Résumé
Modeling fluid flow in fractured rock is required in a wide variety of research domains and applications. As standard continuum models are often not well adapted for this purpose, numerous numerical approaches have been developed that rely on an explicit description of the fractures as one- or two-dimensional discrete elements. Solving Darcy-scale fluid flow in these fracture networks is usually done with either simplified representations of the physics using mesh-free methods at the fracture scale, or complex meshing which is typically computationally expensive. Here, we derive an alternative approach that keeps the computational advantages of mesh-free methods while providing a pertinent representation of the modeled physical processes. To this end, we consider two-dimensional analytical solutions to the Darcy-scale flow problem in rectangular fractures, and we couple these fractures by imposing mass conservation and continuity laws at their intersections. We validate our approach against standard finite-element methods for a number of fracture networks and we show how it allows us to find the most adapted balance between numerical cost and solution accuracy for various synthetic examples and applications. Finally, we use our approach to assess the existence of a representative elementary volume for various 3D fracture networks and determine the corresponding hydraulic properties.