Simulation of laminar to transitional wakes past cylinders with a discontinuous Galerkin inviscid shallow water model

Abstract

Laminar to transitional wakes occur in slow, quasi-steady flows past cylinders at low cylinder Reynolds numbers (R ed ≤ 250). Inviscid numerical solvers of the depth-averaged shallow water equations (SWE) introduce numerical dissipation that, depending on Red , may imitate the mechanisms of viscous turbulent models. However, the numerical dissipation rate in a second-order finite volume (FV2) SWE solver is so large at a practical resolution that this can instead hide these mechanisms. The extra numerical complexity of the second-order discontinuous Galerkin (DG2) SWE solver results in a lower dissipation rate, making it a potential alternative to the FV2 solver to reproduce cylinder wakes. This paper compares the DG2 and FV2 solvers, initially for wake formation behind one cylinder. The findings confirm that DG2 can reproduce the expected wake formations, which FV2 fails to capture, even at a 10-fold finer resolution. It is further demonstrated that DG2 is capable of reproducing key features of the flow fields observed in a laboratory random cylinder array.