New proceedings paper submitted: A Subcell Finite Volume Positivity-Preserving Limiter for DGSEM Discretizations of the Euler Equations

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.

Preprint available at: https://arxiv.org/pdf/2102.06017.pdf

Evolution of the density for a Sedov blast simulation with periodic boundaries

Evolution of the density for a Sedov blast simulation with periodic boundaries