Compressible Euler Equations in radial coordinates solved with finite volume approach.

The compressible Euler equations in radial coordinates are described by the non-linear system of partial differential equations

ρ_t + (ρu)_r = -(d-1)ρu/r
(ρu)_t + (ρu^2 + P)_r = -(d-1)ρu^2/r
E_t + (u(E+P))_r = -(d-1)u(E+P)/r

where ρ, u, P and E are the density, velocity, pressure and energy of the gas being modelled. The parameter d denotes the dimension of the problem. Values from one to three equate to cartesian, cylindrical and sphericl coordinates respectively. The equation of state for an ideal gas is used to close the system and is given by

E=P/(1-γ) + 0.5ρv^2

where γ is the ratio of specific heats for the gas.

Developing locally requires Docker for Windows. Run the command

docker build -t radial-euler .

to build the docker image which pulls the gcc base image containing gfortran and maps the source code into the container.

Then run image with the command:

docker run -i -t -v /f/git/src/github.com/bvwells/radial-euler:/app radial-euler

This command maps the local workspace into the running image so any changes made in the running image will be reflected on the local workspace.

Within the running image generate the make files for the release version by running the command:

cmake .

To build the debug version of the code run the command:

cmake -DCMAKE_BUILD_TYPE=Debug

Build the executable by running the command:

make

The program takes the file variables.data as input to the simulation. The program can be run from the base of the repo with the command:

./bin/radialeuler.exe

The program outputs the solution into the files exact.m.

The output from the simulation can be plotted in Octave by running the plotting file plot_solution.m in the root of the repo.