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arxiv: 2102.06017 · v1 · pith:UZB4NRIU · submitted 2021-02-11 · math.NA · cs.NA· physics.comp-ph

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

Andr\'es M. Rueda-Ram\'irez , Gregor J. Gassner This is my paper

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classification math.NA cs.NAphysics.comp-ph
keywords dgsemlimiterdiscontinuousequationseulerfinitegalerkinpositivity-preserving
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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.

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  1. Invariant-domain-preserving limiting with Adaptive Mesh Refinement for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral Element Methods

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    Sparse invariant-domain-preserving mortar fluxes based on LGL subcell characteristic functions enable convex limiting and AMR for LGL-DGSEM on nonconforming Cartesian interfaces.