In this paper, we are interested in an efficient numerical method for the mixed-dimensional approach to modeling single-phase flow in fractured porous media. The model introduces fractures and their intersections as lower-dimensional structures, and the mortar variable is used for flow coupling between the matrix and fractures. We consider a stable mixed finite element discretization of the problem, which results in a parameter-dependent linear system. For this, we develop block preconditioners based on the well-posedness of the discretization choice. The preconditioned iterative method demonstrates robustness with regard to discretization and physical parameters. The analytical results are verified on several examples of fracture network configurations, and notable results in reduction of number of iterations and computational time are obtained.

在本文中，我们感兴趣的是一种有效的数值方法，可用于对裂隙多孔介质中的单相流进行建模的混合维方法。该模型将裂缝及其交叉点作为低维结构引入，并且将砂浆变量用于矩阵与裂缝之间的流动耦合。我们考虑了问题的稳定混合有限元离散化，这导致了参数相关的线性系统。为此，我们基于离散化选择的正确性开发了块预处理器。预处理的迭代方法证明了在离散化和物理参数方面的鲁棒性。在裂缝网络配置的几个示例上验证了分析结果，并获得了减少迭代次数和减少计算时间的显着结果。