SFB 1313 Publication "Rigorous derivation of discrete fracture models for Darcy flow in the limit of vanishing aperture"

New SFB 1313 publication, published in "Networks and Heterogeneous Media". The work has been developed within the SFB 1313 research project B03.

"Rigorous derivation of discrete fracture models for Darcy flow in the limit of vanishing aperture"

Authors

• Maximilian Hörl (University of Stuttgart, SFB 1313 research project B03)
• Christian Rohde (University of Stuttgart, research projects B03 and C02)

Abstract

We consider single-phase flow in a fractured porous medium governed by Darcy's law with spatially varying hydraulic conductivity matrices in both bulk and fractures. The width-to-length ratio of a fracture is of the order of a small parameter ε and the ratio Κ_f*/ Κ_b* of the characteristic hydraulic conductivities in the fracture and bulk domains is assumed to scale with ε^α  for a parameter α ∈ ℝ. The fracture geometry is parameterized by aperture functions on a submanifold of codimension one. Given a fracture, we derive the limit models as ε → 0. Depending on the value of α, we obtain five different limit models as ε → 0, for which we present rigorous convergence results.