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Copy pathVelocity_Pressure_working.m
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Velocity_Pressure_working.m
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%% SIMPLE
% Code written by Jay Mehta (July 2019).
% Modified by Jay Mehta (November 15, 2019).
%% Clear Everything
clear all
clc
rmpath('Source')
rmpath('Source/dst_idst')
%% Add Paths
addpath('Source')
addpath('Source/dst_idst')
%% Set up the problem domain and the problem object
% Set up the parameters that have to be passed
params = flow_parameters_init;
domain = domain_parameters_init;
% Domain
Nx = 64;
Ny = 64;
domain.Nx = Nx;
domain.Ny = Ny;
x_range = [0 1];
y_range = [0 1];
domain.x_range = x_range;
domain.y_range = y_range;
dx = (x_range(2)-x_range(1))/Nx;
params.dx = dx;
dy = (y_range(2)-y_range(1))/Ny;
%% Setting up the Domain of the Problem
[X_n, Y_n] = DomainSetup(params,domain,"node");
[X_e_x, Y_e_x] = DomainSetup(params,domain,"xe");
[X_e_y, Y_e_y] = DomainSetup(params,domain,"ye");
[X_c,Y_c] = DomainSetup(params,domain,"cell");
domain.X_n = X_n;
domain.Y_n = Y_n;
domain.X_e_x = X_e_x;
domain.Y_e_x = Y_e_x;
domain.X_e_y = X_e_y;
domain.Y_e_y = Y_e_y;
domain.X_c = X_c;
domain.Y_c = Y_c;
%% Initializing the flow parameters
U = 1;
V = 0;
params.U = U;
Re = 100;
nu = U * 1 / Re;
params.nu = nu;
%% Pre-Allocate Memory
velocity = EdgeData(Nx,Ny); % Velocity Field
pressure = CellData(Nx,Ny);
a_p = EdgeData(Nx,Ny);
a_e = EdgeData(Nx,Ny);
a_w = EdgeData(Nx,Ny);
a_n = EdgeData(Nx,Ny);
a_s = EdgeData(Nx,Ny);
d = EdgeData(Nx,Ny);
A_p = CellData(Nx,Ny);
A_e = CellData(Nx,Ny);
A_w = CellData(Nx,Ny);
A_n = CellData(Nx,Ny);
A_s = CellData(Nx,Ny);
p = CellData(Nx,Ny);
p_prime = CellData(Nx,Ny);
rhs = CellData(Nx,Ny);
rf_p = 5e-1;
rf_v = 5e-1;
max_gs_iter = 5;
conv_x = 1;
conv_y = 1;
tol = 1e-3;
%% Apply Boundary Conditions
uB = zeros(1,Nx+1);
uT = U * ones(1,Nx+1);
uL = zeros(1,Ny+2);
uR = zeros(1,Ny+2);
vB = zeros(1,Nx+2);
vT = zeros(1,Nx+1);
vL = zeros(1,Ny+1);
vR = zeros(1,Ny+1);
bc = bc_params(uL,uR,uB,uT,vL,vR,vB,vT);
velocity = apply_bc(bc,velocity);
%% Solving
for iter = 1:1000
velocity_old = velocity;
velocity_x_c = interpol(velocity_old,CellData(Nx,Ny),1);
velocity_x_n = interpol(velocity_old,NodeData(Nx,Ny),1);
velocity_y_c = interpol(velocity_old,CellData(Nx,Ny),2);
velocity_y_n = interpol(velocity_old,NodeData(Nx,Ny),2);
for i = 2:Nx
for j = 2:Ny+1
a_p.x(i,j) = (0.5 * dx * (velocity_x_c.x(i+1,j) - velocity_x_c.x(i,j))...
+ 0.5 * dx * (velocity_y_n.x(i,j) - velocity_y_n.x(i,j-1))...
+ 4*nu)/rf_v;
a_e.x(i,j) = -0.5 * dx * velocity_x_c.x(i+1,j) + nu;
a_w.x(i,j) = 0.5 * dx * velocity_x_c.x(i,j) + nu;
a_n.x(i,j) = -0.5 * dx * velocity_y_n.x(i,j) + nu;
a_s.x(i,j) = 0.5 * dx * velocity_y_n.x(i,j-1) + nu;
d.x(i,j) = dx /a_p.x(i,j);
end
end
for i = 2:Nx+1
for j = 2:Ny
a_p.y(i,j) = (0.5 * dx * (velocity_y_c.x(i,j+1) - velocity_y_c.x(i,j))...
+ 0.5 * dx * (velocity_x_n.x(i,j) - velocity_x_n.x(i-1,j))...
+ 4*nu)/rf_v;
a_e.y(i,j) = -0.5 * dx * velocity_x_n.x(i,j) + nu;
a_w.y(i,j) = 0.5 * dx * velocity_x_n.x(i-1,j) + nu;
a_n.y(i,j) = -0.5 * dx * velocity_y_c.x(i,j+1) + nu;
a_s.y(i,j) = 0.5 * dx * velocity_y_c.x(i,j) + nu;
d.y(i,j) = dx /a_p.y(i,j);
end
end
velocity_star = velocity_old;
for gs_iter = 1:max_gs_iter
for i = 2:Nx
for j = 2:Ny+1
velocity_star.x(i,j) = (a_e.x(i,j) * velocity_star.x(i+1,j)...
+ a_w.x(i,j) * velocity_star.x(i-1,j)...
+ a_n.x(i,j) * velocity_star.x(i,j+1)...
+ a_s.x(i,j) * velocity_star.x(i,j-1)...
- dx * (p.x(i+1,j) - p.x(i,j))...
+ (1-rf_v) * a_p.x(i,j) * velocity_old.x(i,j)) / a_p.x(i,j);
end
end
for i = 2:Nx+1
for j = 2:Ny
velocity_star.y(i,j) = (a_e.y(i,j) * velocity_star.y(i+1,j)...
+ a_w.y(i,j) * velocity_star.y(i-1,j)...
+ a_n.y(i,j) * velocity_star.y(i,j+1)...
+ a_s.y(i,j) * velocity_star.y(i,j-1)...
- dx * (p.x(i,j+1) - p.x(i,j))...
+ (1-rf_v) * a_p.y(i,j) * velocity_old.y(i,j)) / a_p.y(i,j);
end
end
gs_conv(1) = max(max(abs(velocity_star.x-velocity_old.x)));
gs_conv(2) = max(max(abs(velocity_star.y-velocity_old.y)));
gs_conv = max(gs_conv);
end
rhs = CellData(Nx,Ny);
for i = 2:Nx+1
for j = 2:Ny+1
A_p.x(i,j) = d.x(i,j) + d.x(i-1,j) + d.y(i,j) + d.y(i,j-1);
A_e.x(i,j) = d.x(i,j);
A_w.x(i,j) = d.x(i-1,j);
A_n.x(i,j) = d.y(i,j);
A_s.x(i,j) = d.y(i,j-1);
rhs.x(i,j) = -velocity_star.x(i,j) + velocity_star.x(i-1,j)...
- velocity_star.y(i,j) + velocity_star.y(i,j-1);
end
end
p_prime = CellData(Nx,Ny);
for gs_iter = 1:max_gs_iter
for i = 2:Nx+1
for j = 2:Ny+1
p_prime.x(i,j) = (A_e.x(i,j) * p_prime.x(i+1,j)...
+ A_w.x(i,j) * p_prime.x(i-1,j)...
+ A_n.x(i,j) * p_prime.x(i,j+1)...
+ A_s.x(i,j) * p_prime.x(i,j-1)...
+ rhs.x(i,j)) / A_p.x(i,j);
end
end
end
p.x = p.x + rf_p * p_prime.x;
velocity_prime = grad(p_prime);
velocity_prime.x = -velocity_prime.x .* d.x;
velocity_prime.y = -velocity_prime.y .* d.y;
velocity.x = velocity_star.x + velocity_prime.x;
velocity.y = velocity_star.y + velocity_prime.y;
velocity = apply_bc(bc,velocity);
conv_x = norm(velocity_prime.x(2:Nx,2:Ny+1))/norm(velocity.x(2:Nx,2:Ny+1));
conv_y = norm(velocity_prime.y(2:Nx+1,2:Ny))/norm(velocity.y(2:Nx+1,2:Ny));
end
%% Post Processing
gamma = curl_2(velocity);
gamma.x = -gamma.x;
sf = smoothing(NodeData(Nx,Ny),gamma,'sor','tol',1e-3);