A Novel Coupled bES-FEM Formulation with SUPG stabilization for Thermo-Hydro-Mechanical Analysis in Saturated Porous Media

TL;DR

This paper introduces a new stabilized finite element method combining bES-FEM and SUPG techniques to effectively address numerical instabilities in thermo-hydro-mechanical analyses of saturated porous media, validated through benchmarks and real-world simulations.

Contribution

It proposes a novel stabilized bES-FEM with SUPG scheme that mitigates pressure and spurious oscillations in coupled THM problems, enhancing accuracy and stability.

Findings

Effective suppression of pressure oscillations in THM analysis.

Reduced spurious convection-induced oscillations in simulations.

Validated superiority through benchmark tests and real-world applications.

Abstract

Two primary types of numerical instabilities often occur in low-order finite element method (FEM) analyses of thermo-hydro-mechanical (THM) phenomena: (1) pressure oscillations arising improper interpolation of pressure and displacement fields; and (2) spatial oscillations induced by nonlinear convection terms in convection-dominated scenarios. In response to these issues, this paper proposes a novel stabilized edge-based smoothed FEM with a bubble function (bES-FEM) for THM analysis within saturated porous media. In the proposed framework, a cubic bubble function is first incorporated into ES-FEM to efficiently mitigate pressure oscillations that breach the Inf-Sup condition, and then the Streamline Upwind Petrov-Galerkin (SUPG) scheme is adopted in bES-FEM to effectively reduce the spurious oscillations in convection-dominated heat transfer scenarios. The accuracy of the bES-FEM with SUPG formulation for THM coupled problems is validated through a series of five benchmark tests. Moreover, the simulations of open-loop ground source energy systems demonstrate the proposed method's exceptional capability in tackling complex THM challenges in real-world applications. All the obtained results showcase the superiority of proposed bES-FEM with SUPG in eliminating the spatial and pressure oscillations, marking it as a promising tool for the exploration of coupled THM issues.