A new hybrid discrete–continuum numerical approach that explores the key advantages of both discrete and continuum approaches is proposed to model unsaturated seepage flows through porous media. In contrast to existing approaches where a porous medium is often represented by a continuum medium or required a background mesh, the proposed approach explicitly exploits the discrete contact network formed by an assembly of discrete solid particles. Each solid particle is assumed to occupy an equivalent-continuum space, over which the governing equations for unsaturated seepage flow are derived. These governing equations are then discretised and solved on the discrete contact network through a new numerical procedure that links micro-diffusivity to the macro-one. Thanks to this concept, the proposed approach is capable of describing the nature of flow in unsaturated porous media at the microscale level. This unique feature also enables the proposed approach to naturally simulate the water flow through the heterogeneous porous media without any ad hoc treatments. In this paper, the mathematical concept of the proposed approach together with its implementation features and performances for a rigid porous media is presented and discussed. The focus is placed on its application to the discrete element method (DEM), although the proposed concept, in general, can be applied to any other methods possessing similar features.

提出了一种新的离散离散连续体混合数值方法，该方法探索了离散方法和连续体方法的主要优点，以模拟通过多孔介质的非饱和渗流。与多孔介质通常由连续介质代表或需要背景网格的现有方法相反，所提出的方法明确地利用了由离散固体颗粒的集合形成的离散接触网络。假定每个固体颗粒都占据一个等效连续空间，在该空间上可以导出非饱和渗流的控制方程。然后，通过新的将微扩散性与宏一联系起来的数值程序，将这些控制方程离散化并在离散接触网络上求解。有了这个概念，所提出的方法能够在微观水平上描述不饱和多孔介质中流动的性质。这种独特的功能还使所提出的方法能够自然模拟通过非均质多孔介质的水流，而无需任何特殊处理。在本文中，提出并讨论了该方法的数学概念，以及其在刚性多孔介质中的实现特征和性能。尽管通常可以将所提出的概念应用于具有相似特征的任何其他方法，但是重点放在将其应用于离散元素方法（DEM）上。在本文中，提出并讨论了该方法的数学概念，以及其在刚性多孔介质中的实现特征和性能。尽管通常可以将所提出的概念应用于具有相似特征的任何其他方法，但是重点放在将其应用于离散元素方法（DEM）上。在本文中，提出并讨论了该方法的数学概念，以及其在刚性多孔介质中的实现特征和性能。尽管通常可以将所提出的概念应用于具有相似特征的任何其他方法，但是重点放在将其应用于离散元素方法（DEM）上。