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

TL;DR

This paper investigates how entropy projection in high order entropy stable discontinuous Galerkin schemes enhances robustness and reduces the need for additional limiting in under-resolved variable-density flow simulations.

Contribution

It demonstrates numerically that entropy stable DG methods with entropy projection are more robust and less prone to positivity violations in complex flow scenarios.

Findings

Entropy projection improves robustness in DG schemes.

Reduced need for limiting in variable-density flows.

Enhanced stability in under-resolved simulations.

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.