Computation of Compressible and Incompressible Flows with a Space–time Stabilized Finite Element Method

This paper presents the numerical results of compressible and incompressible flow problems through a unified approach based on a stabilized space–time finite element method. The numerical approach is continuous in space and discontinuous in time. The proposed method starts by the use of a stabilized space–time variational formulation, which allows the use of the same order interpolation functions for all solution variables. The numerical technique is tested through comparison with standard compressible and incompressible flow benchmarks. Compressible flow cases include 1D and 2D shock problems. Incompressible flow cases include lid-driven cavity flow and flow over a backward-facing step computed over a range of Re numbers. The results demonstrate high stability and accuracy of the numerical technique over a wide range of flow regimes, suggesting straightforward extension to many flow cases not yet investigated.