An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part II: Subcell finite volume shock capturing

Rueda-Ramírez, Andrés M.; Hennemann, Sebastian; Hindenlang, Florian; Winters, Andrew R.; Gassner, Gregor J.

doi:10.1016/j.jcp.2021.110580

Cited by 21 publications

(14 citation statements)

References 70 publications

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“…Proof. The proof of entropy conservation/stability for the LGL-DGSEM was originally presented by Bohm et al [21], and can also be found in [28], where the exact same notation of this paper is used.…”

Section: Entropy-stable Lgl-dgsem For the Non-conservative Glm-mhd Sy...mentioning

confidence: 99%

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Entropy-Stable Gauss Collocation Methods for Ideal Magneto-Hydrodynamics

Rueda-Ramírez¹,

Hindenlang²,

Chan³

et al. 2022

Preprint

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Section: Entropy-stable Lgl-dgsem For the Non-conservative Glm-mhd Sy...mentioning

confidence: 99%

“…We adopt the notation of [21,18,27,28] to work with vectors of different nature. Spatial vectors are noted with an arrow (e.g.…”

Section: Notationmentioning

confidence: 99%

Entropy-Stable Gauss Collocation Methods for Ideal Magneto-Hydrodynamics

Rueda-Ramírez¹,

Hindenlang²,

Chan³

et al. 2022

Preprint

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“…A particular class of DG methods, known as Discontinuous Galerkin Spectral Element Methods (DGSEM), can be combined with a split-form representation of the governing equations [6] or entropy-stable fluxes [1] to obtain non-linear stability and hence increased robustness. Nevertheless, these schemes still suffer from positivity issues in the presence of shocks [7,12] and under-resolved turbulence.…”

Section: Introductionmentioning

confidence: 99%

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

Rueda-Ramírez¹,

Gassner²

2021

Preprint

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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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“…This article presents our experience with efficient implementation techniques for flux differencing methods based on our open source projects Trixi.jl [56,60] (written in Julia [4]) and FLUXO 1 (written in Fortran), e.g., [59]. These two codes are written in different languages and use different approaches in many aspects.…”

Section: Introductionmentioning

confidence: 99%

Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws

Ranocha¹,

Schlottke-Lakemper²,

Chan³

et al. 2021

Preprint

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Many modern discontinuous Galerkin (DG) methods for conservation laws make use of summation by parts operators and flux differencing to achieve kinetic energy preservation or entropy stability. While these techniques increase the robustness of DG methods significantly, they are also computationally more demanding than standard weak form nodal DG methods. We present several implementation techniques to improve the efficiency of flux differencing DG methods that use tensor product quadrilateral or hexahedral elements, in 2D or 3D respectively. Focus is mostly given to CPUs and DG methods for the compressible Euler equations, although these techniques are generally also useful for GPU computing and other physical systems including the compressible Navier-Stokes and magnetohydrodynamics equations. We present results using two open source codes, Trixi.jl written in Julia and FLUXO written in Fortran, to demonstrate that our proposed implementation techniques are applicable to different code bases and programming languages.

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An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part II: Subcell finite volume shock capturing

Cited by 21 publications

References 70 publications

Entropy-Stable Gauss Collocation Methods for Ideal Magneto-Hydrodynamics

Entropy-Stable Gauss Collocation Methods for Ideal Magneto-Hydrodynamics

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

Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws

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