A Strang-type alternating segment domain decomposition method for 2-D parabolic problems is proposed. The domain can be divided into non-overlapping multi-block sub-domains by the idea of alternating segments. Strang-type splitting technique reduces complexity of the solving of the high dimensional problems by a series of one-dimensional ones. The method is proved to be unconditionally stable and truncation error is analyzed. Numerical experiments show that convergence rates in time and space are both second order.

The simulation of the process and the effects of protection projects lays the foundation of its effective control and defence. A mathematical model of the problem and the upwind fractional step finite difference method are presented. Using this method, the numerical simulation of seawater intrusion in Laizhou Bay Area of Shandong Province is given. The numerical results turn out to be identical with the real measurements, so the prediction of the consequences of protection projects is reasonable.

In this paper, for the two-phase immiscible and miscible displacement problems we propose two kinds-of new numerical methods: the viscosity splitting method and the upwind difference method over arbitraty triangulation pratitions, and discuss their theoretical analyses. The numerical results are very efficient and reasonable for model problem.