Iteratively coupled mixed finite element solver for thermo-hydro-mechanical modeling of permafrost thaw

Abstract

In this paper we consider computational challenges associated with thermo-hydro-mechanical models for simulation of subsidence due to permafrost thaw. The model we outline couples heat conduction with phase change and thermal advection to Biot’s poroelasticity equations with attention paid to the dependence of the constitutive parameters on temperature. Our numerical scheme uses the lowest order mixed finite elements for discretization of thermal and hydrological flow, and Galerkin finite elements for mechanics, and uses an implicit–explicit time stepping. We set up an iterative solver that solves the thermal subproblem followed by the hydro-mechanical subproblem, and demonstrate its robustness in practical heterogeneous permafrost scenarios. We also identify the challenges associated with the roughness of the dependence of mechanical parameters on the temperature.

Keywords

• Thermo-hydro-mechanical models
• Heterogeneous permafrost
• Heat conduction with phase change
• Poroelasticity
• Mixed finite elements
• Nonlinear constitutive relationships