Hydro-mechanical modelling of fractured porous media: Well-posedness and iterative schemes

Abstract: Assessing the safety of deep geological repositories requires rigorous modeling of coupled hydro-mechanical (HM) processes in fractured crystalline rock. This involves addressing complex fracture manifolds where mechanical deformation and fluid flow are linked by non-linear, mutually dependent transmission conditions. We present a mathematical framework for a non-linear HM model incorporating fracture-matrix interactions, non-penetration contact conditions, and aperture-dependent permeability. To solve the resulting evolution problem, we employ the Rothe method for time discretization combined with a fixed-stress iterative splitting scheme. We establish the well-posedness of the formulation, identifying the stability conditions and structural assumptions necessary to guarantee the existence of weak solutions. These theoretical bounds further serve as the foundation for the convergence analysis of the coupled FEM-MHFEM discretization. Numerical experiments are presented to validate the theoretical results and demonstrate the solver's robustness in complex geometries.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. Unless stated otherwise, we will meet on Mondays at 15:40 in the lecture hall K3 (2nd floor)