Numerical methods for flow in fractured porous media

The simulation of multiphase flow in fractured porous media is a computational challenge. A key issue is the efficient and effective coupling between flow in the porous matrix and in the fracture network: the presence of fractures indeed can influence fluid flow at a variety of space scales. Due to their high aspect ratio fractures are usually represented as lower dimensional interfaces coupled with the flow in the surrounding medium by suitable conditions. However, even in this hybrid dimensional approach, geometric conformity can represent a strict constraint for the generation of the computational grid which, with standard numerical discretization techniques, should honour as much as possible the geometry of the fractures without too degenerated/distorted elements. For instance, finite volumes with two point flux approximation (TPFA) demand a good quality of the mesh to mitigate discretization error.
Such standard techniques are here compared with modern computational methods that, even though more complex, are more robust with respect to mesh geometry and can be beneficial for the problem at hand: the extended finite elements and mimetic finite differences. The former allow us to have fractures that are completely irrespective of the underlying grid thanks to suitable enrichments of the finite element spaces. The latter, coupled with a suitable solver for the fracture network, are a promising alternative to finite volumes in the context of matching discretization, since very general grids, with distorted and non-convex elements can be handled while maintaining a good accuracy.


CONTACT: anna.scotti@polimi.it