DOMAIN DECOMPOSITION ALGORITHMS for COMPRESSIBLE 
             EULER's and N. S. EQUATIONS  on UNSTRUCTURED MESHES


                                Xiao-Chuan Cai
                        Department of Computer Science
                       University of Colorado at Boulder

                                Charbel Farhat
                     Department of Aerospace Engineering
                      University of Colorado at Boulder

                                Marcus Sarkis
                        Department of Computer Science
                      University of Colorado at Boulder


In this presentation, we shall discuss recent results on the use of
overllaping Schwarz methods for the numerical solution of steady and
time-dependent compressible Euler and Navier-Stokes equations.  The partial
differential equations are discretized by a combined finite element/finite
volume methods on unstructured meshes and using a MUSCL method.  Several
simulations are reported to compare the performance of domain decomposition
preconditioners for different geometries and regime flows.