An entropy stable discretization for the two dimensional Navier-Stokes equations with stable boundary treatment

We construct an entropy stable finite volume scheme to approximate the two-dimensional Navier-Stokes system on unstructured grids. The convective fluxes are discretized using a vertex-centered entropy-stable scheme on the dual meah. The viscous fluxes are approximated on the primary mesh, taking advantage of the symmetrizability of viscous terms using a specific choice of entopy variables. Homogeneous boundary conditions are imposed weakly to obtain global entropy stablility estimates. The proposed scheme is tested on several benchmark numerical experiments to demonstarte its robustness.

People: Deep Ray, Praveen C, Siddhartha Mishra
Status: Ongoing work