Physics based GMRES preconditioner for compressible and incompressible Navier-Stokes equations

Published in Comput. Methods Appl. Mech. Engrg. Vol. 154 (3–4), pp. 203-228, 1998
doi: 10.1016/S0045-7825(97)00129-1

Abstract

This paper presents the implementation of a local physics preconditioning mass matrix [8] for an unified approach of 3D compressible and incompressible Navier-Stokes equations using an SUPG finite element formulation and GMRES implicit solver. During the last years a lot of effort has been dedicated to finding a unified approach for compressible and 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 problems [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 community. The local feature of the preconditioner presented here means that no communication among processors is needed when working on parallel architectures. Due to these facts we consider that this research can make some contributions towards the development of a unified fluid dynamic model with high rates of convergence for any combination of Mach and Reynolds numbers, being very suitable for massively parallel computations.

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 lead to solutions without physical meaning.