An Edge Based Stabilized Finite Element Method For Solving Compressible Flows: Formulation And Parallel Computation

摘要

This paper presents a finite element formulation for solving multidimensional compressible flows. This method has been inspired by our experience with the SUPG, the Finite Volume and the discontinous-Galerkin methods. Our objective is to obtain a stable and accurate finite element formulation for multidimensional hyperbolic-parabolic problems with particular emphasis on compressible flows. In the proposed formulation, the 'upwinding' effect is introduced by considering the flow characteristics along the normal vectors to the element interfaces. Preliminary numerical results are encouraging, and it is expected that more numerical experiments and theoretical analysis will lead to greater insight into this promising formulation. The computational performance issue is addressed through a parallel implementation of the finite element data structure and the iterative solver. PSPARSLIB and MPI libraries are used for this purpose. The implicit parallel solver developed is based on the nonlinear version of the Flexible GMRES and Additive Schwarz algorithms.