中文摘要：

应用有限差分异质多尺度方法（FDHMM）求解以van Genuchten-Mualem模型或Gardner-Basha模型为本构关系的Richards方程。Richards方程中的水力参数是非均质的。基于一种＂异质＂的离散格式,FDHMM在小的代表性的空间区域内求解细尺度问题,这是通过在不同的网格水平上使用不同的差分格式处理原始方程来实现的。在应用FDHMM求解Richards方程时,对于局部微观模型的求解,既考虑Dirichlet边界也考虑周期边界。为了确保所讨论的方法的有效性,在宏观水流通量的估计中运用了一些前人提出的假设和结论。最后,给出了应用FDHMM求解Richards方程宏观演替的离散格式。

英文摘要：

The finite difference heterogeneous multiscale method（FDHMM） was extended to solve the Richards ’ equation with the van Genuchten-Mualem model or the Gardner-Basha model.Hydraulic parameters in the Richards’ equation are heterogeneous.Based on a heterogeneous discretization approach the FDHMM can deal with the fine scale problems in small representative region in spatial domain,it relies on the use of two different schemes for original equation,and at different grid levels.Both the Dirichlet and the periodic boundary conditions were considered for solving the local microscopic model when the Richards’equation was solved by FDHMM.Some restrictions and conclusions presented by previous researchers were applied to estimate the macroscopic flux in order to assure the efficiency of the discussed method.Lastly,a discrete scheme of macroscopic evolution was given.