Discrete fracture models with reduced-dimensional treatment of conductive and blocking fractures are widely used to simulate fluid flow in fractured porous media. Among these, numerical methods based on interface models are intensively studied, where the fractures are treated as co-dimension one manifolds in a bulk matrix with low-dimensional governing equations. In this paper, we propose a simple yet effective treatment for modeling the fractures on fitted grids in the interior penalty discontinuous Galerkin (IPDG) methods without introducing any additional degrees of freedom or equations on the interfaces. We conduct stability and {\em hp}-analysis for the proposed IPDG method, deriving optimal a priori error bounds concerning mesh size ($h$) and sub-optimal bounds for polynomial degree ($k$) in both the energy norm and the $L^2$ norm. Numerical experiments involving published benchmarks validate our theoretical analysis and demonstrate the method's robust performance. Furthermore, we extend our method to two-phase flows and use numerical tests to confirm the algorithm's validity.

翻译：基于降维处理的导流与阻断裂缝离散裂缝模型广泛应用于模拟断裂多孔介质中的流体流动。其中，基于界面模型的数值方法受到广泛研究，此类方法将裂缝视为嵌入基质体中的余维一流形，并采用低维控制方程描述。本文提出一种简洁高效的处理方法，在基于拟合网格的内罚间断伽辽金方法中，无需引入界面上的额外自由度或方程即可实现裂缝建模。我们对该方法进行了稳定性与{\em hp}-分析，推导了能量范数与$L^2$范数下关于网格尺寸($h$)的最优先验误差界及关于多项式阶数($k$)的次优界。涉及已发表基准问题的数值实验验证了理论分析结果，同时展示了该方法鲁棒的求解性能。此外，我们将该方法扩展至两相流动，并通过数值测试验证了算法的有效性。