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, porous media, preconditioning, non-linear systems.
AB - <p style="text-align: justify;">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. Developing 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.</p>