Post-Doctoral Research Visit F/M Adaptivity (regularization, solvers, meshes) and a posteriori error estimators for the geological sequestration of CO2 in the framework of the SPE 11 benchmark

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Contract type : Fixed-term contract

Level of qualifications required : PhD or equivalent

Fonction : Post-Doctoral Research Visit

Context

 

Assignment

Subject

The recruited person is supposed to work on 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 work more precisely concerns integrated discretization–regularization–linearization–algebraic resolution .

Main goals

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. 

References and links

Description of the problem, a state of the art, and bibliography are available in the scientific papers 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.2017.11.027 and at the following URL: https://project.inria.fr/gatipor/publications/.

Responsibilities

The person recruited will be responsible for theoretical developments and their computer implementation.

Main activities

  • Design of integrated discretization–regularization–linearization–algebraic resolution numerical approaches for approximate solution of partial differential equations (PDEs).
  • Development of a posteriori estimates on the error between the unknown PDE solution u and an available numerical approximation uhj,k,i obtained on a computational mesh Th, regularization step j, linearization step k, and linear algebraic solver step i.
  • Distinguish the different error components, namely the discretization, regularization, linearization, and algebraic resolution ones.
  • Steer all these ingredients adaptively (adaptive regularization, adaptive inexact linearization).
  • Application to the SPE 11 benchmark https://www.spe.org/en/csp/.

Skills

Ph.D. in numerical analysis and scientific computing (finite element methods, linearization methods (Picard, Newton, L-scheme), multigrid/domain decomposition algebraic solvers). Programming skills in C++.

Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage