Efficient entropy stable Gauss collocation methods

2018/09/04 by Jesse Chan, Chan, Jesse, David C. Del Rey Fernández +3 · 3 citations
Engineering · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1809.01178

openalex publication_date 2018/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The construction of high order entropy stable collocation schemes on quadrilateral and hexahedral elements has relied on the use of Gauss-Legendre-Lobatto collocation points and their equivalence with summation-by-parts (SBP) finite difference operators. In this work, we show how to efficiently generalize the construction of semi-discretely entropy stable schemes on tensor product elements to Gauss points and generalized SBP operators. Numerical experiments suggest that the use of Gauss points significantly improves accuracy on curved meshes.

Citations

• The numerical viscosity of entropy stable schemes for systems of conservation laws. I
• Optimal Isoparametric Finite Elements and Error Estimates for Domains Involving Curved Boundaries
• Discretely entropy stable weight-adjusted discontinuous Galerkin methods on curvilinear meshes

Cited by

• Towards provable energy-stable overset grid methods using sub-cell summation-by-parts operators
• An entropy-stable and kinetic energy-preserving macro-element HDG method for compressible flows
• Entropy stable high-order discontinuous Galerkin spectral-element methods on curvilinear, hybrid meshes

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