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

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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### References:

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