A parallel Schwarz method for a convection-diffusion problem

This paper describes a parallel convection-diffusion solver which may be used as part of a Navier-Stokes solver for three-dimensional channel flow at moderately large Reynolds numbers [S. Turek, Efficient Solvers for Incompessible Flow Problems: An Algorithmic Approach in View of Computational Aspects, Springer-Verlag, 1999]. The solver uses a multiplicative Schwarz domain decomposition with overlapping subdomains to solve singularly perturbed convection-diffusion equations where convection is dominant. Upwind finite differences are used for the spatial discretization. The algorithm uses special features of the singularly perturbed convection-diffusion operator. The error due to a local perturbation of the boundary conditions decays extremely fast, in the upwind as well as the crosswind direction, so the overlap in the domain decomposition can be kept to a minimum. The algorithm parallelizes well and is particularly suited for applications in three dimensions. Results of two- and three-dimensional numerical experiments are presented.