Semi-explicit time discretization for linear thermo-poroelasticity
This provides more efficient numerical methods for engineers and scientists modeling coupled thermo-poroelastic systems, though it appears incremental relative to existing decoupling approaches.
The authors tackled the computational challenge of solving coupled thermo-poroelasticity equations by introducing partially and fully decoupled time stepping schemes that allow sequential solving of mechanics, heat, and flow equations. They proved first-order convergence under checkable parameter conditions and demonstrated computational efficiency compared to implicit methods.
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.