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Article

Jacobian Free Methods for Coupling Transport with Chemistry in Heterogenous Porous Media

by 1 and 2,3,*
1
Laboratoire d’Ingénierie Informatique et Systèmes (L2IS), Faculté des Sciences et Techniques, UCAM, 4000 Marrakech, Morrocco
2
Inria, 2 Rue Simone Iff, 75589 Paris, France
3
CERMICS, Ecole des Ponts, 77455 Marne-la-Vallée, France
*
Author to whom correspondence should be addressed.
Academic Editor: Anis Younes
Water 2021, 13(3), 370; https://doi.org/10.3390/w13030370
Received: 24 December 2020 / Revised: 12 January 2021 / Accepted: 25 January 2021 / Published: 31 January 2021
Reactive transport plays an important role in various subsurface applications, including carbon dioxide sequestration, nuclear waste storage, biogeochemistry and the simulation of hydro–thermal reservoirs. The model couples a set of partial differential equations, describing the transport of chemical species, to nonlinear algebraic or differential equations, describing the chemical reactions. Solution methods for the resulting large nonlinear system can be either fully coupled or can iterate between transport and chemistry. This paper extends previous work by the authors where an approach based on the Newton–Krylov method applied to a reduced system has been developed. The main feature of the approach is to solve the nonlinear system in a fully coupled manner while keeping transport and chemistry modules separate. Here we extend the method in two directions. First, we take into account mineral precipitation and dissolution reactions by using an interior point Newton method, so as to avoid the usual combinatorial approach. Second, we study two-dimensional heterogeneous geometries. We show how the method can make use of an existing transport solver, used as a black box. We detail the methods and algorithms for the individual modules, and for the coupling step. We show the performance of the method on synthetic examples. View Full-Text
Keywords: reactive transport; finite volume methods; Newton–Krylov methods; porous media flow and transport reactive transport; finite volume methods; Newton–Krylov methods; porous media flow and transport
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MDPI and ACS Style

Amir, L.; Kern, M. Jacobian Free Methods for Coupling Transport with Chemistry in Heterogenous Porous Media. Water 2021, 13, 370. https://doi.org/10.3390/w13030370

AMA Style

Amir L, Kern M. Jacobian Free Methods for Coupling Transport with Chemistry in Heterogenous Porous Media. Water. 2021; 13(3):370. https://doi.org/10.3390/w13030370

Chicago/Turabian Style

Amir, Laila, and Michel Kern. 2021. "Jacobian Free Methods for Coupling Transport with Chemistry in Heterogenous Porous Media" Water 13, no. 3: 370. https://doi.org/10.3390/w13030370

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