A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes––application to vortex shedding Original Research Article

The variational multiscale formulation of large eddy simulations developed by Hughes and his co-workers for incompressible turbulent flows is first extended to the case of compressible turbulent flows. Next, a finite volume/element discretization on tetrahedral meshes of this method is proposed. This discretization features an economical procedure based on agglomeration for separating a priori the scales, a corresponding projector for eliminating the small scales from the system of equations, and an effective control of the numerical dissipation induced by upwinding. The resulting LES method is validated with the three-dimensional numerical simulation of a low-speed flow past a square cylinder at M∞=0.1 and Re=22,000, and various comparisons with experimental data.