Entropy correction artificial viscosity method to the compressible Navier Stokes equations

  • Park, Raymond (University of Texas at Austin)
  • Chan, Jesse (University of Texas at Austin)

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Entropy stable discontinuous Galerkin (DG) methods display improved robustness for problems with shocks, turbulence, and under-resolved features by enforcing a mathematical entropy inequality. Such methods have traditionally relied on entropy conservative (EC) fluxes that can be computationally expensive to evaluate [1]. An alternative approach for enforcing an entropy inequality is through a minimally dissipative artificial viscosity called entropy correction artificial viscosity (ECAV). We review how to construct an artificial viscosity formulation using the Bassi-Rebay 1 (BR1) and Local Discontinuous Galerkin (LDG) discretization [2], as well as how to impose an entropy stable no-slip/slip adiabatic boundary condition. Then, we present numerical experiments for the Compressible Navier Stokes equations which suggest that ECAV method is capable of tackling difficult problems with complex shock and boundary layer interaction without requiring additional positivity preserving or shock-capturing methods. Finally, we discuss a flux-corrected transport (FCT) version of ECAV, as well as extensions of the proposed approach to non-ideal equation of states.