Reduction de modele basee sur des composants elementaires pour des systemes Thermo-Hydro-Mechaniques

Abstract

The objective of the thesis is to develop a component-based model order reduction 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 (this project is funded by ANDRA, the national agency for radioactive waste management). THM equations model the behaviour of temperature, pore water pressure and solid displacement in the neighborhood of geological reposito- ries, which contain radioactive waste and are responsible for a significant thermal flux towards the Earth’s surface. From a mathematical point of view, the THM system that we solve is a time-dependent and highly nonlinear coupled system; furthermore, the solution to the problem depends on several parameters, which might be related to the geometric configuration (e.g. the number of repositories, their distance or their size) or the material properties of the medium. For example, changes in the position and/or the number of the radioactive repositories might lead to significant changes in the predicted quantities of interest; we would need therefore to solve the numerical model more than once. This problem represents a multi-query problem and it requires the application of component-based parametrized model order reduction (CB-pMOR). First, we start from the high-fidelity finite element discretisation of the two-dimensional THM problem, we develop a monolithic projection-based ROM and we study its per- formance with respect to predictions. Then, we device a CB-pMOR formulation for steady problems in nonlinear mechanics. Finally, we extend the CB formulation and methodology to time-dependent nonlinear problems with internal variables, to tackle the THM problem of interest.

Key words. Model order reduction; Domain decomposition; Nonlinear elasticity; Cou- pled problems.