Some Semi-decoupled Algorithms with Optimal Convergence for a Four-Field Linear Thermo-poroelastic Model

Abstract We propose a parallel semi-decoupled algorithm to efficiently solve a four-field thermo-poroelastic model. At the initial time step, all variables are computed simultaneously using a monolithic solver; thereafter, the system is split into a mixed linear elasticity (M) subproblem and a coupled fluid flow diffusion-heat transfer (FH) subproblem. The two subproblems are then solved in parallel at subsequent time steps. Two other semi-decoupled algorithms based on a sequential strategy are also proposed for comparison. All three algorithms do not require iterative procedures at each time step and are free from stabilization for the linear model studied in this work. 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.