A robust Mixed Finite Element model for coupled Thermo-Hydro-Mechanical problems in unsaturated porous media

Simulating Thermo- Hydro -Mechanical (THM) problems in unsaturated porous media presents significant challenges due to the high nonlinearities of the coupled processes, and the potential for numerical instabilities that may lead to unphysical oscillations in pressure, stress, and temperature solutions. The Mixed Finite Element (MFE) method, known for its accurate local mass conservation even in heterogeneous domains and on unstructured meshes, is widely used to discretize fluid flow in both saturated and unsaturated porous media. However, its application in coupled THM processes under variably saturated conditions has not been thoroughly explored. In this work, a robust MFE scheme based on the lowest order Raviart-Thomas space is developed for the fluid flow and heat transport in deformable unsaturated porous media. This method is integrated with the Crouzeix-Raviart finite element method for the displacement field. To prevent unphysical oscillations induced by the hyperbolic convection term in the heat transport equation, the MFE method is combined with an upwind edge/face centered finite volume scheme. The degrees of freedom of the developed formulation are the hydraulic head, the temperature, and the displacement vectors assigned at the mesh edges. To avoid splitting errors, the coupled THM equations are solved simultaneously using a monolithic scheme. The Method of Lines is employed to transform the partial differential equations into a system of nonlinear ordinary differential equations integrated in time with high-order methods using the DASPK time solver. The developed model is validated by comparisons against analytical and finite element solutions for the one-dimensional thermal consolidation problem. Numerical experiments are performed under saturated and unsaturated conditions to show the robustness of the developed model for the simulation of THM problems in variably saturated porous media.