An Efficient MMOCAA-DDM for Solving Advection Diffusion Equations.

In this paper, an efficient modified method of characteristics with adjust advection (MMOCAA) domain decomposition method (DDM) is analyzed for solving advection diffusion equations. On each non-overlapping block divided sub-domains, we take two half time steps along x-direction and y-direction, to solve the numerical solutions on each sub-domain at every time interval, respectively. The intermediate numerical solutions in the interiors of sub-domains are first computed by redefining three mass fluxes. Then we compute the other intermediate interior numerical solutions by the weighted scheme from the previous modified solutions. Finally, the interior solutions are computed by the splitting implicit solute-flux coupled scheme while the interface fluxes are computed explicitly by the local multi-point weighted scheme. The conservation, stability and convergence of our schemes are proved strictly. Numerical experiments are presented to illustrate the theoretical results and efficiency.