Comparison of Entropy Stable Collocation High-Order DG Methods for Compressible Turbulent Flows
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910900240252928 |
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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 |