AI 中文总结
本文提出一种基于能量原理的非协调有限差分离散裂缝模型，可高效处理裂缝性多孔介质单相流，经数值实验验证其准确性与灵活性。
AI 中文摘要
针对裂缝性多孔介质中的单相流问题，本文提出一种有限差分离散裂缝模型。该方法源自统一能量原理，在笛卡尔网格上实现，无需与裂缝协调。它不引入额外自由度，仅在局部修改基础有限差分格式，可处理高导流裂缝和低渗透屏障，且天然保持离散系统的对称性与正定性。通过低成本局部后处理可恢复屏障引发的压力跃变和裂缝引发的通量，更清晰地表征界面效应。基于 manufactured 解及已发表的二维、三维基准问题的数值实验，验证了该方法对孤立裂缝、复杂网络和各向异性多孔介质的准确性、有效性与灵活性。
英文摘要
We propose a finite difference discrete fracture model for single-phase flow in fractured porous media. The method is derived from a unified energy principle and is implemented on Cartesian grids that need not conform to the fractures. It introduces no additional degrees of freedom, modifies the underlying finite difference scheme only locally, handles both highly conductive fractures and low-permeability barriers, and naturally preserves symmetry and positive definiteness of the discrete system. Barrier-induced pressure jumps and fracture-induced fluxes can be recovered through inexpensive local post-processing, yielding a sharper representation of the interface effects. Numerical experiments based on manufactured solutions and published $2$D and $3$D benchmark problems demonstrate the accuracy, effectiveness, and flexibility of the method for isolated fractures, complex networks, and anisotropic porous media.
