This paper presents a numerical simulation of the single phase Darcy flow model in two-dimensional fractured porous media. Under some physically consistent coupling conditions, the model can be described as a reduced problem by coupling the bulk problem in porous matrix and the fracture problem in fractures. Flows are governed by the primal form of the Darcy’s equations for both the bulk and fractures. The coupled discontinuous finite volume element methods and conforming finite element method are adopted to solve the bulk problem and fracture problem, respectively. We theoretically analyze the well-posedness of the discrete problem, and derive optimal error estimates in standard $L^2$ error and broken $H^1$ error. Numerical experiments include not only the fractures with high permeability as the prior flow conduit, but also the fractures with low permeability as the flow barrier, which demonstrate the accuracy, flexibility and robustness of our discrete formulation for complicated networks of fractures in porous media domain.

本文提出了二维裂缝性多孔介质中单相达西流动模型的数值模拟。在某些物理上一致的耦合条件下，通过耦合多孔基质中的体积问题和裂缝中的裂缝问题，可以将模型描述为简化问题。对于块体和裂缝，流量受达西方程式的原始形式支配。分别采用耦合不连续有限体积元法和相容有限元法分别求解体积问题和断裂问题。我们从理论上分析离散问题的适定性，并得出标准中的最佳误差估计${\mathrm{大号}}^2$ 错误和损坏 $H^{\mathrm{1个}}$错误。数值实验不仅包括高渗透率裂缝作为先导流体管道，而且还包括低渗透率裂缝作为流动屏障，这证明了我们离散公式在多孔介质领域复杂网络中的准确性，柔韧性和耐用性。