The proposed post-doc concerns integrated discretization–regularization–linearization–algebraic resolution numerical simulation of the geological sequestration of CO2, more precisely in the context of the SPE 11 benchmark https://www.spe.org/en/csp/. The main goals are to: 1) Put in place a posteriori error estimators which allow to quantify the error between the numerical approximation (known) and the exact solution (unknown). 2) Develop adaptive balancing strategy for the regularization parameter, the iterative linearization algorithm (Newton), and the iterative linear algebraic solver. This should lead to robust solvers and enable to significantly reduce the usual number of linear and nonlinear iterations. 3) Develop adaptive steering of the choice of time step and of the local mesh refinement. This will lead to adaptive front tracking and automatic recognition of viscous and gravitational phenomena. All these points are requested in the SPE 11 specification and their successful addressing should lead to more robust simulations and significant gain in the total simulation time without compromising the quality of the results. Moreover, control of the precision of approximate solution will be ensured. The work will be carried out in collaboration between the project-team SERENA https://team.inria.fr/serena/ of Inria Paris https://www.inria.fr/centre/paris (joint team with the CERMICS https://cermics-lab.enpc.fr/ laboratory at the Ecole des Ponts ParisTech) and IFP Energies Nouvelles https://www.ifpenergiesnouvelles.fr/.
References
https://doi.org/10.1137/120896918
https://doi.org/10.1016/j.jcp.2014.06.061
https://doi.org/10.1016/j.cma.2023.116558
https://doi.org/10.1016/j.cma.2017.11.027Profile of a candidate
Ph.D. in numerical analysis and scientific computing (finite element or volume methods, linearization methods (Picard, Newton), applications to flows in porous media, programming skills (C, C++, Matlab).Application
Send CV highlighting your background in numerical analysis, scientific computing, flows in porous media, and programming, a very brief motivation letter, and recommendation letter(s) to Martin Vohralík martin.vohralik@inria.fr, Soleiman Yousef soleiman.yousef@ifpen.fr, and Eric Flauraud eric.flauraud@ifpen.fr.
