DNS and LES of the Flow Over Periodic Hills Based on a Discontinuous Galerkin Approach

Abstract

A high-order discontinuous Galerkin (DG) approach is used for the DNS and LES of the flow over periodically arranged hills. In order to assess the capacity of the DG method to capture the Reynolds-number dependent features of the flow, four Reynolds numbers are considered: 2800, 10 595, 19 000, and 37 000. The DG solutions are compared with the reference data available in the literature. For \(Re_b=10\,595\) the no-model and the WALE LES approaches are compared. The hp-convergence analyses performed for the DNS demonstrate the superior performance of increasing the polynomial order as compared to refining the mesh. It appears from this study that the use of a subgrid modelling approach together with an appropriate level of local hp-refinement could greatly improve the solution without penalising the computational cost of the simulation.