PHYSICS-BASED GMRES PRECONDITIONER FOR COMPRESSIBLE AND INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

This paper presents the implementation of a local physics precondition ing mass matrix [8] for an unified approach of 3D compressible and inc ompressible Navier-Stokes equations using an SUPG finite element formu lation and GMRES implicit solver. During the last years a lot of effor t has been dedicated to finding a unified approach for compressible an d incompressible flow in order to treat fluid dynamic problems with a very wide range of Mach and Reynolds numbers [10,26,37]. On the other hand, SUPG finite element formulation and GMRES implicit solver is one of the most robust combinations to solve state of the art CFD problem s [1,6,9,22,29,30,31]. The selection of a good preconditioner and its performance on parallel architecture is another open problem in CFD co mmunity. The local feature of the preconditioner presented here means that no communication among processors is needed when working on paral lel architectures. Due to these facts we consider that this research c an make some contributions towards the development of a unified fluid dynamic model with high rates of convergence for any combination of Ma ch and Reynolds numbers, being very suitable for massively parallel co mputations. Finally, it is important to remark that while this kind of preconditioning produces stabilized results in nearly incompressible regimes the standard version exhibits some numerical drawbacks that le ad to solutions without physical meaning. (C) 1998 Elsevier Science S. A.