A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations

01/27/2022
by   Yimin Lin, et al.
0

High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations require the positivity of thermodynamic quantities in order to guarantee their well-posedness. In this work, we introduce a positivity limiting strategy for entropy-stable discontinuous Galerkin discretizations based on convex limiting. The key ingredient in the limiting procedure is a low order positivity-preserving discretization based on graph viscosity terms. The proposed limiting strategy is both positivity preserving and discretely entropy-stable for the compressible Euler and Navier-Stokes equations. Numerical experiments confirm the high order accuracy and robustness of the proposed strategy.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset