Computation of inviscid compressible flows with the V-SGS stabilization and YZβ shock-capturing

The YZβ shock-capturing technique was introduced recently for use in combination with the streamline-upwind/Petrov-Galerkin formulation of compressible flows in conservation variables. The YZβ shock-capturing parameter is much simpler than an earlier parameter derived from the entropy variables for use in conservation variables. In this paper, we propose to use the YZβ shock-capturing in combination with the variable subgrid scale (V-SGS) formulation of compressible flows in conservation variables. The V-SGS method is based on an approximation of the class of SGS models derived from the Hughes variational multiscale method. We evaluate the performance of the V-SGS and YZβ combination in a number of standard, 2D test problems. Compared to the earlier shock-capturing parameter derived from the entropy variables, in addition to being much simpler, the YZβ shock-capturing parameter yields better shock quality in these test problems.