An edge based stabilized finite element method for solving compressible flows: formulation and parallel implementation

This paper presents a finite element formulation for solving multidimension al compressible flows. This method is inspired by our experience with the S UPG, finite volume (FV) and discontinuous-Galerkin (DG) methods. Our object ive is to obtain a stable and accurate finite element formulation for multi -dimensional hyperbolic-parabolic problems with particular emphasis on comp ressible flows. In the proposed formulation, the upwinding effect is introd uced by considering the flow characteristics along the normal vectors to th e element interfaces. This method is applied for solving inviscid, laminar and turbulent flows. The one-equation turbulence closure model of Spalart-A llmaras (S-A) is used. Several numerical tests are carried out, and a selec tion of two- and three-dimensional experiments is presented. The results ar e encouraging, and it is expected that more numerical experiments and theor etical analysis will lead to a greater insight into this formulation. We al so discuss algorithmic and parallel implementation issues. (C) 2001 Elsevie r Science BN. All rights reserved.