A Unified Model for Thermo- and Multiple-Network Poroelasticity with a Global-in-Time Iterative Decoupling Scheme

TL;DR

This paper presents a unified thermo- and multi-network poroelasticity model reformulated for better analysis, introducing a globally convergent iterative scheme and finite element approximation validated by numerical experiments.

Contribution

The paper develops a novel unified model and a globally convergent iterative decoupling scheme for thermo- and multi-network poroelasticity problems.

Findings

Proved the well-posedness of the reformulated model.

Designed a globally convergent iterative algorithm with proven contraction properties.

Numerical results show optimal convergence and stability, eliminating pressure oscillations.

Abstract

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.