Deconvolution of Subgrid-scales for the Simulation of Shock-turbulence Interaction

We develop and compare two approaches for the proper simulation of flow discontinuities. For the filtered evolution equations the solution is smooth and can be solved for by standard difference schemes without special considerations of discontinuities. Both approaches are based on approximate deconvolution of the filtered solution to obtain a sufficiently accurate representation of the smoothed nonlinear combination of discontinuous fields, e.g., the convection term. One approach is based on a regularized direct deconvolution and requires for stable integration a secondary filter. The other approach is based on an expansion of the filtered field in terms of filter width, which is modified in the vicinity of discontinuities in order to exactly recover the filtered profile. We detail both approaches and investigate their feasibility for the inviscid Burgers equation, isothermal and full Euler equations.