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Krylov methods applied to reactive transport models

Jocelyne Erhel 1
1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
Abstract : 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.
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https://hal.inria.fr/hal-01646268
Contributor : Jocelyne Erhel <>
Submitted on : Thursday, November 23, 2017 - 1:51:40 PM
Last modification on : Thursday, January 7, 2021 - 4:34:54 PM

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  • HAL Id : hal-01646268, version 1

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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⟩

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