Comparison of numerical methods for simulating strongly non-linear 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; Vincent Lagneau; K. Ulrich Mayer; Kerry T. B. Macquarrie

hal-00505371, version 1

Comparison of numerical methods for simulating strongly non-linear and heterogeneous reactive transport problems – the MoMaS benchmark case

Jérôme Carrayrou () ¹, Joachim Hoffmann ², Peter Knabner ², Serge Kräutle ², Caroline De Dieuleveult () ³, Jocelyne Erhel ()^a^, 4, Jan Van Der Lee () ³, Vincent Lagneau ³, K. Ulrich Mayer () ⁵, Kerry T. B. Macquarrie () ⁶

Computational Geosciences 14 (2010) 483-502

Abstract: 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 sub-problems of the so-called "Easy Test Case" of the MoMaS benchmark (Carrayrou et al., this issue). As a group, the codes include iterative and non-iterative 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 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 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.

a – INRIA
1: Laboratoire d'Hydrologie et de Géochimie de Strasbourg (LHyGeS)
CNRS : UMR7517 – Université de Strasbourg – INSU – ENGEES
2: Department Mathematik [Erlangen]
Universität Erlangen-Nürnberg
3: Centre de Géosciences (GEOSCIENCES)
MINES ParisTech - École nationale supérieure des mines de Paris
4: SAGE (INRIA - IRISA)
CNRS : UMR6074 – INRIA – Université de Rennes 1
5: Department of Earth and Ocean Sciences [Vancouver] (EOS)
University of British Columbia
6: Department of Civil Engineering (UNB Civil Engineering)
University of New Brunswick

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Submitted on: Friday, 23 July 2010 14:44:23
Updated on: Friday, 23 July 2010 15:24:20

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DOI: 10.1007/s10596-010-9178-2

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%% hal-00505371, version 1
%% http://hal-ensmp.archives-ouvertes.fr/hal-00505371
@article{carrayrou:hal-00505371,
    hal_id = {hal-00505371},
    url = {http://hal-ensmp.archives-ouvertes.fr/hal-00505371},
    title = {{Comparison of numerical methods for simulating strongly non-linear and heterogeneous reactive transport problems -- the MoMaS benchmark case}},
    author = {Carrayrou, J{\'e}r{\^o}me and Hoffmann, Joachim and Knabner, Peter and Kr{\"a}utle, Serge and De Dieuleveult, Caroline and Erhel, Jocelyne and Van Der Lee, Jan and Lagneau, Vincent and Mayer, K. Ulrich and Macquarrie, Kerry T. B.},
    abstract = {{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 sub-problems of the so-called "Easy Test Case" of the MoMaS benchmark (Carrayrou et al., this issue). As a group, the codes include iterative and non-iterative 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 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 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.}},
    keywords = {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)},
    language = {English},
    affiliation = {Laboratoire d'Hydrologie et de G{\'e}ochimie de Strasbourg - LHyGeS , Department Mathematik [Erlangen] , Centre de G{\'e}osciences - GEOSCIENCES , SAGE - INRIA - IRISA , Department of Earth and Ocean Sciences [Vancouver] - EOS , Department of Civil Engineering - UNB Civil Engineering},
    pages = {483--502},
    journal = {Computational Geosciences},
    volume = {14},
    audience = {international },
    doi = {10.1007/s10596-010-9178-2 },
    year = {2010},
    pdf = {http://hal-ensmp.archives-ouvertes.fr/hal-00505371/PDF/Synthesis\_of\_benchmark\_results-Manuscript-2010-final\_version.pdf},
}

%F hal-00505371, version 1
%0 Journal Article
%U http://hal-ensmp.archives-ouvertes.fr/hal-00505371
%2 INFO:INFO_MO
%T Comparison of numerical methods for simulating strongly non-linear and heterogeneous reactive transport problems – the MoMaS benchmark case
%A Carrayrou, Jérôme
%A Hoffmann, Joachim
%A Knabner, Peter
%A Kräutle, Serge
%A De Dieuleveult, Caroline
%A Erhel, Jocelyne
%A Van Der Lee, Jan
%A Lagneau, Vincent
%A Mayer, K. Ulrich
%A Macquarrie, Kerry T. B.
%+ Laboratoire d'Hydrologie et de Géochimie de Strasbourg - LHyGeS , Department Mathematik [Erlangen] , Centre de Géosciences - GEOSCIENCES , SAGE - INRIA - IRISA , Department of Earth and Ocean Sciences [Vancouver] - EOS , Department of Civil Engineering - UNB Civil Engineering
%X 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 sub-problems of the so-called "Easy Test Case" of the MoMaS benchmark (Carrayrou et al., this issue). As a group, the codes include iterative and non-iterative 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 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 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.
%G English
%2 2009
%R 10.1007/s10596-010-9178-2
%J Computational Geosciences
%2 international
%8 2010-00-00
%V 14
%P 483–502
%K 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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