An adaptive projection‐based model reduction method for nonlinear mechanics with internal variables: Application to thermo‐hydro‐mechanical systems. (21st March 2022)

• Record Type: Journal Article
• Authors: Iollo, Angelo; Sambataro, Giulia; Taddei, Tommaso
• Is Part Of: International journal for numerical methods in engineering. Volume 123:Number 12(2022)
• Page Start: 2894
• Page End: 2918
• Publication Date: 2022-03-21
• Subjects: model order reduction -- nonlinear mechanics -- parameterized partial differential equations; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6964
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: We propose a projection‐based monolithic model order reduction procedure for a class of problems in nonlinear mechanics with internal variables. The work is motivated by applications to thermo‐hydro‐mechanical (THM) systems for radioactive waste disposal. THM equations model the behavior 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 toward 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.