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

Abstract

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 constructed by blending high order solutions with a low order positivity-preserving discretization. The proposed low order discretization is semi-discretely entropy stable, and the proposed limiting strategy is positivity preserving for the compressible Euler and Navier-Stokes equations. Numerical experiments confirm the high order accuracy and robustness of the proposed strategy.

References in corpus (3)

• Positivity-Preserving Entropy-Based Adaptive Filtering for Discontinuous Spectral Element Methods
• Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems
• On the implementation of a robust and efficient finite element-based parallel solver for the compressible Navier-Stokes equations

Cited by in corpus (3)

• Efficient Entropy-Stable Discontinuous Spectral-Element Methods Using Tensor-Product Summation-by-Parts Operators on Triangles and Tetrahedra
• Positivity-preserving entropy filtering for the ideal magnetohydrodynamics equations
• Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints