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

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.

On the Entropy Projection and the Robustness of High Order Entropy Stable Discontinuous Galerkin Schemes for Under-Resolved Flows

“…We perform additional experiments analyzing the robustness of entropy stable DGSEM and Gauss DG for the Kelvin-Helmholtz instability. The domain is [−1, 1] 2 with initial condition from [46]:…”