Large-eddy simulation of shock-turbulence interaction

The approximate deconvolution model (ADM) for large-eddy simulation (LES) is adapted for use with a central fourth-order finite volume (Jameson-type) scheme widely applied for aerodynamics calculations of industrial interest. With ADM, 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 filtered Navier-Stokes equation are computed directly. The effect of scales not represented on the numerical grid is modeled by a relaxation regularization involving a secondary filter operation and a relaxation parameter. The supersonic turbulent boundary layer along a compression ramp at a freestream Mach number of M = 3 and a Reynolds number (based on free-stream quantities and the mean momentum thickness at inflow) of Re_θ = 1685 is computed to evaluate the ability of ADM to represent discontinuities and turbulent flow regions. It was observed that a unified modeling of discontinuities and turbulence required a local adaptation of the secondary filter used for the relaxation regularization. The LES results are compared with corresponding filtered direct-numerical-simulation (DNS) data. Very good agreement between the filtered DNS and the LES is observed for the mean, fluctuating, and averaged wall quantities.