A CONSERVATIVE DOMAIN DECOMPOSITION PROCEDURE FOR NONLINEAR DIFFUSION PROBLEMS ON ARBITRARY QUADRILATERAL GRIDS

The aim of the paper is to construct a conservative domain decomposition procedure for solving nonlinear diffusion equations. In this procedure, the underlying discretization consists of a cell-centered finite volume scheme on arbitrary quadrilateral grids, which is first linearized by the usual Picard nonlinear iteration. Then in each nonlinear iteration step a domain decomposition algorithm for solving the linearized problem is presented, in which Dirichlet boundary data at inner interfaces for subdomain problems are given by the adjacent cell-centered values obtained in the previous nonlinear iteration step. After the Picard nonlinear iteration converges, discrete flux boundary data are constructed at inner interfaces of subdomains. Finally, they serve as Neumann boundary conditions at inner interfaces to solve subdomain problems once more. The procedure is globally conservative since it is locally conservative both in the subdomains and across inner interfaces. Numerical results are presented to examine the performance of the conservative domain decomposition method, in terms of stability, accuracy, conservative error, and parallel speedup.