Krylov methods applied to reactive transport models

Jocelyne Erhel (1)

1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences

Reactive transport models couple advection dispersion equations with chemistry equations. If the reactions are at thermodynamic equilibrium, then the system is a set of partial differential and algebraic equations. After space and implicit time discretizations, a nonlinear system of equations must be solved at each time step. The Jacobian matrix of the nonlinear system can be written with a Kronecker product coupling transport and chemistry. Krylov methods are well-suited to solve such linear systems because the matrix vector product can be done efficiently. The main challenge is to design a preconditioning matrix. We propose here to use the special structure of the matrix. Preliminary experiments show that Krylov methods are much more efficient than a direct method which does not use the coupled structure.

Domaines: Analyse numérique [math.NA]; Calcul parallèle, distribué et partagé [cs.DC]; Géophysique [physics.geo-ph]

Jocelyne Erhel. Krylov methods applied to reactive transport models. SIAM Conference on Mathematical and Computational Issues in the Geosciences, Sep 2017, Erlangen, Germany. ⟨hal-01646268⟩