Comparison of Entropy Stable Collocation High-Order DG Methods for Compressible Turbulent Flows

Fuente: arXiv
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Auteurs principaux: Schwarz, Anna, Kempf, Daniel, Keim, Jens, Kopper, Patrick, Rohde, Christian, Beck, Andrea
Format: Preprint
Publié: 2025
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author Schwarz, Anna
Kempf, Daniel
Keim, Jens
Kopper, Patrick
Rohde, Christian
Beck, Andrea
author_facet Schwarz, Anna
Kempf, Daniel
Keim, Jens
Kopper, Patrick
Rohde, Christian
Beck, Andrea
contents High-order methods are well-suited for the numerical simulation of complex compressible turbulent flows, but require additional stabilization techniques to capture instabilities arising from the underlying non-linear hyperbolic equations. This paper provides a detailed comparison of the effectiveness of entropy stable discontinuous Galerkin methods for the stabilization of compressible (wall-bounded) turbulent flows. For this investigation, an entropy stable discontinuous Galerkin spectral element method is applied on Gauss-Legendre and Gauss-Lobatto nodes. In the compressible regime, an additional stabilization technique for shock capturing based on a convex blending of a low-order finite volume with the high-order discontinuous Galerkin operator is utilized. The present investigation provides a systematic study from convergence tests, to the Taylor-Green vortex and finally to a more intricate turbulent wall-bounded 3D diffuser flow, encompassing both weakly compressible and compressible regimes. The comparison demonstrates that the DGSEM on Gauss-Lobatto nodes is less accurate due to the lower integration accuracy. Conversely, it is faster than the DGSEM on Gauss-Legendre nodes due to a less severe time step restriction and simpler numerical operator. To the author's knowledge, this is the first time for which a comparison of entropy stable DGSEM on Gauss-Lobatto and Gauss-Legendre has been performed for compressible, wall-bounded turbulent flows with separation.
format Preprint
id arxiv_https___arxiv_org_abs_2504_00173
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Comparison of Entropy Stable Collocation High-Order DG Methods for Compressible Turbulent Flows
Schwarz, Anna
Kempf, Daniel
Keim, Jens
Kopper, Patrick
Rohde, Christian
Beck, Andrea
Fluid Dynamics
Computational Physics
High-order methods are well-suited for the numerical simulation of complex compressible turbulent flows, but require additional stabilization techniques to capture instabilities arising from the underlying non-linear hyperbolic equations. This paper provides a detailed comparison of the effectiveness of entropy stable discontinuous Galerkin methods for the stabilization of compressible (wall-bounded) turbulent flows. For this investigation, an entropy stable discontinuous Galerkin spectral element method is applied on Gauss-Legendre and Gauss-Lobatto nodes. In the compressible regime, an additional stabilization technique for shock capturing based on a convex blending of a low-order finite volume with the high-order discontinuous Galerkin operator is utilized. The present investigation provides a systematic study from convergence tests, to the Taylor-Green vortex and finally to a more intricate turbulent wall-bounded 3D diffuser flow, encompassing both weakly compressible and compressible regimes. The comparison demonstrates that the DGSEM on Gauss-Lobatto nodes is less accurate due to the lower integration accuracy. Conversely, it is faster than the DGSEM on Gauss-Legendre nodes due to a less severe time step restriction and simpler numerical operator. To the author's knowledge, this is the first time for which a comparison of entropy stable DGSEM on Gauss-Lobatto and Gauss-Legendre has been performed for compressible, wall-bounded turbulent flows with separation.
title Comparison of Entropy Stable Collocation High-Order DG Methods for Compressible Turbulent Flows
topic Fluid Dynamics
Computational Physics
url https://arxiv.org/abs/2504.00173