We develop an enhanced reduced model for single-phase flow in fractured porous media capable of incorporating more realistic interface conditions at the fracture terminations. In addition to the traditional dimensional model reduction, where the elements of the discrete fracture network are treated as lower dimensional manifolds embedded in the porous matrix, we explore the microscale behavior of the boundary layer flow at the entrances of a fracture bounded by two parallel plates to construct a new set of interface conditions of Robin-type, giving rise to localized pressure jumps at the fracture edges. Within this enriched description, sharper reduced flow and tracer transport mixed-dimensional models are constructed in the asymptotic limit ruled by two small parameters related to the ratio between fracture aperture and entrance developing length and a macroscopic length scale. The discrete flow/transport mixed-dimensional model is discretized by a new discontinuous Galerkin(dG)-based formulation. An adequate version of the Galerkin-Newton method is developed for the numerical treatment of the non-linear Robin interface condition. Considering several fracture arrangements, numerical results illustrate the sharper description of the model proposed herein in predicting flow and tracer transport patterns in fractured media.

中文翻译：

---

包含入口流和边界层过渡效应的裂隙多孔介质的扩展双参数混合维模型


我们为裂隙多孔介质中的单相流开发了一种增强的简化模型，能够在裂隙端接处加入更真实的界面条件。除了传统的维模型约简，其中离散裂缝网络的单元被视为嵌入多孔基体中的低维流形，我们还探索了由两个平行板为界的裂缝入口处边界层流动的微观行为，以构建一组新的 Robin 型界面条件， 在断裂边缘产生局部压力跳跃。在这个丰富的描述中，在渐近极限下构建了更清晰的减流和示踪剂传输混合维度模型，该模型由两个小参数组成，这些参数与裂缝孔径和入口发展长度之间的比率以及宏观长度尺度有关。离散流/输运混合维模型通过一种新的基于非间断 Galerkin（dG） 的公式进行离散化。开发了 Galerkin-Newton 方法的适当版本，用于非线性 Robin 界面条件的数值处理。考虑到几种裂缝排列，数值结果说明了本文提出的模型在预测裂隙介质中的流动和示踪剂传输模式方面的更清晰描述。