Toward structural LES modeling with high-order spectral difference schemes

The combination of the high-order unstructured spectral difference spatial discretization scheme with sub-grid scale modeling for large-eddy simulation was 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 computations of turbulent channel flow at Reτ = 180 and 395 and flow past a confined circular cylinder at ReD = 2580 were compared against direct numerical simulation and particle image velocimetry measurements, respectively. 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.