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Space-time finite element computation of compressible flows involving moving boundaries and interfaces. (English) Zbl 0798.76037

The deformable-spatial-domain/stabilized-space-time formulation is applied to the computation of viscous compressible flows involving moving boundaries and interfaces. The stabilization technique employed is a streamline-upwind/Petrov-Galerkin (SUPG) method, with a modified SUPG stabilization matrix. The stabilized finite element formulation of the governing equations is written over the space-time domain, and therefore the deformation of the spatial domain with respect to time is taken into account automatically. The frequency of remeshing is minimized to minimize the projection errors involved in remeshing and also to increase the parallelization potential of the computations. The implicit systems of equations arising from the space-time finite element discretizations are solved iteratively. It is demonstrated that the combination of the SUPG stabilization and the space-time approach gives the capability of handling complicated compressible flow problems, including those with moving surfaces and shock-boundary layer interactions.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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