Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity

TL;DR

This paper presents a projection-based reduced order modeling approach integrated with an iterative fixed-stress splitting scheme to efficiently solve linear thermo-poroelasticity problems, reducing computational costs in multi-physics simulations.

Contribution

It introduces a decoupled iterative solution combined with reduced order modeling for thermo-poroelasticity, enhancing computational efficiency over traditional methods.

Findings

The method significantly reduces computational time.

Numerical experiments confirm high accuracy with few modes.

The approach effectively handles coupled multi-physics problems.

Abstract

This paper explores an iterative coupling approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order models. One of the main challenges in addressing coupled multi-physics problems is the complexity and computational expenses involved. In this study, we introduce a decoupled iterative solution approach, integrated with reduced order modeling, aimed at augmenting the efficiency of the computational algorithm. The iterative coupling technique we employ builds upon the established fixed-stress splitting scheme that has been extensively investigated for Biot's poroelasticity. By leveraging solutions derived from this coupled iterative scheme, the reduced order model employs an additional Galerkin projection onto a reduced basis space formed by a small number of modes obtained through proper orthogonal decomposition. The effectiveness of the proposed algorithm is demonstrated through numerical experiments, showcasing its computational prowess.