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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.09274 |
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| _version_ | 1866915385823985664 |
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| author | von Wahl, Henry Rebholz, Leo G. Scott, L. Ridgway |
| author_facet | von Wahl, Henry Rebholz, Leo G. Scott, L. Ridgway |
| contents | We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder at Reynolds numbers 500 and 1000, where the solution is observed to be periodic when the problem is sufficiently resolved. Computing the resulting flow is a challenge, even for exactly divergence-free discretization methods, when the scheme does not include sufficient numerical dissipation. We examine the performance of the energy, momentum and angular momentum conserving (EMAC) formulation of the Navier-Stokes equations. This incorporates more physical conservation into the finite element method even when the numerical solution is not exactly divergence-free. Consequently, it has a chance to outperform standard methods, especially for long-time simulations. We find that for lowest-order Taylor-Hood elements, EMAC outperforms the standard convective formulations. However, for higher-order elements, EMAC can become unstable on under-resolved meshes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09274 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Benchmark stress tests for flow past a cylinder at higher Reynolds numbers using EMAC von Wahl, Henry Rebholz, Leo G. Scott, L. Ridgway Numerical Analysis Fluid Dynamics We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder at Reynolds numbers 500 and 1000, where the solution is observed to be periodic when the problem is sufficiently resolved. Computing the resulting flow is a challenge, even for exactly divergence-free discretization methods, when the scheme does not include sufficient numerical dissipation. We examine the performance of the energy, momentum and angular momentum conserving (EMAC) formulation of the Navier-Stokes equations. This incorporates more physical conservation into the finite element method even when the numerical solution is not exactly divergence-free. Consequently, it has a chance to outperform standard methods, especially for long-time simulations. We find that for lowest-order Taylor-Hood elements, EMAC outperforms the standard convective formulations. However, for higher-order elements, EMAC can become unstable on under-resolved meshes. |
| title | Benchmark stress tests for flow past a cylinder at higher Reynolds numbers using EMAC |
| topic | Numerical Analysis Fluid Dynamics |
| url | https://arxiv.org/abs/2507.09274 |