A modified upwind difference domain decomposition method for convection-diffusion equations

摘要

A new, efficient and noniterative type of domain decomposition method is presented for three-dimensional convection-diffusion equations, whose convection term is handled by modified upwind differences. The whole domain is decomposed into several nonoverlapping subdomains. The values on inter-domain boundaries are calculated by reduced-dimensional solver and the solutions in subdomains are computed by implicit upwind procedures completely in parallel. With certain weakened stability constraint, error estimates in discrete l~2 norm is discussed by introducing new inner products and techniques of prior estimates. Finally, the theoretical results are illustrated by linear and nonlinear numerical experiments.