Computational Geosciences

, Volume 14, Issue 3, pp 421–433 | Cite as

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

  • Joachim Hoffmann
  • Serge Kräutle
  • Peter Knabner
Original Paper


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.


Reactive transport Porous media Numerical simulation Size reduction Complementarity problems 

Mathematics Subject Classifications (2000)

90C33 34A09 76S05 35K57 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Joachim Hoffmann
    • 1
  • Serge Kräutle
    • 1
  • Peter Knabner
    • 1
  1. 1.Department of Mathematics, Applied Mathematics 1University of Erlangen-NurembergErlangenGermany

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