Maximilian Hörl, SFB 1313 doctoral researcher at the Institute of Applied Analysis and Numerical Simulation (research project B03), will give his milestone presentation on " Hybrid-Dimensional Modeling of Fluid Flow in Fractured Porous Media " on 25 April 2024.
Date: Thursday, 25 April 2024
Time: 3:00 pm CET
Title: "Hybrid-Dimensional Modeling of Fluid Flow in Fractured Porous Media"
Place: 7.133, Pfaffenwaldring 57, 70569, Stuttgart
Abstract
We consider single-phase flow in a fractured porous medium governed by Darcy’s law with spatially varying matrix-valued hydraulic conductivities in both bulk and fractures. In particular, we account for general fracture geometries parameterized by aperture functions on a submanifold of codimension one. Given a fracture with a width-to-length ratio of the order of a small parameter ε, we derive limit models as ε → 0. In the limit ε → 0, we obtain discrete fracture models where fractures are represented as submanifolds of codimension one. The limit models provide a computationally efficient description with explicit fracture representation, while avoiding thin equi-dimensional subdomains with a need for highly resolved meshes in numerical methods. The ratio K⋆f /K⋆b of the characteristic hydraulic conductivities in the fracture and bulk domains is assumed to scale with εα for a parameter α ∈ R. Depending on the value of α, we obtain five different limit models as ε → 0, for which we present rigorous convergence results.