A Unified Model for Thermo- and Multiple-Network Poroelasticity with a Global-in-Time Iterative Decoupling Scheme
This work addresses the computational challenges in coupled poroelasticity simulations for applications like geomechanics or biomedical engineering, though it appears incremental as it builds on existing models with a new numerical scheme.
The paper tackled the problem of modeling thermo-poroelasticity and multiple-network poroelasticity by introducing a unified total-pressure-based model and a global-in-time iterative decoupling scheme, resulting in a rigorously proven contraction mapping with unconditional convergence and optimal convergence rates in numerical experiments.
This paper introduces a unified model for thermo-poroelasticity and multiple-network poroelasticity, reformulated into a total-pressure-based system. We first establish the well-posedness of the problem via a Galerkin-based argument and subsequently introduce a robust space-time finite element approximation. To efficiently solve the fully coupled system, we propose a global-in-time iterative algorithm that sequentially decouples the mechanics from the transport equations, while incorporating necessary stabilization terms. We explicitly analyze the convergence rate and provide a rigorous proof that the proposed scheme constitutes a contraction mapping under physically relevant conditions, thereby ensuring its unconditional convergence. Numerical experiments confirm the theoretical stability bounds and demonstrate optimal convergence rates in both space and time, yielding solutions free of non-physical pressure oscillations.