Domain Decomposition Algorithms and Computational Fluid Dynamics

Abstract

In the past several years, domain decomposition has been a very popular topic, partly because of the poten tial of parallelization. Although numerous theories and algorithms have been developed for model elliptic problems, they are only recently starting to be tested on realistic applications. This paper investigates the applica tion of some of these methods to two model problems in computational fluid dynamics: two-dimensional con vection-diffusion problems and the incompressible driven cavity flow problem. Our approach is the con struction and analysis of efficient preconditioners for the interface operator to be used in the iterative solution of the interface solution. For the convection-diffusion problems, we discuss the effect of the convection term and its discretization on the performance of some of the preconditioners. For the driven cavity problem, we dis cuss the effectiveness of a class of boundary probe preconditioners.