Fluid flow in rough fractures and the coupling with the mechanical behaviour of the fractures pose great difficulties for numerical modeling approaches due to complex fracture surface topographies, the non-linearity of hydro-mechanical processes and their tightly coupled nature. To this end, we have adapted a fictitious domain method to enable the simulation of hydro-mechanical processes in fracture intersections. The main characteristic of the method is the immersion of the fracture, modelled as a linear elastic solid, in the surrounding computational fluid domain, modelled with the incompressible Navier-Stokes equations. The fluid and the solid problems are coupled with variational transfer operators. Variational transfer operators are also used to solve contact within the fracture using a dual mortar approach and to generate problem-specific fluid meshes. With respect to our applications, the key features of the method are the usage of different finite element discretizations for the solid and the fluid problem and the automatically generated representation of the fluid-solid boundary. We demonstrate that the presented methodology resolves small-scale roughness on the fracture surface, while capturing fluid flow field changes during mechanical loading. Starting with 2D/3D benchmark simulations of intersected fractures, we end with an intersected fracture composed of complex fracture surface topographies, which are in contact under increasing loads. The contributions of this article are as follows: (1) the application of the fictitious domain method to study flow in fractures with intersections, (2) a mortar-based contact solver for the solid problem, (3) generation of problem-specific grids using the geometry information from the variational transfer operators.

由于复杂的裂缝表面形貌，流体力学过程的非线性及其紧密耦合的性质，粗糙裂缝中的流体流动以及与裂缝的力学行为的耦合给数值模拟方法带来了很大的困难。为此，我们采用了一种虚拟域方法，以能够模拟裂缝相交处的水力机械过程。该方法的主要特征是将裂缝（以线性弹性固体模型建模）浸入周围的计算流体域中，并以不可压缩的Navier-Stokes方程建模。流体和固体问题与变分传递算子有关。变分传递算子还用于使用双重砂浆方法解决裂缝内的接触并生成特定于问题的流体网格。就我们的应用而言，该方法的关键特征是针对固体和流体问题使用了不同的有限元离散化方法，以及自动生成的流固边界表示法。我们证明，提出的方法可以解决裂缝表面的小尺度粗糙度，同时捕获机械载荷过程中的流体流场变化。从相交的裂缝的2D / 3D基准模拟开始，我们结束于由复杂的裂缝表面形貌组成的相交的裂缝，这些裂缝在不断增加的载荷下接触。本文的贡献如下：