LES modeling with high-order flux reconstruction and spectral difference schemes

The combination of the high-order unstructured flux reconstruction and spectral difference spatial discretization schemes with sub-grid scale modeling for large-eddy simulation is investigated with particular focus on the consistent implementation of a structural mixed model based on the scale similarity hypothesis. The difficult task of deriving a consistent formulation for the discrete filter within hexahedral elements of arbitrary order led to the development of a new class of three-dimensional constrained discrete filters. Results from different canonical tests cases, including turbulent channel flows and turbulent wakes behind bluff bodies at various Reynolds numbers, are presented. The numerical experiments suggest that the results are sensitive to the use of an sub-grid scale closure, even when a high-order numerical scheme is used, especially when the grid resolution is kept relatively low. The use of the similarity mixed formulation proved to be particularly accurate in reproducing sub-grid scale interactions, confirming that its well-known potential can be realized in conjunction with state-of-the-art high-order numerical schemes.