Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. (English) Zbl 1122.76061

Tezduyar, Tayfun E.; Senga, Masayoshi

Comput. Methods Appl. Mech. Eng. 195, No. 13-16, 1621-1632 (2006).

Summary: The streamline-upwind/Petrov-Galerkin (SUPG) formulation is one of the most widely used stabilized methods in finite element computation of compressible flows. It includes a stabilization parameter that is known as \(\tau\). Typically the SUPG formulation is used in combination with a shock-capturing term that provides additional stability near the shock fronts. The definition of the shock-capturing term includes a shock-capturing parameter. In this paper, we describe, for the finite element formulation of compressible flows based on conservation variables, new ways for determining the \(\tau\) and the shock-capturing parameter. The new definitions for the shock-capturing parameter are much simpler than the ones based on the entropy variables, involve less operations in calculating the shock-capturing term, and yield better shock quality in test computations.

MSC:

76M10	Finite element methods applied to problems in fluid mechanics
76N15	Gas dynamics (general theory)
76L05	Shock waves and blast waves in fluid mechanics

Keywords:

finite element formulation; oblique shock; reflected shock

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