ProjecTracer

Contents

1. Background
2. Variable Definitions
3. Governing Equations
4. File Description
   1. Job Files
   2. H_routines
   3. ProjecTracer_Source
   4. plot_scripts
5. How to Use
6. Legal

Background

2D mantle convection code that uses Lagrangian tracer particles for the advection of tempertaure and compostion. Tracer information is projected onto a fixed Eulerian grid to calculate quantites such as thermal diffusion.

Variable Definitions

• $\lambda$ = aspect ratio
• $x$ = horizontal position ( $x \in [0,\lambda]$ )
• $z$ = vertical position ( $z \in [0,1]$ , increasing upward)
• $t$ = time
• $\psi$ = stream function
• $\mathbf{v}$ = velocity
• $C$ = composition
• $T$ = temperature
• $H$ = internal heating rate
• $\eta$ = viscosity

Governing Equations

Conservation of Mass and Momentum: the Biharmonic Equation

$\left(\frac{\partial^2}{\partial x^2}-\frac{\partial^2}{\partial z^2}\right) \left[ \eta \left(\frac{\partial^2 \psi}{\partial x^2}-\frac{\partial^2 \psi}{\partial z^2}\right) \right] + 4\frac{\partial^2}{\partial x \partial z} \left[ \eta \frac{\partial^2 \psi}{\partial x \partial z} \right] = Ra_T \frac{\partial T}{\partial x} - Ra_C \frac{\partial C}{\partial x}$

Conservation of Eneregy

$\frac{\partial T}{\partial t}+\mathbf{v} \cdot \nabla T = \nabla^2 T+H$

Compositional Transport

$\frac{\partial C}{\partial t}+\mathbf{v} \cdot \nabla C = 0$

File Description

Job Files

compile_script.sh

• Linux script for compiling Fortran source files

ProjecTracer

• Executable for ProjecTracer code

run_job.sh

• Linux script for submitting local OpenMP jobs

H_routines

• Contains Fortran source files for the calculation of $H$ for certain problems
• See https://github.com/seantrim/exact-thermochem-solution for details

ProjecTracer_Source

• Fortran source code files for ProjecTracer code

plot_scripts

• Gnuplot scripts for analysis and visualization

How to Use

1. Specify physical parameters, boundary conditions, and code options (e.g., aspect ratio, Rayleigh numbers, Courant number, etc.) in inputs.nml
   • Entries in the Fortran namelist inputs.nml are fully commented
2. Specify initial conditions for $T$ and $C$ in initial_conditions.f90
   • Variable $H$ is specified in compute_heating subroutine in energy.f90
3. Compile source code using compile_script.sh
   • Linux: $ source compile_script
     • This produces the executable ProjecTracer
   • gfortran 11.3.0 or later is recommended
   • Other compilers may be possible but results should be tested
4. Run ProjecTracer from the command line
   • Specify number of OpenMP processes in run_job.sh then run the script
   • Linux: $ source run_job.sh
     • Job will run in the background

Legal

This repository is subject to the GPLv3 license.

The routines contained within xelbdj2_all_routines.f90 and xgscd_routines.f90 are adapted from routines by Toshio Fukushima available under the CC BY-SA 4.0 license. Original versions of these routines can be found at http://dx.doi.org/10.13140/RG.2.2.27011.66085 and https://www.researchgate.net/publication/233903220_xgscdtxt_Fortran_program_package_to_compute_the_Jacobian_elliptic_functions_snum_cnum_dnum.