The approximate deconvolution model for large-eddy simulation of compressible flows with finite volume schemes

The approximate deconvolution model for large-eddy simulation is formulated for a second-order finite volume scheme. With the approximate deconvolution model, an approximation of the unfiltered solution is obtained by repeated filtering, and given a good approximation of the unfiltered solution, the nonlinear terms of the Navier-Stokes equations are computed directly. The effect of scales not represented on the numerical grid is modeled by a relaxation regularization involving a secondary filter operation. A turbulent channel flow at a Mach number of M = 1.5 and a Reynolds number based on bulk quantities of Re = 3000 is selected for validation of the approximate deconvolution model implementation in a finite volume code. A direct numerical simulation of this configuration has been computed by Coleman et al. Overall, our large-eddy simulation results show good agreement with our filtered direct numerical simulation data. For this rather simple configuration and the low-order spatial discretization, differences between approximate deconvolution model and a no-model computation are found to be small.