# C13. Supersonic vortex study

## Case description

This is a supersonic flow around a quarter circle. It is described in Berger, Marsha, and Andrew Giuliani. “A state redistribution algorithm for finite volume schemes on cut cell meshes.” Journal of Computational Physics 428 (2021): 109820 and Aftosmis, Michael, Datta Gaitonde, and Theodore S. Tavares. “On the accuracy, stability, and monotonicity of various reconstruction algorithms for unstructured meshes.” (1994). It has an exact solution:

$\rho = \rho_i \left\{ 1 + \frac{\gamma-1}{2} M_i^2 \left[1-\left(\frac{r_i^2}{r^2}\right)\right]\right\}$

and $$u=a_i M_i cos(\theta)$$, $$v=-a_i M_i cos(\theta$$, and $$p=\rho^\gamma/\gamma$$. The inner radius, $$r_i=1.0$$, the outer radius, $$r_o = 1.384$$, the Mach number, $$M_i=2.25$$, and the domain size $$[0,0] \times [1.43,1.43]$$. The initial solution is the exact solution and the exact solution is used at the boundaries conditions. The solution is marched for 10 flow throughs, until it reaches steady state.

## Running study

paren=pwd
pelec="${paren}/PeleC3d.gnu.MPI.ex" mpi_ranks=36 res=( 16 32 64 128 ) for i in "${res[@]}"
do
rm -rf "${i}" mkdir "${i}"
cd "${i}" || exit cp "${paren}/inputs_3d" .
hiz="$((0.3575*16/i))" srun -n${mpi_ranks} "${pelec}" inputs_3d amr.n_cell="${i} ${i} 4" geometry.prob_hi="1.43 1.43${hiz}" > out
ls -1v *plt*/Header | tee movie.visit
cd "\${paren}" || exit
done