Volume 16, Issue 1
Preconditioning a Coupled Model for Reactive Transport in Porous Media

Laila AmirMichel Kern

Int. J. Numer. Anal. Mod., 16 (2019), pp. 18-48.

Published online: 2018-10

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  • Abstract

Reactive transport problems involve the coupling between the chemical interactions of different species and their transport by advection and diffusion. It leads to the solution of a non-linear systems of partial differential equations coupled to local algebraic or differential equations. Developping software for these two components involves fairly different techniques, so that methods based on loosely coupled modules are desirable. On the other hand, numerical issues such as robustness and convergence require closer couplings, such as simultaneous solution of the overall system. The method described in this paper allows a separation of transport and chemistry at the software level, while keeping a tight numerical coupling between both subsystems. We give a formulation that eliminates the local chemical concentrations and keeps the total concentrations as unknowns, then recall how each individual subsystem can be solved. The coupled system is solved by a Newton–Krylov method. The block structure of the model is exploited both at the nonlinear level, by eliminating some unknowns, and at the linear level by using block Gauss-Seidel or block Jacobi preconditioning. The methods are applied to a 1D case of the MoMaS benchmark.

  • Keywords

Reactive transport porous media preconditioning non-linear systems.

  • AMS Subject Headings

65F10 65H10 65M22 76S05.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

l.amir@uca.ma (Laila Amir)

michel.kern@inria.fr (Michel Kern)

  • BibTex
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  • TXT
@Article{IJNAM-16-18, author = {Amir , Laila and Kern , Michel}, title = {Preconditioning a Coupled Model for Reactive Transport in Porous Media}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {16}, number = {1}, pages = {18--48}, abstract = {

Reactive transport problems involve the coupling between the chemical interactions of different species and their transport by advection and diffusion. It leads to the solution of a non-linear systems of partial differential equations coupled to local algebraic or differential equations. Developping software for these two components involves fairly different techniques, so that methods based on loosely coupled modules are desirable. On the other hand, numerical issues such as robustness and convergence require closer couplings, such as simultaneous solution of the overall system. The method described in this paper allows a separation of transport and chemistry at the software level, while keeping a tight numerical coupling between both subsystems. We give a formulation that eliminates the local chemical concentrations and keeps the total concentrations as unknowns, then recall how each individual subsystem can be solved. The coupled system is solved by a Newton–Krylov method. The block structure of the model is exploited both at the nonlinear level, by eliminating some unknowns, and at the linear level by using block Gauss-Seidel or block Jacobi preconditioning. The methods are applied to a 1D case of the MoMaS benchmark.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12792.html} }
TY - JOUR T1 - Preconditioning a Coupled Model for Reactive Transport in Porous Media AU - Amir , Laila AU - Kern , Michel JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 18 EP - 48 PY - 2018 DA - 2018/10 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12792.html KW - Reactive transport KW - porous media KW - preconditioning KW - non-linear systems. AB -

Reactive transport problems involve the coupling between the chemical interactions of different species and their transport by advection and diffusion. It leads to the solution of a non-linear systems of partial differential equations coupled to local algebraic or differential equations. Developping software for these two components involves fairly different techniques, so that methods based on loosely coupled modules are desirable. On the other hand, numerical issues such as robustness and convergence require closer couplings, such as simultaneous solution of the overall system. The method described in this paper allows a separation of transport and chemistry at the software level, while keeping a tight numerical coupling between both subsystems. We give a formulation that eliminates the local chemical concentrations and keeps the total concentrations as unknowns, then recall how each individual subsystem can be solved. The coupled system is solved by a Newton–Krylov method. The block structure of the model is exploited both at the nonlinear level, by eliminating some unknowns, and at the linear level by using block Gauss-Seidel or block Jacobi preconditioning. The methods are applied to a 1D case of the MoMaS benchmark.

​Laila Amir & Michel Kern. (2020). Preconditioning a Coupled Model for Reactive Transport in Porous Media. International Journal of Numerical Analysis and Modeling. 16 (1). 18-48. doi:
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