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We are interested in the modelling of thermo-hydro-mechanical (THM) problems that describe the behaviour of a soil in which a weakly compressible fluid evolves. The soil is represented as a porous medium and the fluid is subjected to various mechanical, thermal and hydraulic stresses. This model is used for the simulation of the THM impact of the high level activity radioactive waste exothermicity within a deep geological disposal facility build in a clay-based host rock. To avoid the loss of uniqueness of the numerical solution and, more importantly, problems with the strain localization which are often encountered in soil computations, we shall consider non-locally regularized equations based on a second gradient theory. In this approach, a new primal unknown, modelling the trace of the displacement gradient, is introduced. The objective of this work is to find a parallel and scalable iterative solver for the system of equations after linearization. While extensive research has been carried on linear solvers for poroelasticity, this is not, to our knowledge, the case for the second gradient formulation. In this thesis, we shall present a block preconditioner for the fully coupled THM equations with a second gradient of dilation regularization. It is a block Gauss-Seidel approach, in which a multigrid method is used to precondition the blocks of the displacement, pressure, temperature and micro volume changes. Furthermore, we use a weighted mass matrix as preconditioner for the Lagrange multipliers block. We present numerical results that reflect the good performance of the proposed preconditioner in terms of iteration count of the iterative solver, the robustness of the preconditioner in terms of parameter variation and that is furthermore independent of the mesh size.

Mme Laura Grigori – INRIA – Referee

Mme Carmen Rodrigo – University of Zaragoza – Referee

M. Massimiliano Ferronato –  University of Padova – Examiner

M. Alfredo Buttari – IRIT – Examiner

M. Iain Duff – Rutherford  Appleton Laboratory – Examiner

M. Daniel Ruiz – IRIT – Examiner

M. Michel DAYDE – IRIT – Director

M. Nicolas Tardieu – EDF R & D – Invited member

Mme Carola Kruse – CERFACS – Invited member