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在某些特定条件下,Richards方程的解在时空上呈现陡峭的锋面。为能有效地模拟具有对流占优特性的非饱和多孔介质中的水流问题,推广一种内部惩罚间断有限元(Interior penalty discontinuous Galerkin,IPDG)方法应用于一维非饱和土壤水入渗问题的模拟。针对具有van Genuchten-Mualem模型和Dirichlet入渗边界条件的Richards方程,分别采用间断有限元法和标准有限元方法求解。借助于相对L2模和相对最大模误差进行讨论。几种不同质地的均质土壤水入渗的数值算例结果表明:相比标准有限元方法,间断有限元方法在选取的4种不同网格剖分单元结点上能够有效地模拟非饱和对流占优土壤水流问题,并且能够获得准确的全局质量守恒。
Under certain conditions, the solution of the Richards equation presents a steep frontier in time and space. In order to effectively simulate the water flow in unsaturated porous media with convection dominant characteristic, an interior penalty discontinuous Galerkin (IPDG) method is applied to simulate the problem of one-dimensional unsaturated soil infiltration . Richards equations with van Genuchten-Mualem model and Dirichlet infiltration boundary conditions are solved by the discontinuous finite element method and the standard finite element method, respectively. The discussion is based on the relative L2 mode and the relative maximum mode error. The results of several numerical examples of homogeneous soil water infiltration with different textures show that compared with the standard finite element method, the discontinuous finite element method can simulate the unsaturated convection effectively on the four selected mesh nodes Dominant soil water flow problems, and to obtain accurate global mass conservation.