A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations

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

doi:10.1016/j.jcp.2020.109935

Cited by 67 publications

(62 citation statements)

References 43 publications

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“…We make use of the blended scheme by Hennemann et al [7] that combines a high-order DGSEM discretization with a first-order FV method on the corresponding LGL-subcell grid to obtain an accurate scheme with robust shock-capturing properties. As both schemes are constructed on the same subcell LGL distribution, they are directly compatible and thus the semi-discrete version of (1) is given bẏ…”

Section: Spatial Discretization: Hybrid Fv/dgsem Discretizationmentioning

confidence: 99%

“…The compatible LGL co-located first-order FV discretization proposed by Hennemann et al [7], which interprets the nodal values as the subcell mean values, readṡ…”

Section: Spatial Discretization: Hybrid Fv/dgsem Discretizationmentioning

confidence: 99%

“…Thus, we do not apply shock capturing by connecting α to a troubled cell indicator, e.g. [7], but instead just use α = 0 as our baseline high-order discretization.…”

Section: Kelvin-helmholtz Instabilitymentioning

confidence: 99%

“…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%

“…In this paper, we propose a novel positivity-preserving limiter for DGSEM discretizations that is based on a subcell FV discretization. We make use of the hybrid FV/DGSEM scheme that was recently developed by Hennemann et al [7] for shock capturing. The hybrid FV/DGSEM scheme blends a Legendre-Gauss-Lobatto (LGL) DGSEM discretization with a compatible LGL-subcell Finite Volume (FV) scheme in an element-wise manner.…”

Section: Introductionmentioning

confidence: 99%

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

Rueda-Ramírez¹,

Gassner²

2021

14th WCCM-ECCOMAS Congress

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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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Section: Spatial Discretization: Hybrid Fv/dgsem Discretizationmentioning

confidence: 99%

“…The compatible LGL co-located first-order FV discretization proposed by Hennemann et al [7], which interprets the nodal values as the subcell mean values, readṡ…”

Section: Spatial Discretization: Hybrid Fv/dgsem Discretizationmentioning

confidence: 99%

“…Thus, we do not apply shock capturing by connecting α to a troubled cell indicator, e.g. [7], but instead just use α = 0 as our baseline high-order discretization.…”

Section: Kelvin-helmholtz Instabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Rueda-Ramírez¹,

Gassner²

2021

14th WCCM-ECCOMAS Congress

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Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation

Wu,

Trask,

Chan

2024

Numerical Methods Partial

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High order schemes are known to be unstable in the presence of shock discontinuities or under‐resolved solution features, and have traditionally required additional filtering, limiting, or artificial viscosity to avoid solution blow up. Entropy stable schemes address this instability by ensuring that physically relevant solutions satisfy a semi‐discrete entropy inequality independently of discretization parameters. However, additional measures must be taken to ensure that solutions satisfy physical constraints such as positivity. In this work, we present a high order entropy stable discontinuous Galerkin (ESDG) method for the nonlinear shallow water equations (SWE) on two‐dimensional (2D) triangular meshes which preserves the positivity of the water heights. The scheme combines a low order positivity preserving method with a high order entropy stable method using convex limiting. This method is entropy stable and well‐balanced for fitted meshes with continuous bathymetry profiles.

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Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier–Stokes Equations

Winters

Kopriva

Gassner

et al. 2021

CISM International Centre for Mechanical Sciences

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A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations

Cited by 67 publications

References 43 publications

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

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

Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation

Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier–Stokes Equations

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