Program Overview

This program implements a Riemann solver for the two-dimensional Euler equations on an unstructured triangular mesh using the finite volume method. The HLLC fluxes are computed by solving the x-split Riemann problem at each face, taking advantage of the rotational invariance of the flux vectors. The solver employs an explicit multi-stage Runge-Kutta temporal discretisation, along with a multi-slope MUSCL gradient reconstruction and van Albada limiter to ensure stability and accuracy, especially near discontinuities.

Program Files

root/
│
├── data/                   # saved data folder
│   ├── cp.png              # pressure coefficient plot
│   └── mach.mp4            # mach number animation
│
├── mesh/                   # mesh folder
│   ├── body.txt            # body coordinates (user input)
│   ├── body.py             # generates body.txt
│   ├── geo.py              # generates mesh.geo from body.txt
│   ├── su2.py              # generates mesh.su2 from mesh.geo
│   └── mesh.f90            # generates mesh.txt from mesh.su2
│
├── mods/                   # modules folder
│   ├── mod_mesh.f90        # mesh type and procedures
│   ├── mod_config.f90      # configuration type and procedures
│   ├── mod_solve.f90       # solver procedures
│   ├── mod_flux.f90        # HLLC flux procedures
│   └── mod_utils.f90       # utility procedures
│
├── run.sh                  # script to run program
├── main.f90                # script to run solver
├── read.py                 # script to read and plot saved data
├── config.txt              # configuration for solver (user input)
└── requirements.txt        # dependencies for solver

Clone repository:

git clone https://github.com/obdwinston/Compressible-Flow.git && cd Compressible-Flow

Execute program (for macOS users):

chmod +x run.sh && ./run.sh

For Windows users, you need to modify run.sh accordingly before executing the program. For custom bodies, coordinates in mesh/body.txt should be x y space-delimited and in clockwise order, with no repeated points or intersecting lines.

Solver Verification

Diamond Airfoil

Half-Angle	Mach Number	Angle of Attack
15°	2	0°

mach.mp4

NACA Airfoil

NACA Designation	Mach Number	Angle of Attack
0012	0.8	1.25°

animation.mp4

Solver Theory

References

[1] Toro (2009). Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction.
[2] Blazek (2015). Computational Fluid Dynamics: Principles and Applications.
[3] Hou et al. (2015). An Efficient Unstructured MUSCL Scheme for Solving the 2D Shallow Water Equations.
[4] Curcic (2021). Modern Fortran: Building Efficient Parallel Applications.
[5] Anderson (2020). Modern Compressible Flow with Historical Perspective.
[6] Pulliam (1986). Artificial Dissipation Models for the Euler Equations.