The Upwind Discontinuous Volume Method For The Two-Dimensional Unsaturated Water Movement Problems

In this paper, we fistly propose a numerical simulation method for the following unsaturated water movement problems[62]: as follows:upwind discontinuous finite volume element method, which is a combina-tion of upwind technique and discontinuous finite volume element method proposed by XiuYe. Except for inheriting the advantage of discontinuous finite volume el-ement, such as high-precision, high-parallel, local conservation, it also have the simplicity of space construction. And have some thought of the windward, upwind techniques can eliminate the instability of the numerical solution effectively, and eliminate the nonphysical oscillation successfully.The semi discretization and fully discretization discontinuous finite volume pro-cedures for this problem are proposed in chapter two. And then we propose the auxiliary formulation and give the error analysis. After detailed theoretical analy-sis, the error estimates of L2-norm and|||·|||1,h-norm are obtained. According to numerical examples of chapter three, we proved the effectiveness of this method.