The approximate deconvolution model for compressible flows: Isotropic turbulence and shock-boundary-layer interaction

A formulation of the approximate deconvolution model (ADM) for the large-eddy simulation of flows in complex geometries is detailed and applied to compressible turbulent flows. The paper considers two different issues. First, we study the feasibility of low-order schemes with ADM for large-eddy simulation. As test case compressible decaying isotropic turbulence is considered. Results obtained with low-order finite difference schemes and a pseudospectral scheme are compared with filtered well-resolved direct numerical simulation (DNS) data. It is found that even for low-order schemes very good results can be obtained if the cutoff wavenumber of the filter is adjusted to the modified wavenumber of the differentiation scheme. Second, we consider the application of ADM to large-eddy simulation of the turbulent supersonic boundary layer along a compression ramp, which exhibits considerable physical complexity due to the interaction of shock, separation, and turbulence in an ambient inhomogeneous shear flow. The results compare very well with filtered DNS data and the filtered shock solution is correctly predicted by the ADM procedure, demonstrating that turbulent and non-turbulent subgrid-scales are properly modeled. We found that a computationally expensive shock-capturing technique as used in the DNS was not necessary for stable integration with the LES.