# 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:

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.

## Density

## Magnitude of velocity

## Pressure

## 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
```