Flow in fractured porous media: A review of conceptual models and discretization approaches

The last decade has seen a strong increase of research into flows in fractured porous media, mainly related to subsurface processes, but also in materials science and biological applications. Connected fractures totally dominate flow-patterns, and their representation is therefore a critical part in model design. Due to the fracture's characteristics as approximately planar discontinuities with an extreme size to width ratio, they challenge standard macroscale mathematical and numerical modeling of flow based on averaging. Thus, over the last decades, various, and also fundamentally different, approaches have been developed. This paper reviews common conceptual models and discretization approaches for flow in fractured porous media, with an emphasis on the dominating effects the fractures have on flow processes. In this context, the paper discuss the tight connection between physical and mathematical modeling and simulation approaches. Extensions and research challenges related to transport, multi-phase flow and fluid-solid interaction are also commented on.