中文摘要：

以控制体尺度取粗网格尺度的一半为例，探讨有限差分异质多尺度方法（FDHMM）求解非饱和土壤水流问题的计算效率。考虑两种不同的本构关系，把这种数值方法应用于包括不同的土壤质地和边界条件的几个测试例子中。在应用FDHMM模拟非均质非饱和土壤中的水流问题时，对于局部微观模型的求解，既考虑Dirichlet边界也考虑周期边界。数值实验表明：在仅使用一半微观信息的情况下，FDHMM能够有效地模拟特定土壤中的非稳定非饱和水流问题，单胞问题使用Dirichlet边界条件的FDHMM能大幅度地节省计算费用。数值实验还表明：FDHMM能够获得准确的全局质量守恒，且是一个全局收敛的算法。

英文摘要：

For the case that the cell size equals a half of the coarse mesh size,the efficiency of the finite difference heterogeneous muhiscale method （FDHMM） for transient unsaturated water flow problems in random porous media was discussed. Considering two different constitutive relationships, this method was applied to several test examples with different soil textures and boundary conditions. Both the Dirichlet and the periodic bounday conditions were considered for solving the local microscopic model when the water flow in heterogeneous unsaturated soils was simulated by FDHMM. The numerical experiments demonstrated that, for the case that only a half of the information of the whole microstructure was used, FDHMM could effectively simulate the transient unsaturated water flow in the specific soils, FDHMM with the Dirichlet boundary condition for cell problem could offer remarkable saving in computational cost. The numerical experiments also demonstrated that FDHMM could achieve accurate global mass balance and was a globally convergent algorithm.