Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations

2020/11/22 by Jesse Chan, Yimin Lin, Chan, Jesse +3 · 1 citation
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2011.11089

openalex publication_date 2020/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. In this work, we describe a discretization of viscous terms in the compressible Navier-Stokes equations which enables a simple and explicit imposition of entropy stable no-slip (adiabatic and isothermal) and reflective (symmetry) wall boundary conditions for discontinuous Galerkin (DG) discretizations. Numerical results confirm the robustness and accuracy of the proposed approaches.

Citations

• The numerical viscosity of entropy stable schemes for systems of conservation laws. I
• Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Mortar-based entropy-stable discontinuous Galerkin methods on non-conforming quadrilateral and hexahedral meshes

Cited by

• Entropy stable high-order discontinuous Galerkin spectral-element methods on curvilinear, hybrid meshes
• Entropy-stable in- and outflow boundary conditions for the compressible Navier-Stokes equations

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