Computational Geosciences

, Volume 14, Issue 3, pp 483–502 | Cite as

Comparison of numerical methods for simulating strongly nonlinear and heterogeneous reactive transport problems—the MoMaS benchmark case

  • Jérôme Carrayrou
  • Joachim Hoffmann
  • Peter Knabner
  • Serge Kräutle
  • Caroline de Dieuleveult
  • Jocelyne Erhel
  • Jan Van der Lee
  • V. Lagneau
  • K. Ulrich Mayer
  • Kerry T. B. MacQuarrie
Original Paper


Although multicomponent reactive transport modeling is gaining wider application in various geoscience fields, it continues to present significant mathematical and computational challenges. There is a need to solve and compare the solutions to complex benchmark problems, using a variety of codes, because such intercomparisons can reveal promising numerical solution approaches and increase confidence in the application of reactive transport codes. In this contribution, the results and performance of five current reactive transport codes are compared for the 1D and 2D subproblems of the so-called easy test case of the MoMaS benchmark (Carrayrou et al., Comput Geosci, 2009, this issue). This benchmark presents a simple fictitious reactive transport problem that highlights the main numerical difficulties encountered in real reactive transport problems. As a group, the codes include iterative and noniterative operator splitting and global implicit solution approaches. The 1D easy advective and 1D easy diffusive scenarios were solved using all codes, and, in general, there was a good agreement, with solution discrepancies limited to regions with rapid concentration changes. Computational demands were typically consistent with what was expected for the various solution approaches. The differences between solutions given by the three codes solving the 2D problem are more important. The very high computing effort required by the 2D problem illustrates the importance of parallel computations. The most important outcome of the benchmark exercise is that all codes are able to generate comparable results for problems of significant complexity and computational difficulty.


MoMaS Benchmark Code intercomparison Numerical methods for reactive transport Direct substitution approach (DSA) Differential and algebraic equations (DAE) Sequential iterative approach (SIA) Sequential noniterative approach (SNIA) 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Jérôme Carrayrou
    • 1
  • Joachim Hoffmann
    • 2
  • Peter Knabner
    • 2
  • Serge Kräutle
    • 2
  • Caroline de Dieuleveult
    • 3
    • 4
  • Jocelyne Erhel
    • 3
  • Jan Van der Lee
    • 5
  • V. Lagneau
    • 5
  • K. Ulrich Mayer
    • 6
  • Kerry T. B. MacQuarrie
    • 7
  1. 1.Institut de Mécanique des Fluides et des Solides, Laboratoire d’Hydrogéologie et de Géochimie de StrasbourgUniversity of Strasbourg, UMR 7517 UdS-CNRSStrasbourgFrance
  2. 2.Department of MathematicsUniversity of Erlangen-NurembergErlangenGermany
  3. 3.INRIA RennesCampus de BeaulieuRennesFrance
  4. 4.ANDRAChâtenay-MalabryFrance
  5. 5.Mines ParisTechFontainebleau CedexFrance
  6. 6.Department of Earth and Ocean SciencesUniversity of British ColumbiaVancouverCanada
  7. 7.Department of Civil EngineeringUniversity of New BrunswickFrederictonCanada

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