Modelling of hydro-mechanical processes in heterogeneous fracture intersections using a fictitious domain method with variational transfer operators

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.