On the choice of viscous discontinuous Galerkin discretization for entropy correction artificial viscosity methods

TL;DR

This paper analyzes the discretization of entropy correction artificial viscosity (ECAV) using a local discontinuous Galerkin method, demonstrating its stability, contact preservation, and advantages over traditional shock capturing methods.

Contribution

It provides a rigorous analysis of ECAV discretized with LDG, establishing bounds and properties that improve understanding of its numerical behavior.

Findings

ECAV has an $O(h)$ upper bound on the viscosity coefficient

ECAV does not impose restrictive time-step conditions

ECAV is contact preserving

Abstract

Entropy correction artificial viscosity (ECAV) is an approach for enforcing a semi-discrete entropy inequality through an entropy dissipative correction term. The resulting method can be implemented as an artificial viscosity with an extremely small viscosity coefficient. In this work, we analyze ECAV when the artificial viscosity is discretized using a local discontinuous Galerkin (LDG) method. We prove an $O(h)$ upper bound on the ECAV coefficient, indicating that ECAV does not result in a restrictive time-step condition. We additionally show that ECAV is contact preserving, and compare ECAV to traditional shock capturing artificial viscosity methods.