SFB 1313 Publication "Flow in Porous Media with Fractures of Varying Aperture"

New SFB 1313 publication, published in the "SIAM Journal on Scientific Computing". The work has been developed within the SFB 1313 research project B03.

 "Flow in Porous Media with Fractures of Varying Aperture"

Authors

• Samuel Burbulla (former SFB 1313 researcher, research project B03)
• Maximilian Hörl (University of Stuttgart, SFB 1313 research project B03)
• Christian Rohde (University of Stuttgart, SFB 1313 research project B03)

Abstract

We study single-phase flow in a fractured porous medium at a macroscopic scale that allows us to model fractures individually. The flow is governed by Darcy’s law in both fractures and a porous matrix. We derive a new mixed-dimensional model, where fractures are represented by (n−1)-dimensional interfaces between n-dimensional subdomains for n≥2. In particular, we suggest a generalization of the model in [V. Martin, J. Jaffré, and J. E. Roberts, SIAM J. Sci. Comput., 26 (2005), pp. 1667–1691] by accounting for asymmetric fractures with spatially varying aperture. Thus, the new model is particularly convenient for the description of surface roughness or for modeling curvilinear or winding fractures. The wellposedness of the new model is proven under appropriate conditions. Further, we formulate a discontinuous Galerkin discretization of the new model and validate the model by performing two- and three-dimensional numerical experiments.