A parallel global-implicit 2-D solver for reactive transport problems in porous media based on a reduction scheme and its application to the MoMaS benchmark problem |
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Authors: | Joachim Hoffmann Serge Kr?utle and Peter Knabner |
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Institution: | (1) School of Engineering, Lebanese International University, Beirut, Lebanon;(2) Laboratoire d’Hydrologie et de G?ochimie de Strasbourg, Universit? de Strasbourg/EOST, CNRS, 1 rue de Blessig, 67000 Strasbourg, France; |
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Abstract: | In this article, an approach for the efficient numerical solution of multi-species reactive transport problems in porous media
is described. The objective of this approach is to reformulate the given system of partial and ordinary differential equations
(PDEs, ODEs) and algebraic equations (AEs), describing local equilibrium, in such a way that the couplings and nonlinearities
are concentrated in a rather small number of equations, leading to the decoupling of some linear partial differential equations
from the nonlinear system. Thus, the system is handled in the spirit of a global implicit approach (one step method) avoiding
operator splitting techniques, solved by Newton’s method as the basic algorithmic ingredient. The reduction of the problem
size helps to limit the large computational costs of numerical simulations of such problems. If the model contains equilibrium
precipitation-dissolution reactions of minerals, then these are considered as complementarity conditions and rewritten as
semismooth equations, and the whole nonlinear system is solved by the semismooth Newton method. |
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