Computation of Inviscid Supersonic Flows Around Cylinders and Spheres With the V-SGS Stabilization and $YZβ$ Shock-Capturing

The $YZβ$ shock-capturing technique was introduced originally for use in combination with the streamline-upwind/Petrov–Galerkin (SUPG) formulation of compressible flows in conservation variables. It is a simple residual-based shock-capturing technique. Later it was also combined with the variable subgrid scale (V-SGS) formulation of compressible flows in conservation variables and tested on standard 2D test problems. The V-SGS method is based on an approximation of the class of SGS models derived from the Hughes variational multiscale method. In this paper, we carry out numerical experiments with inviscid supersonic flows around cylinders and spheres to evaluate the performance of the $YZβ$ shock-capturing combined with the V-SGS method. The cylinder computations are carried out at Mach numbers 3 and 8, and the sphere computations are carried out at Mach number 3. The results compare well to those obtained with the $YZβ$ shock-capturing combined with the SUPG formulation, which were shown earlier to compare very favorably to those obtained with the well established OVERFLOW code.