Mixed-Dimensional Modeling for Flow in Fractured Porous Media (Maximilian Hörl, Universität Stuttgart)

07.10.2025 14:00 – 15:00

We consider fluid flow in porous media containing thin heterogeneities such as debris-filled fractures. When the fracture aperture is sufficiently small, it is natural to model fractures as lower-dimensional manifolds embedded in the bulk medium, leading to discrete fracture models at the Darcy scale.
In this talk, we present two approaches for deriving such models that account for general fracture geometries. In the first part, we follow a formal derivation via vertical averaging across a full-dimensional fracture. In the second part, we employ a rigorous approach and derive discrete fracture models in the limit of vanishing aperture ε → 0. Here, the ratio Kf/Kb of characteristic hydraulic conductivities in the fracture and bulk is assumed to scale as εα for
a parameter α ∈ R. Depending on the value of α, this yields five distinct limit models in the vanishing-aperture regime. Additionally, we briefly present an extension of this approach to the Biot system for fractured poroelastic media.
We illustrate our results with numerical experiments based on discontinuous Galerkin discretizations.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre