A projection-based model reduction method for nonlinear mechanics with internal variables: application to thermo-hydro-mechanical systems

TL;DR

This paper introduces a projection-based model reduction technique tailored for nonlinear mechanics with internal variables, specifically applied to thermo-hydro-mechanical systems relevant to radioactive waste disposal, improving computational efficiency.

Contribution

It develops an adaptive sampling strategy and an element-wise empirical quadrature hyper-reduction method for efficient simulation of complex THM systems.

Findings

Validated on a 2D THM system demonstrating reduced computational costs.

Achieved accurate approximation of thermo-hydro-mechanical behavior.

Enhanced efficiency in simulating geological repository scenarios.

Abstract

We propose a projection-based monolithic model order reduction (MOR) procedure for a class of problems in nonlinear mechanics with internal variables. The work is is motivated by applications to thermo-hydro-mechanical (THM) systems for radioactive waste disposal. THM equations model the behaviour of temperature, pore water pressure and solid displacement in the neighborhood of geological repositories, which contain radioactive waste and are responsible for a significant thermal flux towards the Earth's surface. We develop an adaptive sampling strategy based on the POD-Greedy method, and we develop an element-wise empirical quadrature hyper-reduction procedure to reduce assembling costs. We present numerical results for a two-dimensional THM system to illustrate and validate the proposed methodology.