## Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and $$YZ\beta$$ shock-capturing.(English)Zbl 1176.76077

Summary: 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 “$$YZ\beta$$ 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 $$YZ\beta$$ Shock-Capturing compare very favorably to those obtained with the well established OVERFLOW code.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76J20 Supersonic flows

OVERFLOW
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### References:

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