Some semi-decoupled algorithms with optimal convergence for a four-field linear thermo-poroelastic model

TL;DR

This paper introduces three semi-decoupled algorithms for a four-field thermoporoelastic model, achieving optimal convergence and unconditional stability without iterative procedures, validated through rigorous analysis and numerical experiments.

Contribution

The paper presents novel semi-decoupled algorithms with proven optimal convergence and stability for solving a complex thermoporoelastic system efficiently.

Findings

Algorithms are unconditionally stable and optimally convergent.

No iterative procedures needed at each time step.

Validated robustness across various physical parameters.

Abstract

We propose three semi-decoupled algorithms for efficiently solving a four-field thermoporoelastic model. The first two algorithms adopt a sequential strategy: at the initial time step, all variables are computed simultaneously using a monolithic solver; thereafter, the system is split into a mixed linear elasticity subproblem and a coupled pressure-temperature reaction-diffusion subproblem. The two variants differ in the order in which these subproblems are solved. To further improve computational efficiency, we introduce a parallel semidecoupled algorithm. In this approach, the four-field system is solved monolithically only at the first time step, and the two subproblems are then solved in parallel at subsequent time levels. None of the three algorithms requires iterative procedures at each time step, and are free from stabilization. Rigorous analysis confirms their unconditional stability, optimal convergence rates, and robustness under a wide range of physical parameter settings. These theoretical results are further validated by numerical experiments.