A Subcell Finite Volume Positivity-Preserving Limiter for DGSEM Discretizations of the Euler Equations

TL;DR

This paper introduces a positivity-preserving limiter for DGSEM discretizations of the Euler equations, ensuring positive density and pressure in challenging simulations involving shocks and vortices.

Contribution

It develops a hybrid FV/DGSEM scheme that guarantees positivity in compressible Euler simulations, enhancing robustness in under-resolved and shock-dominated flows.

Findings

Ensures positive density and pressure in Euler simulations.

Effective in under-resolved vortex and shock simulations.

Compatible with standard and split-form DGSEM.

Abstract

In this paper, we present a positivity-preserving limiter for nodal Discontinuous Galerkin disctretizations of the compressible Euler equations. We use a Legendre-Gauss-Lobatto (LGL) Discontinuous Galerkin Spectral Element Method (DGSEM) and blend it locally with a consistent LGL-subcell Finite Volume (FV) discretization using a hybrid FV/DGSEM scheme that was recently proposed for entropy stable shock capturing. We show that our strategy is able to ensure robust simulations with positive density and pressure when using the standard and the split-form DGSEM. Furthermore, we show the applicability of our FV positivity limiter in extremely under-resolved vortex dominated simulations and in problems with shocks.