.. _EB-C13:

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
<https://doi.org/10.1016/j.jcp.2020.109820>`_ 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:

.. math::
   \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 :math:`u=a_i M_i cos(\theta)`, :math:`v=-a_i M_i cos(\theta```,
and :math:`p=\rho^\gamma/\gamma`. The inner radius, :math:`r_i=1.0`,
the outer radius, :math:`r_o = 1.384`, the Mach number,
:math:`M_i=2.25`, and the domain size :math:`[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
#######

.. image:: /ebverification/C13/rho.png
   :height: 300pt

Magnitude of velocity
#####################

.. image:: /ebverification/C13/u.png
   :height: 300pt

Pressure
########

.. image:: /ebverification/C13/p.png
   :height: 300pt

Running study
#############

.. code-block:: bash

   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