Improved SUPG formulations for compressible flows

Stabilization and shock-capturing parameters introduced recently for the StreamlineUpwind/Petrov-Galerkin (SUPG) formulation of compressible flows based on conservation variables are assessed in test computations with inviscid supersonic flows and different types of finite element meshes. The new shock-capturing parameters, categorized as "YZbeta Shock-Capturing" in this paper, are compared to earlier parameters derived based on the entropy variables. In addition to being much simpler, the new shock-capturing parameters yield better shock quality the test computations, with more substantial improvements seen for triangular elements.; Numerical experiments with inviscid supersonic flows around cylinders and spheres are carried out to evaluate the stabilization and shock-capturing parameters introduced recently for the Streamline-Upwind/Petrov-Galerkin (SUPG) formulation of compressible flows based on conservation variables. The tests with the cylinders are carried out for both structured and unstructured meshes. The new shock-capturing parameters; which we call "YZbeta Shock-Capturing", are compared to earlier SUPG parameters derived based on the entropy variables. In addition to being much simpler, the new shock-capturing parameters yield better shock quality in the test computations, with more substantial improvements seen for unstructured meshes with triangular and tetrahedral elements. Furthermore, the results obtained with YZbeta Shock-Capturing compare very favorably to those obtained with the well established OVERFLOW code.