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.

Density

../../_images/rho1.png

Magnitude of velocity

../../_images/u1.png

Pressure

../../_images/p.png

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