SPACE-TIME FINITE-ELEMENT COMPUTATION OF COMPRESSIBLE FLOWS INVOLVING MOVING BOUNDARIES AND INTERFACES

The deformable-spatial-domain / stabilized-space-time (DSD/SST) formulation, introduced by Tezduyar et al. is applied to 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 of the problem, 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 equation systems 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.