High-Order Flux Reconstruction Schemes for LES on Tetrahedral Meshes

The use of the high-order Flux Reconstruction (FR) spatial discretization scheme for LES on unstructured meshes is investigated. Simulations of the compressible Taylor-Green vortex at \(Re=1{,}600\) demonstrate that the FR scheme has low numerical dissipation and accurately reproduces the turbulent energy cascade at low resolution, making it ideal for high-order LES. To permit the use of subgrid-scale models incorporating explicit filtering on tetrahedral meshes, a high-order filter acting on the modal form of the solution (i.e. the Dubiner basis functions) is developed. The WALE-Similarity mixed (WSM) model using this filter is employed for LES of the flow over a square cylinder at \(Re=21{,}400\), obtaining reasonable agreement with experiments. Future research will be directed at improved SGS models and filters and at developing high-order hybrid RANS/LES methods.