n", + "↪ + 2⋅y + 2⋅z)⋅cos(x + y + z) - 2⋅ℯ ⋅cos (x + y + z)⎠ + ───────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ t 3 -t ↪\n", + "↪ z)⋅cos(x + y + z) + 2⋅γ⋅ℯ ⋅sin(x + y + z)⋅cos (x + y + z) + 6⋅γ⋅ℯ ⋅sin(x + ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ t 3 t 2 ↪\n", + "↪ y + z)⋅cos(x + y + z) - ℯ ⋅sin (x + y + z)⋅cos(x + y + z) + 2⋅ℯ ⋅sin (x + y ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 2 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ t 3 -t 2 -t ↪\n", + "↪ + z) - 2⋅ℯ ⋅sin(x + y + z)⋅cos (x + y + z) - 12⋅ℯ ⋅sin (x + y + z) + 6⋅ℯ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ -t 2 ⎞ t ⎛ ⎛ ↪\n", + "↪ ⋅sin(x + y + z)⋅cos(x + y + z) + 12⋅ℯ ⋅cos (x + y + z)⎠⋅ℯ ⎜γ⋅⎝(cos(2⋅ ↪\n", + "↪ ─────────────────────────────────────────────────────────── + Re⋅⎜────────── ↪\n", + "↪ ⎝ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ t t ↪\n", + "↪ x + 2⋅y + 2⋅z) + 3)⋅ℯ ⋅cos(x + y + z) - 2⋅ℯ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅y + ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ -t ⎛ ↪\n", + "↪ 2⋅z) - 12⋅sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ ⋅sin(x + y + z) 3⋅γ⋅⎝(cos(2⋅x ↪\n", + "↪ ─────────────────────────────────────────────────────────── + ────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ t t ↪\n", + "↪ + 2⋅y + 2⋅z) + 3)⋅ℯ ⋅cos(x + y + z) - 2⋅ℯ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅y + 2⋅ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ -2⋅t ↪\n", + "↪ z) - 12⋅sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ t -t ↪\n", + "↪ ──────────────────────────────────────────── + γ⋅ℯ ⋅cos(x + y + z) - γ⋅ℯ ⋅s ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ Re ↪\n", + "\n", + "↪ ↪\n", + "↪ 2 -t ↪\n", + "↪ in (x + y + z)⋅cos(x + y + z) + γ⋅ℯ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) - ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎛ t t ↪\n", + "↪ ⎝(cos(2⋅x + 2⋅y + 2⋅z) + 3)⋅ℯ ⋅cos(x + y + z) - 2⋅ℯ ⋅sin(x + y + z)⋅sin(2⋅x ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ -t ⎛ ↪\n", + "↪ + 2⋅y + 2⋅z) - 12⋅sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ ⋅sin(x + y + z) 3⋅⎝(co ↪\n", + "↪ ─────────────────────────────────────────────────────────────────── - ────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ t t ↪\n", + "↪ s(2⋅x + 2⋅y + 2⋅z) + 3)⋅ℯ ⋅cos(x + y + z) - 2⋅ℯ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ -2⋅t ↪\n", + "↪ y + 2⋅z) - 12⋅sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ t ↪\n", + "↪ ────────────────────────────────────────────────── - ℯ ⋅cos(x + y + z) - sin ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ 2 -t 3 -t 2 ↪\n", + "↪ (x + y + z) - 2⋅ℯ ⋅sin (x + y + z) + 3⋅ℯ ⋅sin (x + y + z)⋅cos(x + y + z) ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ -t -t -t ↪\n", + "↪ - ℯ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) - 3⋅ℯ ⋅sin(x + y + z) + ℯ ⋅sin(2 ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ ⎛ -t -t ↪\n", + "↪ ⎟ 2⋅t μ⋅⎝- 10⋅ℯ ⋅sin(x + y + z) - 2⋅ℯ ⋅co ↪\n", + "↪ ⋅x + 2⋅y + 2⋅z)⋅cos(x + y + z)⎟⋅ℯ - ───────────────────────────────────── ↪\n", + "↪ ⎠ 3 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ 2⋅t⎞ \n", + "↪ s(x + y + z)⎠⋅ℯ ⎟ -2⋅t\n", + "↪ ──────────────────⎟⋅ℯ \n", + "↪ ⎠ \n", + "↪ ─────────────────────────\n", + "↪ " + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "res_srhov = solve(Eqrhov_2, srhov)[0]\n", + "res_srhov" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "4a003d20", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(Re*(gamma*exp(t)*sin(x + y + z)**2*cos(x + y + z) + 2*gamma*exp(t)*cos(x + y + z)**3 + exp(t)*sin(2*x + 2*y + 2*z)*cos(x + y + z) - 2*exp(t)*cos(x + y + z)**3) + Re*(gamma*exp(t)*sin(x + y + z)**3*cos(x + y + z) + 2*gamma*exp(t)*sin(x + y + z)*cos(x + y + z)**3 + 6*gamma*exp(-t)*sin(x + y + z)*cos(x + y + z) - exp(t)*sin(x + y + z)**3*cos(x + y + z) + 2*exp(t)*sin(x + y + z)**2 - 2*exp(t)*sin(x + y + z)*cos(x + y + z)**3 - 12*exp(-t)*sin(x + y + z)**2 + 6*exp(-t)*sin(x + y + z)*cos(x + y + z) + 12*exp(-t)*cos(x + y + z)**2)*exp(t)/2 + Re*(gamma*((cos(2*x + 2*y + 2*z) + 3)*exp(t)*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 12*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z)/4 + 3*gamma*((cos(2*x + 2*y + 2*z) + 3)*exp(t)*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 12*sin(x + y + z)*cos(x + y + z))*exp(-2*t)/4 + gamma*exp(t)*cos(x + y + z) - gamma*exp(-t)*sin(x + y + z)**2*cos(x + y + z) + gamma*exp(-t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - ((cos(2*x + 2*y + 2*z) + 3)*exp(t)*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 12*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z)/4 - 3*((cos(2*x + 2*y + 2*z) + 3)*exp(t)*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 12*sin(x + y + z)*cos(x + y + z))*exp(-2*t)/4 - exp(t)*cos(x + y + z) - sin(x + y + z)**2 - 2*exp(-t)*sin(x + y + z)**3 + 3*exp(-t)*sin(x + y + z)**2*cos(x + y + z) - exp(-t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 3*exp(-t)*sin(x + y + z) + exp(-t)*sin(2*x + 2*y + 2*z)*cos(x + y + z))*exp(2*t) - mu*(-10*exp(-t)*sin(x + y + z) - 2*exp(-t)*cos(x + y + z))*exp(2*t)/3)*exp(-2*t)/Re\n" + ] + } + ], + "source": [ + "print(res_srhov)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "20ed7adb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/latex": [ + "$\\displaystyle \\frac{\\left(Re \\left(\\gamma e^{t} \\sin^{2}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + 2 \\gamma e^{t} \\cos^{3}{\\left(x + y + z \\right)} - e^{t} \\sin^{2}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + \\frac{e^{t} \\sin{\\left(2 x + 2 y + 2 z \\right)} \\cos{\\left(x + y + z \\right)}}{2}\\right) + \\frac{Re \\left(\\gamma e^{t} \\sin^{3}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + 2 \\gamma e^{t} \\sin{\\left(x + y + z \\right)} \\cos^{3}{\\left(x + y + z \\right)} + 6 \\gamma e^{- t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - e^{t} \\sin^{3}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\cos^{3}{\\left(x + y + z \\right)} + 2 e^{t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - 6 e^{- t} \\sin^{2}{\\left(x + y + z \\right)} - 30 e^{- t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + 6 e^{- t} \\cos^{2}{\\left(x + y + z \\right)}\\right) e^{t}}{2} + Re \\left(\\frac{\\gamma \\left(\\left(\\cos{\\left(2 x + 2 y + 2 z \\right)} + 3\\right) e^{t} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 12 \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\sin{\\left(x + y + z \\right)}}{4} + \\frac{3 \\gamma \\left(\\left(\\cos{\\left(2 x + 2 y + 2 z \\right)} + 3\\right) e^{t} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 12 \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- 2 t}}{4} + \\gamma e^{t} \\cos{\\left(x + y + z \\right)} - \\gamma e^{- t} \\sin^{2}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + \\gamma e^{- t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - \\frac{\\left(\\left(\\cos{\\left(2 x + 2 y + 2 z \\right)} + 3\\right) e^{t} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 12 \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\sin{\\left(x + y + z \\right)}}{4} - \\frac{3 \\left(\\left(\\cos{\\left(2 x + 2 y + 2 z \\right)} + 3\\right) e^{t} \\cos{\\left(x + y + z \\right)} - 2 e^{t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 12 \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- 2 t}}{4} - e^{t} \\cos{\\left(x + y + z \\right)} - \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - e^{- t} \\sin^{3}{\\left(x + y + z \\right)} + e^{- t} \\sin^{2}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - 3 e^{- t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} + \\frac{e^{- t} \\sin{\\left(2 x + 2 y + 2 z \\right)} \\cos{\\left(x + y + z \\right)}}{2} - 3 e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{2 t} - \\frac{\\mu \\left(- e^{- t} \\sin{\\left(x + y + z \\right)} - 11 e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{2 t}}{3}\\right) e^{- 2 t}}{Re}$" + ], + "text/plain": [ + "⎛ ⎛ ↪\n", + "⎜ ⎜ t 2 t 3 t 2 ↪\n", + "⎜Re⋅⎜γ⋅ℯ ⋅sin (x + y + z)⋅cos(x + y + z) + 2⋅γ⋅ℯ ⋅cos (x + y + z) - ℯ ⋅sin (x ↪\n", + "⎝ ⎝ ↪\n", + "────────────────────────────────────────────────────────────────────────────── ↪\n", + " ↪\n", + "\n", + "↪ t ⎞ ⎛ t ↪\n", + "↪ ℯ ⋅sin(2⋅x + 2⋅y + 2⋅z)⋅cos(x + y + z)⎟ Re⋅⎝γ⋅ℯ ↪\n", + "↪ + y + z)⋅cos(x + y + z) + ──────────────────────────────────────⎟ + ──────── ↪\n", + "↪ 2 ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ 3 t 3 ↪\n", + "↪ ⋅sin (x + y + z)⋅cos(x + y + z) + 2⋅γ⋅ℯ ⋅sin(x + y + z)⋅cos (x + y + z) + 6⋅ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ -t t 3 ↪\n", + "↪ γ⋅ℯ ⋅sin(x + y + z)⋅cos(x + y + z) - ℯ ⋅sin (x + y + z)⋅cos(x + y + z) - 2⋅ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ t 3 t ↪\n", + "↪ ℯ ⋅sin(x + y + z)⋅cos (x + y + z) + 2⋅ℯ ⋅sin(x + y + z)⋅cos(x + y + z) - 6⋅ℯ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 2 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ -t 2 -t -t 2 ↪\n", + "↪ ⋅sin (x + y + z) - 30⋅ℯ ⋅sin(x + y + z)⋅cos(x + y + z) + 6⋅ℯ ⋅cos (x + y ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ t ⎛ ⎛ t t ↪\n", + "↪ + z)⎠⋅ℯ ⎜γ⋅⎝(cos(2⋅x + 2⋅y + 2⋅z) + 3)⋅ℯ ⋅cos(x + y + z) - 2⋅ℯ ⋅sin(x ↪\n", + "↪ ───────── + Re⋅⎜──────────────────────────────────────────────────────────── ↪\n", + "↪ ⎝ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ -t ↪\n", + "↪ + y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) - 12⋅sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ ⋅sin(x ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎛ t t ↪\n", + "↪ + y + z) 3⋅γ⋅⎝(cos(2⋅x + 2⋅y + 2⋅z) + 3)⋅ℯ ⋅cos(x + y + z) - 2⋅ℯ ⋅sin(x + ↪\n", + "↪ ───────── + ──────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ -2⋅t ↪\n", + "↪ y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) - 12⋅sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ ↪\n", + "↪ ────────────────────────────────────────────────────────────────────── + γ⋅ℯ ↪\n", + "↪ 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ Re ↪\n", + "\n", + "↪ ↪\n", + "↪ t -t 2 -t ↪\n", + "↪ ⋅cos(x + y + z) - γ⋅ℯ ⋅sin (x + y + z)⋅cos(x + y + z) + γ⋅ℯ ⋅sin(x + y + ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎛ t ↪\n", + "↪ ⎝(cos(2⋅x + 2⋅y + 2⋅z) + 3)⋅ℯ ⋅cos(x + y + z) - 2⋅ ↪\n", + "↪ z)⋅sin(2⋅x + 2⋅y + 2⋅z) - ────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ t ⎞ ↪\n", + "↪ ℯ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) - 12⋅sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ -t ⎛ t t ↪\n", + "↪ ⋅sin(x + y + z) 3⋅⎝(cos(2⋅x + 2⋅y + 2⋅z) + 3)⋅ℯ ⋅cos(x + y + z) - 2⋅ℯ ⋅s ↪\n", + "↪ ───────────────── - ──────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎞ -2⋅t ↪\n", + "↪ in(x + y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) - 12⋅sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ t -t 3 ↪\n", + "↪ - ℯ ⋅cos(x + y + z) - sin(x + y + z)⋅cos(x + y + z) - ℯ ⋅sin (x + y + z) + ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ -t 2 -t ↪\n", + "↪ ℯ ⋅sin (x + y + z)⋅cos(x + y + z) - 3⋅ℯ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅y + 2 ↪\n", + "↪ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ -t ⎞ ↪\n", + "↪ ℯ ⋅sin(2⋅x + 2⋅y + 2⋅z)⋅cos(x + y + z) -t ⎟ 2⋅t ↪\n", + "↪ ⋅z) + ─────────────────────────────────────── - 3⋅ℯ ⋅cos(x + y + z)⎟⋅ℯ - ↪\n", + "↪ 2 ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ ↪\n", + "\n", + "↪ ⎛ -t -t ⎞ 2⋅t⎞ \n", + "↪ μ⋅⎝- ℯ ⋅sin(x + y + z) - 11⋅ℯ ⋅cos(x + y + z)⎠⋅ℯ ⎟ -2⋅t\n", + "↪ ─────────────────────────────────────────────────────⎟⋅ℯ \n", + "↪ 3 ⎠ \n", + "↪ ─────────────────────────────────────────────────────────────\n", + "↪ " + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "res_srhow = solve(Eqrhow_2, srhow)[0]\n", + "res_srhow" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "0dbe7487", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(Re*(gamma*exp(t)*sin(x + y + z)**2*cos(x + y + z) + 2*gamma*exp(t)*cos(x + y + z)**3 - exp(t)*sin(x + y + z)**2*cos(x + y + z) + exp(t)*sin(2*x + 2*y + 2*z)*cos(x + y + z)/2) + Re*(gamma*exp(t)*sin(x + y + z)**3*cos(x + y + z) + 2*gamma*exp(t)*sin(x + y + z)*cos(x + y + z)**3 + 6*gamma*exp(-t)*sin(x + y + z)*cos(x + y + z) - exp(t)*sin(x + y + z)**3*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*cos(x + y + z)**3 + 2*exp(t)*sin(x + y + z)*cos(x + y + z) - 6*exp(-t)*sin(x + y + z)**2 - 30*exp(-t)*sin(x + y + z)*cos(x + y + z) + 6*exp(-t)*cos(x + y + z)**2)*exp(t)/2 + Re*(gamma*((cos(2*x + 2*y + 2*z) + 3)*exp(t)*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 12*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z)/4 + 3*gamma*((cos(2*x + 2*y + 2*z) + 3)*exp(t)*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 12*sin(x + y + z)*cos(x + y + z))*exp(-2*t)/4 + gamma*exp(t)*cos(x + y + z) - gamma*exp(-t)*sin(x + y + z)**2*cos(x + y + z) + gamma*exp(-t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - ((cos(2*x + 2*y + 2*z) + 3)*exp(t)*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 12*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z)/4 - 3*((cos(2*x + 2*y + 2*z) + 3)*exp(t)*cos(x + y + z) - 2*exp(t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 12*sin(x + y + z)*cos(x + y + z))*exp(-2*t)/4 - exp(t)*cos(x + y + z) - sin(x + y + z)*cos(x + y + z) - exp(-t)*sin(x + y + z)**3 + exp(-t)*sin(x + y + z)**2*cos(x + y + z) - 3*exp(-t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) + exp(-t)*sin(2*x + 2*y + 2*z)*cos(x + y + z)/2 - 3*exp(-t)*cos(x + y + z))*exp(2*t) - mu*(-exp(-t)*sin(x + y + z) - 11*exp(-t)*cos(x + y + z))*exp(2*t)/3)*exp(-2*t)/Re\n" + ] + } + ], + "source": [ + "print(res_srhow)" + ] + }, + { + "cell_type": "markdown", + "id": "a2ee2a5e", + "metadata": {}, + "source": [ + "### Solve $s_{\\rho E}$" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "b44b8872", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/latex": [ + "$\\displaystyle - \\frac{3 M^{2} \\gamma^{2} \\kappa \\left(- \\frac{5 \\sin{\\left(x + y + z \\right)} \\cos{\\left(2 \\left(x + y + z\\right) \\right)}}{4} - \\frac{3 \\sin{\\left(x + y + z \\right)}}{4} - \\sin{\\left(2 \\left(x + y + z\\right) \\right)} \\cos{\\left(x + y + z \\right)} + 3 e^{- t} \\sin^{2}{\\left(x + y + z \\right)} - 3 e^{- t} \\cos^{2}{\\left(x + y + z \\right)}\\right) e^{- t}}{Re} + \\frac{3 M^{2} \\gamma^{2} \\kappa e^{- 2 t} \\sin^{2}{\\left(x + y + z \\right)}}{Re} - \\frac{3 M^{2} \\gamma^{2} \\kappa e^{- 2 t} \\cos^{2}{\\left(x + y + z \\right)}}{Re} + \\frac{3 M^{2} \\gamma \\kappa \\left(- \\frac{5 \\sin{\\left(x + y + z \\right)} \\cos{\\left(2 \\left(x + y + z\\right) \\right)}}{4} - \\frac{3 \\sin{\\left(x + y + z \\right)}}{4} - \\sin{\\left(2 \\left(x + y + z\\right) \\right)} \\cos{\\left(x + y + z \\right)} + 3 e^{- t} \\sin^{2}{\\left(x + y + z \\right)} - 3 e^{- t} \\cos^{2}{\\left(x + y + z \\right)}\\right) e^{- t}}{Re} - \\frac{3 M^{2} \\gamma \\kappa e^{- 2 t} \\sin^{2}{\\left(x + y + z \\right)}}{Re} + \\frac{3 M^{2} \\gamma \\kappa e^{- 2 t} \\cos^{2}{\\left(x + y + z \\right)}}{Re} + \\gamma \\left(\\frac{5 e^{- t} \\cos{\\left(x + y + z \\right)}}{8} + \\frac{3 e^{- t} \\cos{\\left(3 x + 3 y + 3 z \\right)}}{8} - \\frac{3 e^{- 2 t} \\sin{\\left(2 x + 2 y + 2 z \\right)}}{2}\\right) \\sin{\\left(2 x + 2 y + 2 z \\right)} - \\frac{\\gamma \\left(\\frac{5 e^{- t} \\cos{\\left(x + y + z \\right)}}{8} + \\frac{3 e^{- t} \\cos{\\left(3 x + 3 y + 3 z \\right)}}{8} - \\frac{3 e^{- 2 t} \\sin{\\left(2 x + 2 y + 2 z \\right)}}{2}\\right) \\cos{\\left(2 x + 2 y + 2 z \\right)}}{2} + \\frac{\\gamma \\left(\\frac{5 e^{- t} \\cos{\\left(x + y + z \\right)}}{8} + \\frac{3 e^{- t} \\cos{\\left(3 x + 3 y + 3 z \\right)}}{8} - \\frac{3 e^{- 2 t} \\sin{\\left(2 x + 2 y + 2 z \\right)}}{2}\\right)}{2} + 3 \\gamma \\left(- \\frac{e^{- t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)}}{2} + \\frac{e^{- t} \\cos{\\left(x + y + z \\right)} \\cos{\\left(2 x + 2 y + 2 z \\right)}}{4} + \\frac{3 e^{- t} \\cos{\\left(x + y + z \\right)}}{4} - 3 e^{- 2 t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\sin{\\left(x + y + z \\right)} + 6 \\gamma \\left(- \\frac{e^{- t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)}}{2} + \\frac{e^{- t} \\cos{\\left(x + y + z \\right)} \\cos{\\left(2 x + 2 y + 2 z \\right)}}{4} + \\frac{3 e^{- t} \\cos{\\left(x + y + z \\right)}}{4} - 3 e^{- 2 t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\cos{\\left(x + y + z \\right)} - 2 \\gamma \\sin^{2}{\\left(x + y + z \\right)} + 2 \\gamma \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + 2 \\gamma \\cos^{2}{\\left(x + y + z \\right)} - \\gamma e^{- t} \\sin^{5}{\\left(x + y + z \\right)} + \\gamma e^{- t} \\sin^{4}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - \\gamma e^{- t} \\sin^{3}{\\left(x + y + z \\right)} \\cos^{2}{\\left(x + y + z \\right)} + 2 \\gamma e^{- t} \\sin^{2}{\\left(x + y + z \\right)} \\cos^{3}{\\left(x + y + z \\right)} + 2 \\gamma e^{- t} \\sin{\\left(x + y + z \\right)} \\cos^{4}{\\left(x + y + z \\right)} - 6 \\gamma e^{- t} \\sin{\\left(x + y + z \\right)} + 3 \\gamma e^{- t} \\cos{\\left(x + y + z \\right)} - 5 \\gamma e^{- 2 t} \\sin^{4}{\\left(x + y + z \\right)} + \\frac{9 \\gamma e^{- 2 t} \\sin^{3}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}}{2} - 6 \\gamma e^{- 2 t} \\sin^{2}{\\left(x + y + z \\right)} \\cos^{2}{\\left(x + y + z \\right)} + 7 \\gamma e^{- 2 t} \\sin{\\left(x + y + z \\right)} \\cos^{3}{\\left(x + y + z \\right)} + 4 \\gamma e^{- 2 t} \\cos^{4}{\\left(x + y + z \\right)} - 6 \\gamma e^{- 3 t} \\sin^{3}{\\left(x + y + z \\right)} + 3 \\gamma e^{- 3 t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 3 \\gamma e^{- 3 t} \\sin{\\left(2 x + 2 y + 2 z \\right)} \\cos{\\left(x + y + z \\right)} + 6 \\gamma e^{- 3 t} \\cos^{3}{\\left(x + y + z \\right)} + \\left(- \\frac{e^{- t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(2 x + 2 y + 2 z \\right)}}{4} - \\frac{3 e^{- t} \\sin{\\left(x + y + z \\right)}}{4} - 3 e^{- 2 t} \\sin^{2}{\\left(x + y + z \\right)} - 6 e^{- 2 t} \\cos^{2}{\\left(x + y + z \\right)}\\right) e^{t} \\sin{\\left(x + y + z \\right)} + e^{t} \\sin{\\left(x + y + z \\right)} + \\frac{\\sin^{4}{\\left(x + y + z \\right)}}{2} + \\sin^{2}{\\left(x + y + z \\right)} \\cos^{2}{\\left(x + y + z \\right)} + \\frac{3 e^{- t} \\sin^{3}{\\left(x + y + z \\right)}}{2} + 3 e^{- t} \\sin{\\left(x + y + z \\right)} \\cos^{2}{\\left(x + y + z \\right)} - \\frac{3 e^{- t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(2 x + 2 y + 2 z \\right)}}{4} - \\frac{9 e^{- t} \\sin{\\left(x + y + z \\right)}}{4} - e^{- 2 t} \\sin^{4}{\\left(x + y + z \\right)} - 3 e^{- 2 t} \\sin^{2}{\\left(x + y + z \\right)} \\cos^{2}{\\left(x + y + z \\right)} - 9 e^{- 2 t} \\sin^{2}{\\left(x + y + z \\right)} + 2 e^{- 2 t} \\sin{\\left(x + y + z \\right)} \\cos^{3}{\\left(x + y + z \\right)} + 2 e^{- 2 t} \\cos^{4}{\\left(x + y + z \\right)} - 18 e^{- 2 t} \\cos^{2}{\\left(x + y + z \\right)} - 3 e^{- 3 t} \\sin^{3}{\\left(x + y + z \\right)} + \\frac{9 e^{- 3 t} \\sin^{2}{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}}{2} - 3 e^{- 3 t} \\sin{\\left(x + y + z \\right)} \\sin{\\left(2 x + 2 y + 2 z \\right)} - 18 e^{- 3 t} \\sin{\\left(x + y + z \\right)} \\cos^{2}{\\left(x + y + z \\right)} + 3 e^{- 3 t} \\sin{\\left(2 x + 2 y + 2 z \\right)} \\cos{\\left(x + y + z \\right)} + 3 e^{- 3 t} \\cos^{3}{\\left(x + y + z \\right)} - \\frac{4 \\mu e^{- 2 t} \\sin^{2}{\\left(x + y + z \\right)}}{Re} + \\frac{8 \\mu e^{- 2 t} \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}}{3 Re} + \\frac{4 \\mu e^{- 2 t} \\cos^{2}{\\left(x + y + z \\right)}}{Re}$" + ], + "text/plain": [ + " ↪\n", + " 2 2 ⎛ 5⋅sin(x + y + z)⋅cos(2⋅(x + y + z)) 3⋅sin(x + y + z) ↪\n", + " 3⋅M ⋅γ ⋅κ⋅⎜- ─────────────────────────────────── - ──────────────── - sin(2⋅ ↪\n", + " ⎝ 4 4 ↪\n", + "- ──────────────────────────────────────────────────────────────────────────── ↪\n", + " ↪\n", + "\n", + "↪ ↪\n", + "↪ -t 2 -t 2 ⎞ ↪\n", + "↪ (x + y + z))⋅cos(x + y + z) + 3⋅ℯ ⋅sin (x + y + z) - 3⋅ℯ ⋅cos (x + y + z)⎟ ↪\n", + "↪ ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ Re ↪\n", + "\n", + "↪ ↪\n", + "↪ -t ↪\n", + "↪ ⋅ℯ 2 2 -2⋅t 2 2 2 -2⋅t 2 3 ↪\n", + "↪ 3⋅M ⋅γ ⋅κ⋅ℯ ⋅sin (x + y + z) 3⋅M ⋅γ ⋅κ⋅ℯ ⋅cos (x + y + z) ↪\n", + "↪ ──── + ─────────────────────────────── - ─────────────────────────────── + ─ ↪\n", + "↪ Re Re ↪\n", + "\n", + "↪ ↪\n", + "↪ 2 ⎛ 5⋅sin(x + y + z)⋅cos(2⋅(x + y + z)) 3⋅sin(x + y + z) ↪\n", + "↪ ⋅M ⋅γ⋅κ⋅⎜- ─────────────────────────────────── - ──────────────── - sin(2⋅(x ↪\n", + "↪ ⎝ 4 4 ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ R ↪\n", + "\n", + "↪ ↪\n", + "↪ -t 2 -t 2 ⎞ ↪\n", + "↪ + y + z))⋅cos(x + y + z) + 3⋅ℯ ⋅sin (x + y + z) - 3⋅ℯ ⋅cos (x + y + z)⎟⋅ℯ ↪\n", + "↪ ⎠ ↪\n", + "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n", + "↪ e ↪\n", + "\n", + "↪ ↪\n", + "↪ -t ↪\n", + "↪ 2 -2⋅t 2 2 -2⋅t 2 ⎛ ↪\n", + "↪ 3⋅M ⋅γ⋅κ⋅ℯ ⋅sin (x + y + z) 3⋅M ⋅γ⋅κ⋅ℯ ⋅cos (x + y + z) ⎜5⋅ ↪\n", + "↪ ── - ────────────────────────────── + ────────────────────────────── + γ⋅⎜── ↪\n", + "↪ Re Re ⎝ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -t -t -2⋅t ↪\n", + "↪ ℯ ⋅cos(x + y + z) 3⋅ℯ ⋅cos(3⋅x + 3⋅y + 3⋅z) 3⋅ℯ ⋅sin(2⋅x + 2⋅y + 2⋅ ↪\n", + "↪ ────────────────── + ────────────────────────── - ────────────────────────── ↪\n", + "↪ 8 8 2 ↪\n", + "\n", + "↪ ⎛ -t -t ↪\n", + "↪ ⎜5⋅ℯ ⋅cos(x + y + z) 3⋅ℯ ⋅cos(3⋅x + 3⋅y + 3 ↪\n", + "↪ ⎞ γ⋅⎜──────────────────── + ─────────────────────── ↪\n", + "↪ z)⎟ ⎝ 8 8 ↪\n", + "↪ ──⎟⋅sin(2⋅x + 2⋅y + 2⋅z) - ───────────────────────────────────────────────── ↪\n", + "↪ ⎠ ↪\n", + "\n", + "↪ -2⋅t ⎞ ⎛ -t ↪\n", + "↪ ⋅z) 3⋅ℯ ⋅sin(2⋅x + 2⋅y + 2⋅z)⎟ ⎜5⋅ℯ ⋅cos(x + ↪\n", + "↪ ─── - ────────────────────────────⎟⋅cos(2⋅x + 2⋅y + 2⋅z) γ⋅⎜────────────── ↪\n", + "↪ 2 ⎠ ⎝ 8 ↪\n", + "↪ ──────────────────────────────────────────────────────── + ───────────────── ↪\n", + "↪ 2 ↪\n", + "\n", + "↪ -t -2⋅t ⎞ ↪\n", + "↪ y + z) 3⋅ℯ ⋅cos(3⋅x + 3⋅y + 3⋅z) 3⋅ℯ ⋅sin(2⋅x + 2⋅y + 2⋅z)⎟ ↪\n", + "↪ ────── + ────────────────────────── - ────────────────────────────⎟ ⎛ ↪\n", + "↪ 8 2 ⎠ ⎜ ↪\n", + "↪ ─────────────────────────────────────────────────────────────────── + 3⋅γ⋅⎜- ↪\n", + "↪ 2 ⎝ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -t -t ↪\n", + "↪ ℯ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) ℯ ⋅cos(x + y + z)⋅cos(2⋅x + 2⋅y ↪\n", + "↪ ─────────────────────────────────────── + ───────────────────────────────── ↪\n", + "↪ 2 4 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -t ⎞ ↪\n", + "↪ + 2⋅z) 3⋅ℯ ⋅cos(x + y + z) -2⋅t ⎟ -t ↪\n", + "↪ ────── + ──────────────────── - 3⋅ℯ ⋅sin(x + y + z)⋅cos(x + y + z)⎟⋅ℯ ⋅s ↪\n", + "↪ 4 ⎠ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ -t -t ↪\n", + "↪ ⎜ ℯ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) ℯ ⋅cos(x + ↪\n", + "↪ in(x + y + z) + 6⋅γ⋅⎜- ─────────────────────────────────────── + ─────────── ↪\n", + "↪ ⎝ 2 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -t ↪\n", + "↪ y + z)⋅cos(2⋅x + 2⋅y + 2⋅z) 3⋅ℯ ⋅cos(x + y + z) -2⋅t ↪\n", + "↪ ──────────────────────────── + ──────────────────── - 3⋅ℯ ⋅sin(x + y + z) ↪\n", + "↪ 4 4 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎞ ↪\n", + "↪ ⎟ -t 2 ↪\n", + "↪ ⋅cos(x + y + z)⎟⋅ℯ ⋅cos(x + y + z) - 2⋅γ⋅sin (x + y + z) + 2⋅γ⋅sin(x + y + ↪\n", + "↪ ⎠ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 -t 5 -t 4 ↪\n", + "↪ z)⋅cos(x + y + z) + 2⋅γ⋅cos (x + y + z) - γ⋅ℯ ⋅sin (x + y + z) + γ⋅ℯ ⋅sin ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -t 3 2 -t ↪\n", + "↪ (x + y + z)⋅cos(x + y + z) - γ⋅ℯ ⋅sin (x + y + z)⋅cos (x + y + z) + 2⋅γ⋅ℯ ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 3 -t 4 ↪\n", + "↪ ⋅sin (x + y + z)⋅cos (x + y + z) + 2⋅γ⋅ℯ ⋅sin(x + y + z)⋅cos (x + y + z) - ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -t -t -2⋅t 4 ↪\n", + "↪ 6⋅γ⋅ℯ ⋅sin(x + y + z) + 3⋅γ⋅ℯ ⋅cos(x + y + z) - 5⋅γ⋅ℯ ⋅sin (x + y + z) ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -2⋅t 3 ↪\n", + "↪ 9⋅γ⋅ℯ ⋅sin (x + y + z)⋅cos(x + y + z) -2⋅t 2 2 ↪\n", + "↪ + ──────────────────────────────────────── - 6⋅γ⋅ℯ ⋅sin (x + y + z)⋅cos ( ↪\n", + "↪ 2 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -2⋅t 3 -2⋅t 4 ↪\n", + "↪ x + y + z) + 7⋅γ⋅ℯ ⋅sin(x + y + z)⋅cos (x + y + z) + 4⋅γ⋅ℯ ⋅cos (x + y ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -3⋅t 3 -3⋅t ↪\n", + "↪ + z) - 6⋅γ⋅ℯ ⋅sin (x + y + z) + 3⋅γ⋅ℯ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅y + ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -3⋅t -3⋅t 3 ↪\n", + "↪ 2⋅z) - 3⋅γ⋅ℯ ⋅sin(2⋅x + 2⋅y + 2⋅z)⋅cos(x + y + z) + 6⋅γ⋅ℯ ⋅cos (x + y ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎛ -t -t ↪\n", + "↪ ⎜ ℯ ⋅sin(x + y + z)⋅cos(2⋅x + 2⋅y + 2⋅z) 3⋅ℯ ⋅sin(x + y + z) ↪\n", + "↪ + z) + ⎜- ─────────────────────────────────────── - ──────────────────── - ↪\n", + "↪ ⎝ 4 4 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ⎞ ↪\n", + "↪ -2⋅t 2 -2⋅t 2 ⎟ t t ↪\n", + "↪ 3⋅ℯ ⋅sin (x + y + z) - 6⋅ℯ ⋅cos (x + y + z)⎟⋅ℯ ⋅sin(x + y + z) + ℯ ⋅si ↪\n", + "↪ ⎠ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 4 -t ↪\n", + "↪ sin (x + y + z) 2 2 3⋅ℯ ⋅sin ↪\n", + "↪ n(x + y + z) + ─────────────── + sin (x + y + z)⋅cos (x + y + z) + ───────── ↪\n", + "↪ 2 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 3 -t ↪\n", + "↪ (x + y + z) -t 2 3⋅ℯ ⋅sin(x + y + z)⋅c ↪\n", + "↪ ──────────── + 3⋅ℯ ⋅sin(x + y + z)⋅cos (x + y + z) - ────────────────────── ↪\n", + "↪ 2 4 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -t ↪\n", + "↪ os(2⋅x + 2⋅y + 2⋅z) 9⋅ℯ ⋅sin(x + y + z) -2⋅t 4 -2⋅t ↪\n", + "↪ ─────────────────── - ──────────────────── - ℯ ⋅sin (x + y + z) - 3⋅ℯ ↪\n", + "↪ 4 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 2 2 -2⋅t 2 -2⋅t ↪\n", + "↪ ⋅sin (x + y + z)⋅cos (x + y + z) - 9⋅ℯ ⋅sin (x + y + z) + 2⋅ℯ ⋅sin(x + ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ 3 -2⋅t 4 -2⋅t 2 ↪\n", + "↪ y + z)⋅cos (x + y + z) + 2⋅ℯ ⋅cos (x + y + z) - 18⋅ℯ ⋅cos (x + y + z) ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -3⋅t 2 ↪\n", + "↪ -3⋅t 3 9⋅ℯ ⋅sin (x + y + z)⋅cos(x + y + z) -3⋅ ↪\n", + "↪ - 3⋅ℯ ⋅sin (x + y + z) + ────────────────────────────────────── - 3⋅ℯ ↪\n", + "↪ 2 ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ t -3⋅t 2 ↪\n", + "↪ ⋅sin(x + y + z)⋅sin(2⋅x + 2⋅y + 2⋅z) - 18⋅ℯ ⋅sin(x + y + z)⋅cos (x + y + ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -3⋅t -3⋅t 3 ↪\n", + "↪ z) + 3⋅ℯ ⋅sin(2⋅x + 2⋅y + 2⋅z)⋅cos(x + y + z) + 3⋅ℯ ⋅cos (x + y + z) ↪\n", + "↪ ↪\n", + "\n", + "↪ ↪\n", + "↪ ↪\n", + "↪ -2⋅t 2 -2⋅t ↪\n", + "↪ 4⋅μ⋅ℯ ⋅sin (x + y + z) 8⋅μ⋅ℯ ⋅sin(x + y + z)⋅cos(x + y + z) 4⋅μ⋅ ↪\n", + "↪ - ───────────────────────── + ─────────────────────────────────────── + ──── ↪\n", + "↪ Re 3⋅Re ↪\n", + "\n", + "↪ \n", + "↪ \n", + "↪ -2⋅t 2 \n", + "↪ ℯ ⋅cos (x + y + z)\n", + "↪ ─────────────────────\n", + "↪ Re " + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "res_srhoE = solve(EqrhoE_2, srhoE)[0]\n", + "res_srhoE" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "2ed84a48", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-3*M**2*gamma**2*kappa*(-5*sin(x + y + z)*cos(2*(x + y + z))/4 - 3*sin(x + y + z)/4 - sin(2*(x + y + z))*cos(x + y + z) + 3*exp(-t)*sin(x + y + z)**2 - 3*exp(-t)*cos(x + y + z)**2)*exp(-t)/Re + 3*M**2*gamma**2*kappa*exp(-2*t)*sin(x + y + z)**2/Re - 3*M**2*gamma**2*kappa*exp(-2*t)*cos(x + y + z)**2/Re + 3*M**2*gamma*kappa*(-5*sin(x + y + z)*cos(2*(x + y + z))/4 - 3*sin(x + y + z)/4 - sin(2*(x + y + z))*cos(x + y + z) + 3*exp(-t)*sin(x + y + z)**2 - 3*exp(-t)*cos(x + y + z)**2)*exp(-t)/Re - 3*M**2*gamma*kappa*exp(-2*t)*sin(x + y + z)**2/Re + 3*M**2*gamma*kappa*exp(-2*t)*cos(x + y + z)**2/Re + gamma*(5*exp(-t)*cos(x + y + z)/8 + 3*exp(-t)*cos(3*x + 3*y + 3*z)/8 - 3*exp(-2*t)*sin(2*x + 2*y + 2*z)/2)*sin(2*x + 2*y + 2*z) - gamma*(5*exp(-t)*cos(x + y + z)/8 + 3*exp(-t)*cos(3*x + 3*y + 3*z)/8 - 3*exp(-2*t)*sin(2*x + 2*y + 2*z)/2)*cos(2*x + 2*y + 2*z)/2 + gamma*(5*exp(-t)*cos(x + y + z)/8 + 3*exp(-t)*cos(3*x + 3*y + 3*z)/8 - 3*exp(-2*t)*sin(2*x + 2*y + 2*z)/2)/2 + 3*gamma*(-exp(-t)*sin(x + y + z)*sin(2*x + 2*y + 2*z)/2 + exp(-t)*cos(x + y + z)*cos(2*x + 2*y + 2*z)/4 + 3*exp(-t)*cos(x + y + z)/4 - 3*exp(-2*t)*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z) + 6*gamma*(-exp(-t)*sin(x + y + z)*sin(2*x + 2*y + 2*z)/2 + exp(-t)*cos(x + y + z)*cos(2*x + 2*y + 2*z)/4 + 3*exp(-t)*cos(x + y + z)/4 - 3*exp(-2*t)*sin(x + y + z)*cos(x + y + z))*exp(-t)*cos(x + y + z) - 2*gamma*sin(x + y + z)**2 + 2*gamma*sin(x + y + z)*cos(x + y + z) + 2*gamma*cos(x + y + z)**2 - gamma*exp(-t)*sin(x + y + z)**5 + gamma*exp(-t)*sin(x + y + z)**4*cos(x + y + z) - gamma*exp(-t)*sin(x + y + z)**3*cos(x + y + z)**2 + 2*gamma*exp(-t)*sin(x + y + z)**2*cos(x + y + z)**3 + 2*gamma*exp(-t)*sin(x + y + z)*cos(x + y + z)**4 - 6*gamma*exp(-t)*sin(x + y + z) + 3*gamma*exp(-t)*cos(x + y + z) - 5*gamma*exp(-2*t)*sin(x + y + z)**4 + 9*gamma*exp(-2*t)*sin(x + y + z)**3*cos(x + y + z)/2 - 6*gamma*exp(-2*t)*sin(x + y + z)**2*cos(x + y + z)**2 + 7*gamma*exp(-2*t)*sin(x + y + z)*cos(x + y + z)**3 + 4*gamma*exp(-2*t)*cos(x + y + z)**4 - 6*gamma*exp(-3*t)*sin(x + y + z)**3 + 3*gamma*exp(-3*t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 3*gamma*exp(-3*t)*sin(2*x + 2*y + 2*z)*cos(x + y + z) + 6*gamma*exp(-3*t)*cos(x + y + z)**3 + (-exp(-t)*sin(x + y + z)*cos(2*x + 2*y + 2*z)/4 - 3*exp(-t)*sin(x + y + z)/4 - 3*exp(-2*t)*sin(x + y + z)**2 - 6*exp(-2*t)*cos(x + y + z)**2)*exp(t)*sin(x + y + z) + exp(t)*sin(x + y + z) + sin(x + y + z)**4/2 + sin(x + y + z)**2*cos(x + y + z)**2 + 3*exp(-t)*sin(x + y + z)**3/2 + 3*exp(-t)*sin(x + y + z)*cos(x + y + z)**2 - 3*exp(-t)*sin(x + y + z)*cos(2*x + 2*y + 2*z)/4 - 9*exp(-t)*sin(x + y + z)/4 - exp(-2*t)*sin(x + y + z)**4 - 3*exp(-2*t)*sin(x + y + z)**2*cos(x + y + z)**2 - 9*exp(-2*t)*sin(x + y + z)**2 + 2*exp(-2*t)*sin(x + y + z)*cos(x + y + z)**3 + 2*exp(-2*t)*cos(x + y + z)**4 - 18*exp(-2*t)*cos(x + y + z)**2 - 3*exp(-3*t)*sin(x + y + z)**3 + 9*exp(-3*t)*sin(x + y + z)**2*cos(x + y + z)/2 - 3*exp(-3*t)*sin(x + y + z)*sin(2*x + 2*y + 2*z) - 18*exp(-3*t)*sin(x + y + z)*cos(x + y + z)**2 + 3*exp(-3*t)*sin(2*x + 2*y + 2*z)*cos(x + y + z) + 3*exp(-3*t)*cos(x + y + z)**3 - 4*mu*exp(-2*t)*sin(x + y + z)**2/Re + 8*mu*exp(-2*t)*sin(x + y + z)*cos(x + y + z)/(3*Re) + 4*mu*exp(-2*t)*cos(x + y + z)**2/Re\n" + ] + } + ], + "source": [ + "print(res_srhoE)" + ] + }, + { + "cell_type": "markdown", + "id": "c4058e93", + "metadata": {}, + "source": [ + "## Lamb vector computation" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "80743b00", + "metadata": {}, + "outputs": [], + "source": [ + "def curl(f):\n", + " return Array([diff(f[2],y) - diff(f[1],z),\n", + " diff(f[0],z) - diff(f[2],x),\n", + " diff(f[1],x) - diff(f[0],y)])" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "87253eed", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\left(- \\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)}\\right) v{\\left(x,y,z,t \\right)} - \\left(\\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} - \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)}\\right) w{\\left(x,y,z,t \\right)}\\\\- \\left(- \\frac{\\partial}{\\partial y} u{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial x} v{\\left(x,y,z,t \\right)}\\right) u{\\left(x,y,z,t \\right)} + \\left(- \\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)}\\right) w{\\left(x,y,z,t \\right)}\\\\\\left(\\frac{\\partial}{\\partial z} u{\\left(x,y,z,t \\right)} - \\frac{\\partial}{\\partial x} w{\\left(x,y,z,t \\right)}\\right) u{\\left(x,y,z,t \\right)} - \\left(- \\frac{\\partial}{\\partial z} v{\\left(x,y,z,t \\right)} + \\frac{\\partial}{\\partial y} w{\\left(x,y,z,t \\right)}\\right) v{\\left(x,y,z,t \\right)}\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡ ⎛ ∂ ∂ ⎞ ⎛∂ ↪\n", + "⎢ ⎜- ──(u(x, y, z, t)) + ──(v(x, y, z, t))⎟⋅v(x, y, z, t) - ⎜──(u(x, y, z, t) ↪\n", + "⎢ ⎝ ∂y ∂x ⎠ ⎝∂z ↪\n", + "⎢ ↪\n", + "⎢ ⎛ ∂ ∂ ⎞ ⎛ ∂ ↪\n", + "⎢- ⎜- ──(u(x, y, z, t)) + ──(v(x, y, z, t))⎟⋅u(x, y, z, t) + ⎜- ──(v(x, y, z, ↪\n", + "⎢ ⎝ ∂y ∂x ⎠ ⎝ ∂z ↪\n", + "⎢ ↪\n", + "⎢ ⎛∂ ∂ ⎞ ⎛ ∂ ↪\n", + "⎢ ⎜──(u(x, y, z, t)) - ──(w(x, y, z, t))⎟⋅u(x, y, z, t) - ⎜- ──(v(x, y, z, t) ↪\n", + "⎣ ⎝∂z ∂x ⎠ ⎝ ∂z ↪\n", + "\n", + "↪ ∂ ⎞ ⎤\n", + "↪ ) - ──(w(x, y, z, t))⎟⋅w(x, y, z, t) ⎥\n", + "↪ ∂x ⎠ ⎥\n", + "↪ ⎥\n", + "↪ ∂ ⎞ ⎥\n", + "↪ t)) + ──(w(x, y, z, t))⎟⋅w(x, y, z, t)⎥\n", + "↪ ∂y ⎠ ⎥\n", + "↪ ⎥\n", + "↪ ∂ ⎞ ⎥\n", + "↪ ) + ──(w(x, y, z, t))⎟⋅v(x, y, z, t) ⎥\n", + "↪ ∂y ⎠ ⎦" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "vorticity = curl(vel)\n", + "LambVector = Matrix(vel).cross(Matrix(vorticity))\n", + "LambVector\n" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "05613c50", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\left(\\frac{\\partial}{\\partial x} e^{- t} \\sin{\\left(x + y + z \\right)} - \\frac{\\partial}{\\partial y} e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\sin{\\left(x + y + z \\right)} - \\left(- \\frac{\\partial}{\\partial x} e^{- t} \\cos{\\left(x + y + z \\right)} + \\frac{\\partial}{\\partial z} e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\cos{\\left(x + y + z \\right)}\\\\- \\left(\\frac{\\partial}{\\partial x} e^{- t} \\sin{\\left(x + y + z \\right)} - \\frac{\\partial}{\\partial y} e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\cos{\\left(x + y + z \\right)} + \\left(- \\frac{\\partial}{\\partial z} e^{- t} \\sin{\\left(x + y + z \\right)} + \\frac{\\partial}{\\partial y} e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\cos{\\left(x + y + z \\right)}\\\\- \\left(- \\frac{\\partial}{\\partial z} e^{- t} \\sin{\\left(x + y + z \\right)} + \\frac{\\partial}{\\partial y} e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\sin{\\left(x + y + z \\right)} + \\left(- \\frac{\\partial}{\\partial x} e^{- t} \\cos{\\left(x + y + z \\right)} + \\frac{\\partial}{\\partial z} e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\cos{\\left(x + y + z \\right)}\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡ ⎛∂ ⎛ -t ⎞ ∂ ⎛ -t ⎞⎞ -t ⎛ ∂ ↪\n", + "⎢ ⎜──⎝ℯ ⋅sin(x + y + z)⎠ - ──⎝ℯ ⋅cos(x + y + z)⎠⎟⋅ℯ ⋅sin(x + y + z) - ⎜- ─ ↪\n", + "⎢ ⎝∂x ∂y ⎠ ⎝ ∂ ↪\n", + "⎢ ↪\n", + "⎢ ⎛∂ ⎛ -t ⎞ ∂ ⎛ -t ⎞⎞ -t ⎛ ↪\n", + "⎢ - ⎜──⎝ℯ ⋅sin(x + y + z)⎠ - ──⎝ℯ ⋅cos(x + y + z)⎠⎟⋅ℯ ⋅cos(x + y + z) + ⎜- ↪\n", + "⎢ ⎝∂x ∂y ⎠ ⎝ ↪\n", + "⎢ ↪\n", + "⎢ ⎛ ∂ ⎛ -t ⎞ ∂ ⎛ -t ⎞⎞ -t ⎛ ↪\n", + "⎢- ⎜- ──⎝ℯ ⋅sin(x + y + z)⎠ + ──⎝ℯ ⋅cos(x + y + z)⎠⎟⋅ℯ ⋅sin(x + y + z) + ⎜- ↪\n", + "⎣ ⎝ ∂z ∂y ⎠ ⎝ ↪\n", + "\n", + "↪ ⎛ -t ⎞ ∂ ⎛ -t ⎞⎞ -t ⎤\n", + "↪ ─⎝ℯ ⋅cos(x + y + z)⎠ + ──⎝ℯ ⋅cos(x + y + z)⎠⎟⋅ℯ ⋅cos(x + y + z) ⎥\n", + "↪ x ∂z ⎠ ⎥\n", + "↪ ⎥\n", + "↪ ∂ ⎛ -t ⎞ ∂ ⎛ -t ⎞⎞ -t ⎥\n", + "↪ ──⎝ℯ ⋅sin(x + y + z)⎠ + ──⎝ℯ ⋅cos(x + y + z)⎠⎟⋅ℯ ⋅cos(x + y + z) ⎥\n", + "↪ ∂z ∂y ⎠ ⎥\n", + "↪ ⎥\n", + "↪ ∂ ⎛ -t ⎞ ∂ ⎛ -t ⎞⎞ -t ⎥\n", + "↪ ──⎝ℯ ⋅cos(x + y + z)⎠ + ──⎝ℯ ⋅cos(x + y + z)⎠⎟⋅ℯ ⋅cos(x + y + z)⎥\n", + "↪ ∂x ∂z ⎠ ⎦" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "LambVector_1 = LambVector.subs([(rho,rho_ms), (u,u_ms), (v,v_ms), (w,w_ms), (E,E_ms)])\n", + "LambVector_1" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "221bd905", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\left(e^{- t} \\sin{\\left(x + y + z \\right)} + e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\sin{\\left(x + y + z \\right)}\\\\\\left(- 2 e^{- t} \\sin{\\left(x + y + z \\right)} - 2 e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\cos{\\left(x + y + z \\right)}\\\\\\left(e^{- t} \\sin{\\left(x + y + z \\right)} + e^{- t} \\cos{\\left(x + y + z \\right)}\\right) e^{- t} \\sin{\\left(x + y + z \\right)}\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡ ⎛ -t -t ⎞ -t ⎤\n", + "⎢ ⎝ℯ ⋅sin(x + y + z) + ℯ ⋅cos(x + y + z)⎠⋅ℯ ⋅sin(x + y + z) ⎥\n", + "⎢ ⎥\n", + "⎢⎛ -t -t ⎞ -t ⎥\n", + "⎢⎝- 2⋅ℯ ⋅sin(x + y + z) - 2⋅ℯ ⋅cos(x + y + z)⎠⋅ℯ ⋅cos(x + y + z)⎥\n", + "⎢ ⎥\n", + "⎢ ⎛ -t -t ⎞ -t ⎥\n", + "⎣ ⎝ℯ ⋅sin(x + y + z) + ℯ ⋅cos(x + y + z)⎠⋅ℯ ⋅sin(x + y + z) ⎦" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "LambVector_1.simplify()\n", + "LambVector_1" + ] + }, + { + "cell_type": "markdown", + "id": "331ac378", + "metadata": {}, + "source": [ + "### Integrate in time" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "b61b3784", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\frac{\\left(- \\sin^{2}{\\left(x + y + z \\right)} - \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- 2 t}}{2} + \\frac{\\sin^{2}{\\left(x + y + z \\right)}}{2} + \\frac{\\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}}{2}\\\\\\left(\\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} + \\cos^{2}{\\left(x + y + z \\right)}\\right) e^{- 2 t} - \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)} - \\cos^{2}{\\left(x + y + z \\right)}\\\\\\frac{\\left(- \\sin^{2}{\\left(x + y + z \\right)} - \\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}\\right) e^{- 2 t}}{2} + \\frac{\\sin^{2}{\\left(x + y + z \\right)}}{2} + \\frac{\\sin{\\left(x + y + z \\right)} \\cos{\\left(x + y + z \\right)}}{2}\\end{matrix}\\right]$" + ], + "text/plain": [ + "⎡⎛ 2 ⎞ -2⋅t 2 ↪\n", + "⎢⎝- sin (x + y + z) - sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ sin (x + y + z) ↪\n", + "⎢───────────────────────────────────────────────────────── + ─────────────── + ↪\n", + "⎢ 2 2 ↪\n", + "⎢ ↪\n", + "⎢ ⎛ 2 ⎞ -2⋅t ↪\n", + "⎢ ⎝sin(x + y + z)⋅cos(x + y + z) + cos (x + y + z)⎠⋅ℯ - sin(x + y + z)⋅cos ↪\n", + "⎢ ↪\n", + "⎢⎛ 2 ⎞ -2⋅t 2 ↪\n", + "⎢⎝- sin (x + y + z) - sin(x + y + z)⋅cos(x + y + z)⎠⋅ℯ sin (x + y + z) ↪\n", + "⎢───────────────────────────────────────────────────────── + ─────────────── + ↪\n", + "⎣ 2 2 ↪\n", + "\n", + "↪ ⎤\n", + "↪ sin(x + y + z)⋅cos(x + y + z)⎥\n", + "↪ ─────────────────────────────⎥\n", + "↪ 2 ⎥\n", + "↪ ⎥\n", + "↪ 2 ⎥\n", + "↪ (x + y + z) - cos (x + y + z) ⎥\n", + "↪ ⎥\n", + "↪ ⎥\n", + "↪ sin(x + y + z)⋅cos(x + y + z)⎥\n", + "↪ ─────────────────────────────⎥\n", + "↪ 2 ⎦" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t0 = S(0)\n", + "tf = S(4)\n", + "res_lamb = integrate(LambVector_1, (t, t0, t))\n", + "res_lamb" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "3e829231", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(-sin(x + y + z)**2 - sin(x + y + z)*cos(x + y + z))*exp(-2*t)/2 + sin(x + y + z)**2/2 + sin(x + y + z)*cos(x + y + z)/2\n" + ] + } + ], + "source": [ + "print(res_lamb[2])" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "base", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Solver/test/NavierStokes/LambVector/SETUP/ProblemFile.f90 b/Solver/test/NavierStokes/LambVector/SETUP/ProblemFile.f90 new file mode 100644 index 000000000..da8da5d48 --- /dev/null +++ b/Solver/test/NavierStokes/LambVector/SETUP/ProblemFile.f90 @@ -0,0 +1,811 @@ +module MMS + use SMConstants + use SolutionFile + implicit none + public evalManufacturedSolution, compareLambVector + + contains + pure subroutine evalManufacturedSolution(x, y, z, t, res) + use SMConstants + implicit none + real(rp), intent(in) :: x, y, z, t + real(rp), intent(out) :: res(5) + + real(rp) :: rho_ms, u_ms, v_ms, w_ms, e_ms + + rho_ms = 3.0_rp + sin(x+y+z)*exp(t) + u_ms = cos(x+y+z)*exp(-t) + v_ms = sin(x+y+z)*exp(-t) + w_ms = cos(x+y+z)*exp(-t) + e_ms = rho_ms * (u_ms**2+v_ms**2+w_ms**2) / 2.0_rp + 1.0_rp + + res(1) = rho_ms + res(2) = rho_ms * u_ms + res(3) = rho_ms * v_ms + res(4) = rho_ms * w_ms + res(5) = rho_ms * e_ms + end subroutine + + pure subroutine evalLambVector(x, y, z, t, res) + use SMConstants + implicit none + real(rp), intent(in) :: x, y, z, t + real(rp), intent(out) :: res(NDIM) + + res(IX) = (exp(-t)*sin(x+y+z)+exp(-t)*cos(x+y+z))*exp(-t)*sin(x+y+z) + res(IY) = (-2.0_rp*exp(-t)*sin(x+y+z)-2.0_rp*exp(-t)*cos(x+y+z))*exp(-t)*cos(x+y+z) + res(IZ) = (exp(-t)*sin(x+y+z)+exp(-t)*cos(x+y+z))*exp(-t)*sin(x+y+z) + end subroutine + + pure subroutine evalLambVectorIntegral(x, y, z, t, res) + use SMConstants + implicit none + real(rp), intent(in) :: x, y, z, t + real(rp), intent(out) :: res(NDIM) + + res(IX) = (-sin(x + y + z)**2 - sin(x + y + z)*cos(x + y + z))*exp(-2.0_rp*t)/2.0_rp + sin(x + y + z)**2/2.0_rp + sin(x + y + z)*cos(x + y + z)/2.0_rp + res(IY) = (sin(x + y + z)*cos(x + y + z) + cos(x + y + z)**2)*exp(-2.0_rp*t) - sin(x + y + z)*cos(x + y + z) - cos(x + y + z)**2 + res(IZ) = (-sin(x + y + z)**2 - sin(x + y + z)*cos(x + y + z))*exp(-2.0_rp*t)/2.0_rp + sin(x + y + z)**2/2.0_rp + sin(x + y + z)*cos(x + y + z)/2.0_rp + end subroutine + + subroutine compareLambVector(Nelem, elements, success) + use SMConstants + use ElementClass + implicit none + integer, intent(in) :: Nelem + type(Element) :: elements(Nelem) + logical, intent(inout) :: success + + ! Local variables + INTEGER :: eID + INTEGER :: i, j, k, Nx, Ny, Nz + integer :: fid, pos + REAL(KIND=RP) :: t, u(NDIM), x(NDIM) + real(rp), allocatable :: u_h(:,:,:,:) + real(rp) :: Qerror + + t = 0.1_rp + + open(newunit=fid, file="RESULTS/TGV_0000000020.Lamb.hsol", status="old", action="read", & + form="unformatted" , access="stream") + + do eID = 1, SIZE( elements) + Nx = elements(eID) % Nxyz(1) + Ny = elements(eID) % Nxyz(2) + Nz = elements(eID) % Nxyz(3) + + ! Compare the values obtained (saved in file) with the analytical ones + allocate(u_h(1:NDIM,0:Nx,0:Ny,0:Nz)) + pos = POS_INIT_DATA + ( elements(eID) % globID)*5_AddrInt*SIZEOF_INT + 1_AddrInt*NDIM* elements(eID) % offsetIO*SIZEOF_RP + read(fid, pos=pos) u_h + + DO k = 0, Nz + DO j = 0, Ny + DO i = 0, Nx + x = elements(eID) % geom % x(:,i,j,k) + call evalLambVector(x(1),x(2),x(3),t, u) + + Qerror = maxval(abs(u_h(:,i,j,k) - u)) + if (Qerror > 0.01_rp) then + print *, "eID: ", eID + write(STD_OUT,'(3(A,I0))') "i: ", i, ", j: ", j, ", k: ", k + print *, "Lamb vector analytical: ", u + print *, "Lamb vector read: ", u_h(:,i,j,k) + success = .false. + return + end if + end do + end do + end do + deallocate(u_h) + end do + + end subroutine compareLambVector + + subroutine compareLambVectorStats(Nelem, elements, t, success) + use SMConstants + use ElementClass + implicit none + integer, intent(in) :: Nelem + type(Element) :: elements(Nelem) + real(rp), intent(in) :: t + logical, intent(out) :: success + + ! Local variables + INTEGER :: eID + INTEGER :: i, j, k, Nx, Ny, Nz + integer :: fid, pos + REAL(KIND=RP) :: u(NDIM), x(NDIM) + real(rp), allocatable :: u_h(:,:,:,:) + real(rp) :: Qerror + + open(newunit=fid, file="RESULTS/TGV.Lamb.stats.hsol", status="old", action="read", & + form="unformatted" , access="stream") + + do eID = 1, SIZE(elements) + Nx = elements(eID) % Nxyz(1) + Ny = elements(eID) % Nxyz(2) + Nz = elements(eID) % Nxyz(3) + + ! Compare the values obtained (saved in file) with the analytical ones + allocate(u_h(1:NDIM,0:Nx,0:Ny,0:Nz)) + pos = POS_INIT_DATA + ( elements(eID) % globID)*5_AddrInt*SIZEOF_INT + 1_AddrInt*NDIM* elements(eID) % offsetIO*SIZEOF_RP + read(fid, pos=pos) u_h + + DO k = 0, Nz + DO j = 0, Ny + DO i = 0, Nx + x = elements(eID) % geom % x(:,i,j,k) + call evalLambVectorIntegral(x(1),x(2),x(3),t, u) + u = u / t + + Qerror = maxval(abs(u_h(:,i,j,k) - u)) + if (Qerror > 0.05_rp) then + print *, "eID: ", eID + write(STD_OUT,'(3(A,I0))') "i: ", i, ", j: ", j, ", k: ", k + print *, "Lamb vector integral analytical: ", u + print *, "Lamb vector integral read: ", u_h(:,i,j,k) + print *, "error: ", Qerror + success = .false. + return + end if + end do + end do + end do + deallocate(u_h) + end do + + end subroutine compareLambVectorStats +end module MMS +! +!//////////////////////////////////////////////////////////////////////// +! +! The Problem File contains user defined procedures +! that are used to "personalize" i.e. define a specific +! problem to be solved. These procedures include initial conditions, +! exact solutions (e.g. for tests), etc. and allow modifications +! without having to modify the main code. +! +! The procedures, *even if empty* that must be defined are +! +! UserDefinedSetUp +! UserDefinedInitialCondition(mesh) +! UserDefinedPeriodicOperation(mesh) +! UserDefinedFinalize(mesh) +! UserDefinedTermination +! +!//////////////////////////////////////////////////////////////////////// +! + SUBROUTINE UserDefinedStartup +! +! -------------------------------- +! Called before any other routines +! -------------------------------- +! + IMPLICIT NONE + END SUBROUTINE UserDefinedStartup +! +!//////////////////////////////////////////////////////////////////////// +! + SUBROUTINE UserDefinedFinalSetup(mesh & +#if defined(NAVIERSTOKES) + , thermodynamics_ & + , dimensionless_ & + , refValues_ & +#endif +#if defined(CAHNHILLIARD) + , multiphase_ & +#endif + ) +! +! ---------------------------------------------------------------------- +! Called after the mesh is read in to allow mesh related initializations +! or memory allocations. +! ---------------------------------------------------------------------- +! + USE HexMeshClass + use PhysicsStorage + use FluidData + IMPLICIT NONE + class(HexMesh) :: mesh +#if defined(NAVIERSTOKES) + type(Thermodynamics_t), intent(in) :: thermodynamics_ + type(Dimensionless_t), intent(in) :: dimensionless_ + type(RefValues_t), intent(in) :: refValues_ +#endif +#if defined(CAHNHILLIARD) + type(Multiphase_t), intent(in) :: multiphase_ +#endif + END SUBROUTINE UserDefinedFinalSetup +! +!//////////////////////////////////////////////////////////////////////// +! + subroutine UserDefinedInitialCondition(mesh & +#if defined(NAVIERSTOKES) + , thermodynamics_ & + , dimensionless_ & + , refValues_ & +#endif +#if defined(CAHNHILLIARD) + , multiphase_ & +#endif + ) +! +! ------------------------------------------------ +! called to set the initial condition for the flow +! - by default it sets an uniform initial +! condition. +! ------------------------------------------------ +! + use smconstants + use physicsstorage + use hexmeshclass + use fluiddata + use MMS + implicit none + class(hexmesh) :: mesh +#if defined(NAVIERSTOKES) + type(Thermodynamics_t), intent(in) :: thermodynamics_ + type(Dimensionless_t), intent(in) :: dimensionless_ + type(RefValues_t), intent(in) :: refValues_ +#endif +#if defined(CAHNHILLIARD) + type(Multiphase_t), intent(in) :: multiphase_ +#endif +! +! --------------- +! Local variables +! --------------- +! + REAL(KIND=RP) :: x(3) + INTEGER :: i, j, k, eID + REAL(KIND=RP) :: rho , u , v , w , p + REAL(KIND=RP) :: L, u_0, rho_0, p_0 + integer :: Nx, Ny, Nz +#if defined(NAVIERSTOKES) + + L = 1.0_RP + u_0 = 1.0_RP + rho_0 = 1.0_RP + p_0 = 100.0_RP + + associate( gamma => thermodynamics_ % gamma ) + DO eID = 1, SIZE(mesh % elements) + Nx = mesh % elements(eID) % Nxyz(1) + Ny = mesh % elements(eID) % Nxyz(2) + Nz = mesh % elements(eID) % Nxyz(3) + + DO k = 0, Nz + DO j = 0, Ny + DO i = 0, Nx + x = mesh % elements(eID) % geom % x(:,i,j,k) + call evalManufacturedSolution(x(1), x(2), x(3), 0.0_rp, mesh % elements(eID) % storage % Q(:,i,j,k)) + END DO + END DO + END DO + + END DO + end associate +#endif + + end subroutine UserDefinedInitialCondition +#if defined(NAVIERSTOKES) + subroutine UserDefinedState1(x, t, nHat, Q, thermodynamics_, dimensionless_, refValues_) +! +! ------------------------------------------------- +! Used to define an user defined boundary condition +! ------------------------------------------------- +! + use SMConstants + use PhysicsStorage + use FluidData + implicit none + real(kind=RP), intent(in) :: x(NDIM) + real(kind=RP), intent(in) :: t + real(kind=RP), intent(in) :: nHat(NDIM) + real(kind=RP), intent(inout) :: Q(NCONS) + type(Thermodynamics_t), intent(in) :: thermodynamics_ + type(Dimensionless_t), intent(in) :: dimensionless_ + type(RefValues_t), intent(in) :: refValues_ + end subroutine UserDefinedState1 + + subroutine UserDefinedGradVars1(x, t, nHat, Q, U, GetGradients, thermodynamics_, dimensionless_, refValues_) + use SMConstants + use PhysicsStorage + use FluidData + use VariableConversion, only: GetGradientValues_f + implicit none + real(kind=RP), intent(in) :: x(NDIM) + real(kind=RP), intent(in) :: t + real(kind=RP), intent(in) :: nHat(NDIM) + real(kind=RP), intent(in) :: Q(NCONS) + real(kind=RP), intent(inout) :: U(NGRAD) + procedure(GetGradientValues_f) :: GetGradients + type(Thermodynamics_t), intent(in) :: thermodynamics_ + type(Dimensionless_t), intent(in) :: dimensionless_ + type(RefValues_t), intent(in) :: refValues_ + end subroutine UserDefinedGradVars1 + + subroutine UserDefinedNeumann1(x, t, nHat, U_x, U_y, U_z) +! +! -------------------------------------------------------- +! Used to define a Neumann user defined boundary condition +! -------------------------------------------------------- +! + use SMConstants + use PhysicsStorage + use FluidData + implicit none + real(kind=RP), intent(in) :: x(NDIM) + real(kind=RP), intent(in) :: t + real(kind=RP), intent(in) :: nHat(NDIM) + real(kind=RP), intent(inout) :: U_x(NGRAD) + real(kind=RP), intent(inout) :: U_y(NGRAD) + real(kind=RP), intent(inout) :: U_z(NGRAD) + end subroutine UserDefinedNeumann1 +#endif +! +!//////////////////////////////////////////////////////////////////////// +! + SUBROUTINE UserDefinedPeriodicOperation(mesh, time, dt, Monitors) +! +! ---------------------------------------------------------- +! Called at the output interval to allow periodic operations +! to be performed +! ---------------------------------------------------------- +! + use SMConstants + USE HexMeshClass +#if defined(NAVIERSTOKES) + use MonitorsClass +#endif + IMPLICIT NONE + class(HexMesh) :: mesh + real(kind=RP) :: time + real(kind=RP) :: dt +#if defined(NAVIERSTOKES) + type(Monitor_t), intent(in) :: monitors +#else + logical, intent(in) :: monitors +#endif + + END SUBROUTINE UserDefinedPeriodicOperation +! +!//////////////////////////////////////////////////////////////////////// +! +#if defined(NAVIERSTOKES) + subroutine UserDefinedSourceTermNS(xyz, Q, t, S, thermodynamics_, dimensionless_, refValues_) +! +! -------------------------------------------- +! Called to apply source terms to the equation +! -------------------------------------------- +! + use SMConstants + USE HexMeshClass + use PhysicsStorage + use FluidData + IMPLICIT NONE + real(kind=RP), intent(in) :: xyz(NDIM) + real(kind=RP), intent(in) :: Q(NCONS) + real(kind=RP), intent(in) :: t + real(kind=RP), intent(inout) :: S(NCONS) + type(Thermodynamics_t), intent(in) :: thermodynamics_ + type(Dimensionless_t), intent(in) :: dimensionless_ + type(RefValues_t), intent(in) :: refValues_ + + real(kind=RP) :: x,y,z + real(kind=RP) :: Pr, M, gamma, lambda, mu, Re, kappa + x = xyz(1) + y = xyz(2) + z = xyz(3) + Pr = dimensionless_ % Pr + M = dimensionless_ % Mach + gamma = thermodynamics_ % gamma + lambda = thermodynamics_ % lambda + mu = refValues_ % mu + Re = dimensionless_ % Re + kappa = mu * dimensionless_ % mu_to_kappa +! +! Usage example +! ------------- +! S(:) = x(1) + x(2) + x(3) + time + S = 0.0_RP + S(IRHO) = ((exp(t)*sin(x + y + z) - 2.0_rp*sin(x + y + z)**2 + sin(x + y + z)*cos(x + y + z) - 6.0_rp*exp(-t)*sin(x + y + z) + 3.0_rp*exp(-t)*cos(x + y + z))*exp(t) + exp(t)*sin(x + y + z)*cos(x + y + z) + 2.0_rp*exp(t)*cos(x + y + z)**2)*exp(-t) + S(IRHOU) = (Re*(gamma*exp(t)*sin(x + y + z)**2*cos(x + y + z) + 2.0_rp*gamma*exp(t)*cos(x + y + z)**3.0_rp - exp(t)*sin(x + y + z)**2*cos(x + y + z) + exp(t)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)*cos(x + y + z)/2.0_rp) + Re*(gamma*exp(t)*sin(x + y + z)**3*cos(x + y + z) + 2.0_rp*gamma*exp(t)*sin(x + y + z)*cos(x + y + z)**3.0_rp + 6.0_rp*gamma*exp(-t)*sin(x + y + z)*cos(x + y + z) - exp(t)*sin(x + y + z)**3*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*cos(x + y + z)**3.0_rp + 2.0_rp*exp(t)*sin(x + y + z)*cos(x + y + z) - 6.0_rp*exp(-t)*sin(x + y + z)**2.0_rp - 30.0_rp*exp(-t)*sin(x + y + z)*cos(x + y + z) + 6.0_rp*exp(-t)*cos(x + y + z)**2.0_rp)*exp(t)/2.0_rp + Re*(gamma*((cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + 3)*exp(t)*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 12.0_rp*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z)/4.0_rp + 3.0_rp*gamma*((cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + 3)*exp(t)*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 12.0_rp*sin(x + y + z)*cos(x + y + z))*exp(-2.0_rp*t)/4.0_rp + gamma*exp(t)*cos(x + y + z) - gamma*exp(-t)*sin(x + y + z)**2*cos(x + y + z) + gamma*exp(-t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - ((cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + 3)*exp(t)*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 12.0_rp*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z)/4.0_rp - 3.0_rp*((cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + 3)*exp(t)*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 12.0_rp*sin(x + y + z)*cos(x + y + z))*exp(-2.0_rp*t)/4.0_rp - exp(t)*cos(x + y + z) - sin(x + y + z)*cos(x + y + z) - exp(-t)*sin(x + y + z)**3.0_rp + exp(-t)*sin(x + y + z)**2*cos(x + y + z) - 3.0_rp*exp(-t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + exp(-t)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)*cos(x + y + z)/2.0_rp - 3.0_rp*exp(-t)*cos(x + y + z))*exp(2.0_rp*t) - mu*(-exp(-t)*sin(x + y + z) - 11.0_rp*exp(-t)*cos(x + y + z))*exp(2.0_rp*t)/3.0_rp)*exp(-2.0_rp*t)/Re + S(IRHOV) = (Re*(gamma*exp(t)*sin(x + y + z)**2*cos(x + y + z) + 2.0_rp*gamma*exp(t)*cos(x + y + z)**3.0_rp + exp(t)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)*cos(x + y + z) - 2.0_rp*exp(t)*cos(x + y + z)**3.0_rp) + Re*(gamma*exp(t)*sin(x + y + z)**3*cos(x + y + z) + 2.0_rp*gamma*exp(t)*sin(x + y + z)*cos(x + y + z)**3.0_rp + 6.0_rp*gamma*exp(-t)*sin(x + y + z)*cos(x + y + z) - exp(t)*sin(x + y + z)**3*cos(x + y + z) + 2.0_rp*exp(t)*sin(x + y + z)**2.0_rp - 2.0_rp*exp(t)*sin(x + y + z)*cos(x + y + z)**3.0_rp - 12.0_rp*exp(-t)*sin(x + y + z)**2.0_rp + 6.0_rp*exp(-t)*sin(x + y + z)*cos(x + y + z) + 12.0_rp*exp(-t)*cos(x + y + z)**2.0_rp)*exp(t)/2.0_rp + Re*(gamma*((cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + 3)*exp(t)*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 12.0_rp*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z)/4.0_rp + 3.0_rp*gamma*((cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + 3)*exp(t)*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 12.0_rp*sin(x + y + z)*cos(x + y + z))*exp(-2.0_rp*t)/4.0_rp + gamma*exp(t)*cos(x + y + z) - gamma*exp(-t)*sin(x + y + z)**2*cos(x + y + z) + gamma*exp(-t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - ((cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + 3)*exp(t)*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 12.0_rp*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z)/4.0_rp - 3.0_rp*((cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + 3)*exp(t)*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 12.0_rp*sin(x + y + z)*cos(x + y + z))*exp(-2.0_rp*t)/4.0_rp - exp(t)*cos(x + y + z) - sin(x + y + z)**2.0_rp - 2.0_rp*exp(-t)*sin(x + y + z)**3.0_rp + 3.0_rp*exp(-t)*sin(x + y + z)**2*cos(x + y + z) - exp(-t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 3.0_rp*exp(-t)*sin(x + y + z) + exp(-t)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)*cos(x + y + z))*exp(2.0_rp*t) - mu*(-10.0_rp*exp(-t)*sin(x + y + z) - 2.0_rp*exp(-t)*cos(x + y + z))*exp(2.0_rp*t)/3.0_rp)*exp(-2.0_rp*t)/Re + S(IRHOW) = (Re*(gamma*exp(t)*sin(x + y + z)**2*cos(x + y + z) + 2.0_rp*gamma*exp(t)*cos(x + y + z)**3.0_rp - exp(t)*sin(x + y + z)**2*cos(x + y + z) + exp(t)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)*cos(x + y + z)/2.0_rp) + Re*(gamma*exp(t)*sin(x + y + z)**3*cos(x + y + z) + 2.0_rp*gamma*exp(t)*sin(x + y + z)*cos(x + y + z)**3.0_rp + 6.0_rp*gamma*exp(-t)*sin(x + y + z)*cos(x + y + z) - exp(t)*sin(x + y + z)**3*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*cos(x + y + z)**3.0_rp + 2.0_rp*exp(t)*sin(x + y + z)*cos(x + y + z) - 6.0_rp*exp(-t)*sin(x + y + z)**2.0_rp - 30.0_rp*exp(-t)*sin(x + y + z)*cos(x + y + z) + 6.0_rp*exp(-t)*cos(x + y + z)**2.0_rp)*exp(t)/2.0_rp + Re*(gamma*((cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + 3)*exp(t)*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 12.0_rp*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z)/4.0_rp + 3.0_rp*gamma*((cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + 3)*exp(t)*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 12.0_rp*sin(x + y + z)*cos(x + y + z))*exp(-2.0_rp*t)/4.0_rp + gamma*exp(t)*cos(x + y + z) - gamma*exp(-t)*sin(x + y + z)**2*cos(x + y + z) + gamma*exp(-t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - ((cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + 3)*exp(t)*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 12.0_rp*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z)/4.0_rp - 3.0_rp*((cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + 3)*exp(t)*cos(x + y + z) - 2.0_rp*exp(t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 12.0_rp*sin(x + y + z)*cos(x + y + z))*exp(-2.0_rp*t)/4.0_rp - exp(t)*cos(x + y + z) - sin(x + y + z)*cos(x + y + z) - exp(-t)*sin(x + y + z)**3.0_rp + exp(-t)*sin(x + y + z)**2*cos(x + y + z) - 3.0_rp*exp(-t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) + exp(-t)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)*cos(x + y + z)/2.0_rp - 3.0_rp*exp(-t)*cos(x + y + z))*exp(2.0_rp*t) - mu*(-exp(-t)*sin(x + y + z) - 11.0_rp*exp(-t)*cos(x + y + z))*exp(2.0_rp*t)/3.0_rp)*exp(-2.0_rp*t)/Re + S(IRHOE) = -3.0_rp*M**2*gamma**2*kappa*(-5.0_rp*sin(x + y + z)*cos(2.0_rp*(x + y + z))/4.0_rp - 3.0_rp*sin(x + y + z)/4.0_rp - sin(2.0_rp*(x + y + z))*cos(x + y + z) + 3.0_rp*exp(-t)*sin(x + y + z)**2.0_rp - 3.0_rp*exp(-t)*cos(x + y + z)**2.0_rp)*exp(-t)/Re + 3.0_rp*M**2*gamma**2*kappa*exp(-2.0_rp*t)*sin(x + y + z)**2.0_rp/Re - 3.0_rp*M**2*gamma**2*kappa*exp(-2.0_rp*t)*cos(x + y + z)**2.0_rp/Re + 3.0_rp*M**2*gamma*kappa*(-5.0_rp*sin(x + y + z)*cos(2.0_rp*(x + y + z))/4.0_rp - 3.0_rp*sin(x + y + z)/4.0_rp - sin(2.0_rp*(x + y + z))*cos(x + y + z) + 3.0_rp*exp(-t)*sin(x + y + z)**2.0_rp - 3.0_rp*exp(-t)*cos(x + y + z)**2.0_rp)*exp(-t)/Re - 3.0_rp*M**2*gamma*kappa*exp(-2.0_rp*t)*sin(x + y + z)**2.0_rp/Re + 3.0_rp*M**2*gamma*kappa*exp(-2.0_rp*t)*cos(x + y + z)**2.0_rp/Re + gamma*(5.0_rp*exp(-t)*cos(x + y + z)/8.0_rp + 3.0_rp*exp(-t)*cos(3.0_rp*x + 3.0_rp*y + 3.0_rp*z)/8.0_rp - 3.0_rp*exp(-2.0_rp*t)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)/2.0_rp)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - gamma*(5.0_rp*exp(-t)*cos(x + y + z)/8.0_rp + 3.0_rp*exp(-t)*cos(3.0_rp*x + 3.0_rp*y + 3.0_rp*z)/8.0_rp - 3.0_rp*exp(-2.0_rp*t)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)/2.0_rp)*cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)/2.0_rp + gamma*(5.0_rp*exp(-t)*cos(x + y + z)/8.0_rp + 3.0_rp*exp(-t)*cos(3.0_rp*x + 3.0_rp*y + 3.0_rp*z)/8.0_rp - 3.0_rp*exp(-2.0_rp*t)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)/2.0_rp)/2.0_rp + 3.0_rp*gamma*(-exp(-t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)/2.0_rp + exp(-t)*cos(x + y + z)*cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)/4.0_rp + 3.0_rp*exp(-t)*cos(x + y + z)/4.0_rp - 3.0_rp*exp(-2.0_rp*t)*sin(x + y + z)*cos(x + y + z))*exp(-t)*sin(x + y + z) + 6.0_rp*gamma*(-exp(-t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)/2.0_rp + exp(-t)*cos(x + y + z)*cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)/4.0_rp + 3.0_rp*exp(-t)*cos(x + y + z)/4.0_rp - 3.0_rp*exp(-2.0_rp*t)*sin(x + y + z)*cos(x + y + z))*exp(-t)*cos(x + y + z) - 2.0_rp*gamma*sin(x + y + z)**2.0_rp + 2.0_rp*gamma*sin(x + y + z)*cos(x + y + z) + 2.0_rp*gamma*cos(x + y + z)**2.0_rp - gamma*exp(-t)*sin(x + y + z)**5.0_rp + gamma*exp(-t)*sin(x + y + z)**4*cos(x + y + z) - gamma*exp(-t)*sin(x + y + z)**3*cos(x + y + z)**2.0_rp + 2.0_rp*gamma*exp(-t)*sin(x + y + z)**2*cos(x + y + z)**3.0_rp + 2.0_rp*gamma*exp(-t)*sin(x + y + z)*cos(x + y + z)**4.0_rp - 6.0_rp*gamma*exp(-t)*sin(x + y + z) + 3.0_rp*gamma*exp(-t)*cos(x + y + z) - 5.0_rp*gamma*exp(-2.0_rp*t)*sin(x + y + z)**4.0_rp + 9.0_rp*gamma*exp(-2.0_rp*t)*sin(x + y + z)**3*cos(x + y + z)/2.0_rp - 6.0_rp*gamma*exp(-2.0_rp*t)*sin(x + y + z)**2*cos(x + y + z)**2.0_rp + 7.0_rp*gamma*exp(-2.0_rp*t)*sin(x + y + z)*cos(x + y + z)**3.0_rp + 4.0_rp*gamma*exp(-2.0_rp*t)*cos(x + y + z)**4.0_rp - 6.0_rp*gamma*exp(-3.0_rp*t)*sin(x + y + z)**3.0_rp + 3.0_rp*gamma*exp(-3.0_rp*t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 3.0_rp*gamma*exp(-3.0_rp*t)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)*cos(x + y + z) + 6.0_rp*gamma*exp(-3.0_rp*t)*cos(x + y + z)**3.0_rp + (-exp(-t)*sin(x + y + z)*cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)/4.0_rp - 3.0_rp*exp(-t)*sin(x + y + z)/4.0_rp - 3.0_rp*exp(-2.0_rp*t)*sin(x + y + z)**2.0_rp - 6.0_rp*exp(-2.0_rp*t)*cos(x + y + z)**2.0_rp)*exp(t)*sin(x + y + z) + exp(t)*sin(x + y + z) + sin(x + y + z)**4.0_rp/2.0_rp + sin(x + y + z)**2*cos(x + y + z)**2.0_rp + 3.0_rp*exp(-t)*sin(x + y + z)**3.0_rp/2.0_rp + 3.0_rp*exp(-t)*sin(x + y + z)*cos(x + y + z)**2.0_rp - 3.0_rp*exp(-t)*sin(x + y + z)*cos(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)/4.0_rp - 9.0_rp*exp(-t)*sin(x + y + z)/4.0_rp - exp(-2.0_rp*t)*sin(x + y + z)**4.0_rp - 3.0_rp*exp(-2.0_rp*t)*sin(x + y + z)**2*cos(x + y + z)**2.0_rp - 9.0_rp*exp(-2.0_rp*t)*sin(x + y + z)**2.0_rp + 2.0_rp*exp(-2.0_rp*t)*sin(x + y + z)*cos(x + y + z)**3.0_rp + 2.0_rp*exp(-2.0_rp*t)*cos(x + y + z)**4.0_rp - 18.0_rp*exp(-2.0_rp*t)*cos(x + y + z)**2.0_rp - 3.0_rp*exp(-3.0_rp*t)*sin(x + y + z)**3.0_rp + 9.0_rp*exp(-3.0_rp*t)*sin(x + y + z)**2*cos(x + y + z)/2.0_rp - 3.0_rp*exp(-3.0_rp*t)*sin(x + y + z)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z) - 18.0_rp*exp(-3.0_rp*t)*sin(x + y + z)*cos(x + y + z)**2.0_rp + 3.0_rp*exp(-3.0_rp*t)*sin(2.0_rp*x + 2.0_rp*y + 2.0_rp*z)*cos(x + y + z) + 3.0_rp*exp(-3.0_rp*t)*cos(x + y + z)**3.0_rp - 4.0_rp*mu*exp(-2.0_rp*t)*sin(x + y + z)**2.0_rp/Re + 8.0_rp*mu*exp(-2.0_rp*t)*sin(x + y + z)*cos(x + y + z)/(3.0_rp*Re) + 4.0_rp*mu*exp(-2.0_rp*t)*cos(x + y + z)**2.0_rp/Re + + + + + + end subroutine UserDefinedSourceTermNS +#endif +! +!//////////////////////////////////////////////////////////////////////// +! + SUBROUTINE UserDefinedFinalize(mesh, time, iter, maxResidual & +#if defined(NAVIERSTOKES) + , thermodynamics_ & + , dimensionless_ & + , refValues_ & +#endif +#if defined(CAHNHILLIARD) + , multiphase_ & +#endif + , monitors, & + elapsedTime, & + CPUTime ) +! +! -------------------------------------------------------- +! Called after the solution computed to allow, for example +! error tests to be performed +! -------------------------------------------------------- +! + use SMConstants + use FTAssertions + USE HexMeshClass + use PhysicsStorage + use FluidData + use MonitorsClass + use MMS + IMPLICIT NONE + class(HexMesh) :: mesh + REAL(KIND=RP) :: time + integer :: iter + real(kind=RP) :: maxResidual +#if defined(NAVIERSTOKES) + type(Thermodynamics_t), intent(in) :: thermodynamics_ + type(Dimensionless_t), intent(in) :: dimensionless_ + type(RefValues_t), intent(in) :: refValues_ +#endif +#if defined(CAHNHILLIARD) + type(Multiphase_t), intent(in) :: multiphase_ +#endif + type(Monitor_t), intent(in) :: monitors + real(kind=RP), intent(in) :: elapsedTime + real(kind=RP), intent(in) :: CPUTime +! +! --------------- +! Local variables +! --------------- +! +#if defined(NAVIERSTOKES) + CHARACTER(LEN=29) :: testName = "MMS Lamb Vector" + REAL(KIND=RP) :: Qerror + REAL(KIND=RP), ALLOCATABLE :: QExpected(:,:,:,:) + INTEGER :: eID + INTEGER :: i, j, k, Nx, Ny, Nz + TYPE(FTAssertionsManager), POINTER :: sharedManager + LOGICAL :: Qsuccess + integer :: rank + integer :: fid + REAL(KIND=RP) :: u(NCONS), uh(NCONS), x(NDIM), wi, wj, wk + REAL(KIND=RP) :: error_mesh, error_elem + logical :: useGaussLobatto = .false. + ! + ! Gauss-Lobatto quadrature weights, orders 1..8 + ! + real(kind=RP) :: wGL_1(0:1) + data wGL_1 / & + 1.00000000000000000e+00_RP, & + 1.00000000000000000e+00_RP / + + real(kind=RP) :: wGL_2(0:2) + data wGL_2 / & + 3.33333333333333315e-01_RP, & + 1.33333333333333326e+00_RP, & + 3.33333333333333315e-01_RP / + + real(kind=RP) :: wGL_3(0:3) + data wGL_3 / & + 1.66666666666666657e-01_RP, & + 8.33333333333333370e-01_RP, & + 8.33333333333333370e-01_RP, & + 1.66666666666666657e-01_RP / + + real(kind=RP) :: wGL_4(0:4) + data wGL_4 / & + 1.00000000000000006e-01_RP, & + 5.44444444444444398e-01_RP, & + 7.11111111111111138e-01_RP, & + 5.44444444444444398e-01_RP, & + 1.00000000000000006e-01_RP / + + real(kind=RP) :: wGL_5(0:5) + data wGL_5 / & + 6.66666666666666657e-02_RP, & + 3.78474956297846943e-01_RP, & + 5.54858377035486461e-01_RP, & + 5.54858377035486461e-01_RP, & + 3.78474956297846943e-01_RP, & + 6.66666666666666657e-02_RP / + + real(kind=RP) :: wGL_6(0:6) + data wGL_6 / & + 4.76190476190476164e-02_RP, & + 2.76826047361565741e-01_RP, & + 4.31745381209862611e-01_RP, & + 4.87619047619047619e-01_RP, & + 4.31745381209862611e-01_RP, & + 2.76826047361565741e-01_RP, & + 4.76190476190476164e-02_RP / + + real(kind=RP) :: wGL_7(0:7) + data wGL_7 / & + 3.57142857142857123e-02_RP, & + 2.10704227143506007e-01_RP, & + 3.41122692483504408e-01_RP, & + 4.12458794658703720e-01_RP, & + 4.12458794658703720e-01_RP, & + 3.41122692483504408e-01_RP, & + 2.10704227143506007e-01_RP, & + 3.57142857142857123e-02_RP / + + real(kind=RP) :: wGL_8(0:8) + data wGL_8 / & + 2.77777777777777762e-02_RP, & + 1.65495361560805576e-01_RP, & + 2.74538712500161652e-01_RP, & + 3.46428510973046389e-01_RP, & + 3.71519274376417241e-01_RP, & + 3.46428510973046389e-01_RP, & + 2.74538712500161652e-01_RP, & + 1.65495361560805576e-01_RP, & + 2.77777777777777762e-02_RP / + + ! + ! Gauss quadrature weights, orders 1..5 + ! + real(kind=RP) :: wG_1(0:1) + data wG_1 / & + 1.00000000000000000e+00_RP, & + 1.00000000000000000e+00_RP / + + real(kind=RP) :: wG_2(0:2) + data wG_2 / & + 0.55555555555555569_RP, & + 0.88888888888888884_RP, & + 0.55555555555555569_RP / + + real(kind=RP) :: wG_3(0:3) + data wG_3 / & + 0.34785484513745385_RP, & + 0.65214515486254632_RP, & + 0.65214515486254632_RP, & + 0.34785484513745385_RP / + + real(kind=RP) :: wG_4(0:4) + data wG_4 / & + 0.23692688505618911_RP, & + 0.47862867049936669_RP, & + 0.56888888888888889_RP, & + 0.47862867049936669_RP, & + 0.23692688505618911_RP / + + real(kind=RP) :: wG_5(0:5) + data wG_5 / & + 0.17132449237917019_RP, & + 0.36076157304813833_RP, & + 0.46791393457269093_RP, & + 0.46791393457269093_RP, & + 0.36076157304813833_RP, & + 0.17132449237917019_RP / + + real(kind=RP) :: wG_6(0:6) + data wG_6 / & + 0.12948496616886979_RP, & + 0.27970539148927670_RP, & + 0.38183005050511903_RP, & + 0.41795918367346940_RP, & + 0.38183005050511903_RP, & + 0.27970539148927670_RP, & + 0.12948496616886979_RP / + + real(kind=RP) :: wG_7(0:7) + data wG_7 / & + 0.10122853629037630_RP, & + 0.22238103445337470_RP, & + 0.31370664587788727_RP, & + 0.36268378337836193_RP, & + 0.36268378337836193_RP, & + 0.31370664587788727_RP, & + 0.22238103445337470_RP, & + 0.10122853629037630_RP / + + real(kind=RP) :: wG_8(0:8) + data wG_8 / & + 8.1274388361574565E-002_RP, & + 0.18064816069485751_RP, & + 0.26061069640293549_RP, & + 0.31234707704000264_RP, & + 0.33023935500125978_RP, & + 0.31234707704000264_RP, & + 0.26061069640293549_RP, & + 0.18064816069485751_RP, & + 8.1274388361574565E-002_RP / + + Qsuccess = .true. + + CALL initializeSharedAssertionsManager + sharedManager => sharedAssertionsManager() + + open(newunit=fid, file="MMS_Q_degree5", status="old", action="read", & + form="unformatted" , access="stream") + + ! Compute point-wise L2 norm + error_mesh = 0.0_rp + DO eID = 1, SIZE(mesh % elements) + Nx = mesh % elements(eID) % Nxyz(1) + Ny = mesh % elements(eID) % Nxyz(2) + Nz = mesh % elements(eID) % Nxyz(3) + + ! Compare the values obtained with the expected (saved in file) + allocate(QExpected(1:NCONS,0:Nx,0:Ny,0:Nz)) + read(fid) QExpected(:,:,:,:) + Qerror = maxval(abs(QExpected - mesh % elements(eID) % storage % Q)) + if (Qerror > 1e-12) then + Qsuccess = .false. + end if + deallocate(QExpected) + + + error_elem = 0.0_rp + DO k = 0, Nz + DO j = 0, Ny + DO i = 0, Nx + x = mesh % elements(eID) % geom % x(:,i,j,k) + call evalManufacturedSolution(x(1),x(2),x(3),time,u) + uh = mesh % elements(eID) % storage % Q(:,i,j,k) + + if (.not. useGaussLobatto) then + select case(Nx) + case(1) ; wi = wG_1(i) + case(2) ; wi = wG_2(i) + case(3) ; wi = wG_3(i) + case(4) ; wi = wG_4(i) + case(5) ; wi = wG_5(i) + case(6) ; wi = wG_6(i) + case(7) ; wi = wG_7(i) + case(8) ; wi = wG_8(i) + case default + print *, "MMS: order", Nx, "not tabulated (max=8)" ; error stop + end select + select case(Ny) + case(1) ; wj = wG_1(j) + case(2) ; wj = wG_2(j) + case(3) ; wj = wG_3(j) + case(4) ; wj = wG_4(j) + case(5) ; wj = wG_5(j) + case(6) ; wj = wG_6(j) + case(7) ; wj = wG_7(j) + case(8) ; wj = wG_8(j) + case default + print *, "MMS: order", Ny, "not tabulated (max=8)" ; error stop + end select + select case(Nz) + case(1) ; wk = wG_1(k) + case(2) ; wk = wG_2(k) + case(3) ; wk = wG_3(k) + case(4) ; wk = wG_4(k) + case(5) ; wk = wG_5(k) + case(6) ; wk = wG_6(k) + case(7) ; wk = wG_7(k) + case(8) ; wk = wG_8(k) + case default + print *, "MMS: order", Nz, "not tabulated (max=8)" ; error stop + end select + else ! Gauss - Lobatto + select case(Nx) + case(1) ; wi = wGL_1(i) + case(2) ; wi = wGL_2(i) + case(3) ; wi = wGL_3(i) + case(4) ; wi = wGL_4(i) + case(5) ; wi = wGL_5(i) + case(6) ; wi = wGL_6(i) + case(7) ; wi = wGL_7(i) + case(8) ; wi = wGL_8(i) + case default + print *, "MMS: order", Nx, "not tabulated (max=8)" ; error stop + end select + select case(Ny) + case(1) ; wj = wGL_1(j) + case(2) ; wj = wGL_2(j) + case(3) ; wj = wGL_3(j) + case(4) ; wj = wGL_4(j) + case(5) ; wj = wGL_5(j) + case(6) ; wj = wGL_6(j) + case(7) ; wj = wGL_7(j) + case(8) ; wj = wGL_8(j) + case default + print *, "MMS: order", Ny, "not tabulated (max=8)" ; error stop + end select + select case(Nz) + case(1) ; wk = wGL_1(k) + case(2) ; wk = wGL_2(k) + case(3) ; wk = wGL_3(k) + case(4) ; wk = wGL_4(k) + case(5) ; wk = wGL_5(k) + case(6) ; wk = wGL_6(k) + case(7) ; wk = wGL_7(k) + case(8) ; wk = wGL_8(k) + case default + print *, "MMS: order", Nz, "not tabulated (max=8)" ; error stop + end select + end if + error_elem = error_elem + wi*wj*wk & + * mesh % elements(eID) % geom % jacobian(i,j,k) & + * norm2(u - uh)**2 + + ! error_elem = error_elem + norm2(u - uh) + END DO + END DO + END DO + error_mesh = error_mesh + error_elem + END DO + + ! close(fid) + + error_mesh = sqrt(error_mesh / SIZE(mesh % elements)) + print *, "Error in L2 norm: ", error_mesh + + CALL FTAssertEqual(expectedValue = 3.4755642143319206E-005_rp, & + actualValue = error_mesh, & + tol = 1.0e-7_RP, & + msg = "L2 norm") + + CALL FTAssertEqual(expectedValue = .true., & + actualValue = Qsuccess, & + msg = "Error when comparing obtained Q from the reference one in file.") + + ! + ! Lamb vector comparison + ! + Qsuccess = .true. + call compareLambVector(SIZE(mesh % elements), mesh % elements, Qsuccess) + CALL FTAssertEqual(expectedValue = .true., & + actualValue = Qsuccess, & + msg = "Error when comparing the Lamb vector.") + + Qsuccess = .true. + call compareLambVectorStats(SIZE(mesh % elements), mesh % elements, time, Qsuccess) + CALL FTAssertEqual(expectedValue = .true., & + actualValue = Qsuccess, & + msg = "Error when comparing the Lamb vector stats.") + + + CALL sharedManager % summarizeAssertions(title = testName,iUnit = 6) + + WRITE(6,*) + + CALL finalizeSharedAssertionsManager + CALL detachSharedAssertionsManager + + ! Save solution to file for the test + ! block + ! integer :: fid + ! open(newunit=fid, file="MMS_Q_degree5", status="replace", action="write", & + ! form="unformatted" , access="stream") + ! DO eID = 1, SIZE(mesh % elements) + ! write(fid) mesh % elements(eID) % storage % Q + ! end do + ! close(fid) + ! end block +#endif + + + END SUBROUTINE UserDefinedFinalize +! +!//////////////////////////////////////////////////////////////////////// +! + SUBROUTINE UserDefinedTermination +! +! ----------------------------------------------- +! Called at the the end of the main driver after +! everything else is done. +! ----------------------------------------------- +! + IMPLICIT NONE + END SUBROUTINE UserDefinedTermination + diff --git a/Solver/test/NavierStokes/LambVector/TaylorGreen.control b/Solver/test/NavierStokes/LambVector/TaylorGreen.control new file mode 100644 index 000000000..dabf03747 --- /dev/null +++ b/Solver/test/NavierStokes/LambVector/TaylorGreen.control @@ -0,0 +1,71 @@ +Flow equations = "NS" +mesh file name = "../../TestMeshes/TaylorGreen8.mesh" + +restart file name = "RESULTS/TGV.rst" +solution file name = "RESULTS/TGV.rst" +restart = .false. + +Discretization nodes = "Gauss" + +Polynomial order = 5 + +simulation type = "time-accurate" +final time = 0.100001 +dt = 0.005 +Number of time steps = 10000 + +Output Interval = 1 +Number of plot points = 2 +Convergence tolerance = 1.d-10 + +!cfl = 0.4 +!dcfl = 0.4 +mach number = 0.08 +Reynolds number = 1600.0 + +riemann solver = "Roe" + +AOA theta = 0.0 +AOA phi = 0.0 + +!autosave mode = "time" +!autosave interval = 0.1 + +save Lamb vector = .true. +save Lamb vector mode = "time" +save Lamb vector interval = 0.1 +save lamb vector stats = .true. + +#define statistics + starting iteration = 1 +#end + +#define boundary front + type = periodic + coupled boundary = back +#end + +#define boundary bottom + type = periodic + coupled boundary = top +#end + +#define boundary top + type = periodic + coupled boundary = bottom +#end + +#define boundary back + type = periodic + coupled boundary = front +#end + +#define boundary left + type = periodic + coupled boundary = right +#end + +#define boundary right + type = periodic + coupled boundary = left +#end diff --git a/Solver/test/NavierStokes/LambVector/horses2plt b/Solver/test/NavierStokes/LambVector/horses2plt new file mode 120000 index 000000000..6290868a7 --- /dev/null +++ b/Solver/test/NavierStokes/LambVector/horses2plt @@ -0,0 +1 @@ +../../../bin/horses2plt \ No newline at end of file