The Domain Decomposition Method Of The 2-Dimensional Convection-Diffusion Parabolic Problems

The groundawater quality model usually can be described as convection-diffusion equations or problems including this type of partial differential equation set. By means of rainfall, irrigation, etc, sewage from plants and mines, chemical fertilizer used in farming work and life sewage in town places usually getted into the underground and polluted the groundwater. Pollutes dissolved in the water convected and diffused along with the groundwater. Consequently, it is an important subject to simulate and predict the groundwater water quality development through numerical method.With the rapid of development of parallel computers and parallel algorithms, the Domain Decomposition Method (DDM) gets more recognition. It also provides a new method and a new thought. DDM is one of the most active research and application fields in current parallel numeric computation. The original solution can be translated into the sub-problems. The DDM divide the calculation domain into some sub=domains and the shape of sub-domain is regular as far as possible. The domain decomposition has many advantages:1) It can divide big problem into some little problems to reduce the calculation scale;2)Fast algorithms can be applied on the regular sub domains;3)It uses local quasi-uniform meshes nor the global one and even uses different discrete methods to calculate in different subdomains;4)It can use different mathematic models in different subdomains;5)The algorithm is parallel, that is, the calculate steps are processed in sub-domain independently.Finite difference method is one of the main numerical method to solve transport problem.It is sufficient for problems with diffusion term dominated or convection term not dominated.Yet when convection dominated diffusion,the problem is singularly perturbed with a boundary layer,and the solution has a great gradient alternation in the boundary layer.It will be nonphysically oscillated when the general finite difference method is used, which is not conform to the actual asymptotic property. As to the singular- perturbed problems,the arbitrary grid or uniform grid is not a good method, especially for multidimensional problems. The calculation is far beyond the hardware capability,and it is very hard to realize the uniform convergence on the uniform meshes.