Benchmark stress tests for flow past a cylinder at higher Reynolds numbers using EMAC

Purpose The purpose of this paper is to considers 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. Design/methodology/approach The authors 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. Findings The study finds 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. Originality/value This paper presents new results for a challenging test case where accurate simulations over a long time-period are necessary. To the best of the authors’ knowledge, the instability of EMAC for higher-order Taylor–Hood elements on coarse meshes has not been previously observed.