AI 中文总结
本文提出一种通过局部刚度矩阵修正的非拟合有限元离散裂缝模型，可高效建模低渗透屏障，经数值测试验证了其有效性。
AI 中文摘要
有限元方法是多孔介质流动最广泛使用的离散化方法之一，其针对高导流裂缝的离散裂缝模型（DFMs）已成熟建立。相比之下，低渗透屏障长期难以适配该框架，因为它们会产生连续单元无法直接表征的压力不连续性。本文提出一种线性有限元方法的简单扩展，通过对每个被屏障切割单元的局部刚度矩阵进行闭式修正来建模低渗透屏障。该方法保留完全相同的$H^1$协调$P^1$有限元空间，维持原始稀疏模式与对称正定性，无需网格拟合，且在远离屏障处与标准有限元方法一致。此外，一种廉价的纯局部后处理步骤可恢复在屏障界面处具有陡峭跃变的不连续压力场，从而消除连续解中存在的单元素宽度的模糊效应。通过 manufactured 解的收敛研究以及文献中的二维和三维基准问题，证实了该方法的有效性。
英文摘要
Finite element methods are among the most widely used discretizations for flow in porous media, and their discrete fracture models (DFMs) for highly conductive fractures are well-established. Low-permeability barriers, by contrast, have long resisted this framework because they induce pressure discontinuities that continuous elements cannot represent directly. In this paper, we propose a simple extension of the linear finite element method for modeling low-permeability barriers through a closed-form modification of the local stiffness matrix of each barrier-cut element. The method retains exactly the same $H^1$-conforming $P^1$-finite element space, preserves the original sparsity pattern and symmetric positive definiteness, requires no mesh fitting, and coincides with the standard finite element method away from barriers. Moreover, an inexpensive, purely local post-processing step recovers the discontinuous pressure field with a sharp jump at the barrier interface, thereby removing the one-element-wide smearing present in the continuous solution. Convergence studies with manufactured solutions and two- and three-dimensional benchmark problems from the literature confirm the effectiveness of the method.
