Semi-explicit time discretization for linear thermo-poroelasticity

TL;DR

This paper introduces decoupled time stepping schemes for linear thermo-poroelasticity that are computationally efficient, guaranteed to converge under certain conditions, and validated through numerical experiments.

Contribution

It proposes new partially and fully decoupled schemes for thermo-poroelasticity with proven convergence and efficiency advantages over existing methods.

Findings

Schemes achieve first-order convergence.

Numerical validation confirms theoretical results.

Decoupling improves computational efficiency.

Abstract

Within this paper, we introduce partially and fully decoupled time stepping schemes for linear thermo-poroelasticity. This means that the mechanics, heat, and flow equations can be solved sequentially. We provide sufficient conditions on the material parameters, which can be checked a priori, guaranteeing first-order convergence of the introduced schemes. Hence, the proposed methods have the same order as the implicit Euler scheme but are computationally more efficient due to the decoupling of the system equations. Numerical examples validate the proven convergence results and analyze the sharpness of the mentioned parameter condition. Further, we compare the schemes with other decoupling schemes from the literature.