Computation of inviscid compressible flows with the V‐SGS stabilization and <i>YZ</i>β shock‐capturing

Abstract The YZ β shock‐capturing technique was introduced recently for use in combination with the streamline‐upwind/Petrov–Galerkin formulation of compressible flows in conservation variables. The YZ β 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 YZ β 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 YZ β 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 YZ β shock‐capturing parameter yields better shock quality in these test problems. Copyright © 2007 John Wiley &amp; Sons, Ltd.