A global strategy for solving reactive transport equations

Journal of Computational Physics

Volumn 228, Issue 17, 2009, Pages 6395-6410

  de Dieuleveult, C ^a   Erhel, J ^b   Kern, M ^b  

^a ANDRA   (France)

^b INRIA   (France)

Author keywords

DAE solver; Nonlinear system; Reactive transport

Indexed keywords

ALGEBRA; NONLINEAR EQUATIONS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

DIFFERENTIAL ALGEBRAIC EQUATION SOLV; DIFFERENTIAL/ALGEBRAIC EQUATIONS; EQUATION SOLVERS; GEOCHEMICALS; GLOBAL STRATEGIES; ITERATIVE APPROACH; PARTIAL DIFFERENTIAL-ALGEBRAIC EQUATIONS; REACTIVE TRANSPORT; REACTIVE TRANSPORT MODELLING; TRANSPORT EQUATION;

NEWTON-RAPHSON METHOD;

EID: 67650456649     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.05.044     Document Type: Article

References (38)

1. Bethke C.M. Geochemical Reaction Modeling: Concepts and Applications (1996), Oxford University Press
2. Walter A., Frind E., Blowes D., Ptacek C., and Molson J. Modeling of multicomponent reactive transport in groundwater. 1. Model development and evaluation. Water Resour. Res. 30 11 (1994) 3137-3148
3. Zysset A., Stauffer F., and Dracos T. Modeling of chemically reactive groundwater transport. Water Resour. Res. 30 7 (1994) 2217-2228
4. C.I. Steefel, K.T. MacQuarrie, Approaches to modeling of reactive transport in porous media, in: P. Lichtner, C. Steefel, E. Oelkers (Eds.), Reactive Transport in Porous Media, vol. 34 of Rev. Mineral., Mineral. Soc. Am., 1996, pp. 83-125.
5. Yeh G.T., and Tripathi V.S. A critical evaluation of recent developments in hydrogeochemical transport models of reactive multichemical components. Water Resour. Res. 25 (1989) 93-108
6. Carrayrou J., MosT R., and Behra P. Operator-splitting procedures for reactive transport and comparison of mass balance errors. J. Contam. Hydrol. 68 3-4 (2004) 239-268
7. Valocchi A., Street R., and Roberts P. Transport of ion-exchanging solutes in groundwater: chromatographic theory and field simulation. Water Resour. Res. 17 5 (1981) 1517-1527
8. Miller C., and Benson L. Simulation of solute transport in a chemically reactive heterogeneous system: model development and application. Water Resour. Res. 19 (1983) 381-391
9. Cirpka O., and Helmig R. Comparison of approaches for the coupling of chemistry to transport in groundwater systems. Notes Numer. Fluid Dynam. 59 (1997) 102-120
10. Saaltink M., Ayora C., and Carrera J. A mathematical formulation for reactive transport that eliminates mineral concentrations. Water Resour. Res. 34 7 (1998) 1649-1656
11. Saaltink M., Carrera J., and Ayora C. On the behavior of approaches to simulate reactive transport. J. Contam. Hydrol. 48 (2001) 213-235
12. Molins S., Carrera J., Ayora C., and Saaltink M.W. A formulation for decoupling components in reactive transport problems. Water Resour. Res. 40 (2004) W10301
13. Hammond G., Valocchi A., and Lichtner P. Application of Jacobian-free Newton-Krylov with physics-based preconditioning to biogeochemical transport. Adv. Water Resour. 28 (2005) 359-376
14. KrSutle S., and Knabner P. A reduction scheme for coupled multicomponent transport-reaction problems in porous media: generalization to problems with heterogeneous equilibrium reactions. Water Resour. Res. 43 (2007) W03429
15. Morel F., and Morgan J. A numerical method for computing equilibria in aqueous chemical systems. Environ. Sci. Tech. 6 1 (1972) 58-67
16. Morel F., and Hering J. Principles and Applications of Aquatic Chemistry. second ed. (1993), Wiley, New York
17. Lucille P.L., Burnol A., and Ollar P. Chemtrap: a hydrogeochemical model for reactive transport in porous media. Hydrol. Process. 14 (2000) 2261-2277
18. Kirkner D., and Reeves H. Multicomponent mass transport with homogeneous and heterogeneous chemical reactions: effect of the chemistry on the choice of numerical algorithm. 1. Theory. Water Resour. Res. 24 (1988) 1719-1729
19. N. Bouillard, P. Montarnal, R. Herbin, Development of numerical methods for the reactive transport of chemical species in a porous media: a nonlinear conjugate gradient method, in: Int. Conf. Comput. Method Coupled Probl. Sci. Eng. Coupled Probl. 2005, ECCOMAS Conference, Santorini Island, Greece, 2005.
20. Hundsdorfer W., and Verwer J. Numerical solution of time-dependent advection-diffusion-reaction equations. Springer Series in Computational Mathematics vol. 33 (2003), Springer-Verlag, Berlin
21. E. Hairer, G. Wanner, Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems, No. 14 in SCM, Springer-Verlag, 1991.
22. D. Parkhurst, C. Appelo, User's guide to PHREEQC (version 2)-a computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations, Tech. Rep., U.S. Geological Survey Water-Resources Investigations Report 99-4259, 1999.
23. Appelo C. Some calculations on multicomponent transport with cation exchange in aquifers. Groundwater 32 (1994) 968-975
24. Appelo C., and Postma D. Geochemistry Groundwater and Pollution. second ed. (2005), A.A. Balkema
25. Hoteit H., Ackerer P., MosT R., Erhel J., and Philippe B. New two-dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes. Int. J. Numer. Method Eng. 61 (2004) 2566-2593
26. Barry D.A., Miller C.T., Culligan P.J., and Bajracharya K. Analysis of split operator methods for nonlinear and multispecies groundwater chemical transport models. Math. Comput. Simul. 43 (1997) 331-341
27. J. vander Lee, L. deWindt, CHESS tutorial and cookbook, updated for version 3.0, user's manual, Tech. Rep. LHM/RD/02/13, École des Mines de Paris, France, 2002.
28. Kanney J.F., Miller C.T., and Kelley C.T. Convergence of iterative split operator approaches for approximating nonlinear reactive transport problems. Adv. Water Resour. 26 (2003) 247-261
29. Saaltink M., Carrera J., and Ayora C. A comparison of two approaches for reactive transport modelling. J. Geochem. Explor. 69-70 (2000) 97-101
30. Ortega J., and Rheinboldt W. Iterative Solution of Nonlinear Equations in Several Variables. Computer Science and Applied Mathematics (1970), Academic Press
31. J. Carrayrou, ModTlisation du transport de solutTs rTactifs en milieu poreux saturT, ThFse de doctorat, UniversitT Louis Pasteur, Strasbourg, 2001.
32. Montarnal P., Dimier A., Deville E., Adam E., Gaombalet J., Bengaouer A., Loth L., and Chavant C. Coupling methodology within the software platform Alliances. In: Papadrakakis E.O.M., and Schrefler B. (Eds). Int. Conf. on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2005 (2005), CIMNE, Barcelona
33. Holstad A. A mathematical and numerical model for reactive fluid flow systems. Comput. Geosci. 4 (2000) 103-139
34. L. Amir, M. Kern, Newton-Krylov methods for coupling transport with chemistry in porous media, in: P. Binning, P. Engesgaard, H. Dahle, G. Pinder, W.G. Gray (Eds.), XVI International Conference on Computational Methods in Water Resources (CMWR XVI), 2006. .
35. Shen H., and Nicolaidis N. A direct substitution method for multicomponent solute transport in groundwater. Groundwater 35 1 (1997) 67-78
36. A.C. Hindmarsh, P.N. Brown, K.E. Grant, S.L. Lee, R.Serban, D.E. Shumaker, C.S. Woodward, SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers, ACM Trans. Math. Softw. 31 (2005) 363-396 (also available as LLNL Technical Report UCRL-JP-200037).
37. R. Eymard, T. Galloudt, R. Herbin, Finite volume methods, Handbook of Numerical Analysis, vol. VII, North-Holland, Amsterdam, 2000, pp. 713-1020.
38. C. de Dieuleveult, An efficient and robust global method for reactive transport, Ph.D. Thesis, University of Rennes 1, December 2008.