Méthodes numériques avancées pour les problèmes à forte raideur en transport réactif

The simulation of reactive transport in porous media is a major challenge for many IFPEN projects, especially in relation to new underground energies such as CO2 sequestration, geothermal energy and hydrogen storage. Unfortunately, the performance of reactive transport codes is today strongly limited by numerical difficulties arising from the modeling of chemical reactions. These difficulties appear under various facets, but all of them can be traced back to a problem of stiffness of the equations to be solved. In view of these difficulties, IFPEN wants to differentiate itself from the competing codes by a breakthrough technology.
This thesis proposes to explore several advanced numerical techniques aimed at overcoming four of the most salient and representative stiffness difficulties:
•    The nonparametric interior-point method for the resolution of algebraic systems containing complementarity conditions which allow us to handle the appearance and disappearance of phases.
•    The automatic selection of the main unknowns for a system of equations ─ by parameterization or by Cartesian representation ─ in order to guarantee a good conditioning in all operating regimes and all ranges of values.
•    The expression of chemical reactions with free or limited kinetics using a gradient flow structure, which in turn leads to the design of numerical schemes with better convergence properties.
•    The homotopic continuation method, as well as its reformulation in the language of interior points, to facilitate the convergence of implicit schemes with large time steps imposed by users.
This project is a natural extension of several prior doctoral works at IFPEN, the tools of which are synthesized and enhanced for a new and more ambitious application that is reactive transport. The items listed above are not independent of each other, but form a coherent package that meets the needs identified by the engineers
 

Keywords : Équations de complémentarité, solveurs non-linéaires, méthode de Newton, méthodes de points intérieurs, méthode de paramétrage, continuation homotopique, transport réactif.