On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows

2022/03/19 by Jesse Chan, Chan, Jesse, Hendrik Ranocha +7 · 2 citations
Computer Science · Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2203.10238

arxiv created 2022/03/19 · arxiv updated 2022/03/22

Abstract

High order entropy stable schemes provide improved robustness for computational simulations of fluid flows. However, additional stabilization and positivity preserving limiting can still be required for variable-density flows with under-resolved features. We demonstrate numerically that entropy stable DG methods which incorporate an "entropy projection" are less likely to require additional limiting to retain positivity for certain types of flows. We conclude by investigating potential explanations for this observed improvement in robustness.

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• Entropy stable finite difference methods via entropy correction artificial viscosity and knapsack limiting
• Entropy stable high-order discontinuous Galerkin spectral-element methods on curvilinear, hybrid meshes

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