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Bibliographic Details
Main Authors: von Wahl, Henry, Rebholz, Leo G., Scott, L. Ridgway
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2507.09274
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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