Free Access
Issue
ESAIM: M2AN
Volume 43, Number 6, November-December 2009
Page(s) 1157 - 1183
DOI https://doi.org/10.1051/m2an/2009033
Published online 01 August 2009
  1. T. Barth and M. Ohlberger, Finite volume methods: foundation and analysis, in Encyclopedia of Computational Mechanics, E. Stein, R. de Borst and T.J.R. Hughes Eds., John Wiley & Sons, Ltd (2004). [Google Scholar]
  2. P. Bastian and S. Lang, Couplex benchmark computations with UG. Computat. Geosci. 8 (2004) 125–147. [CrossRef] [Google Scholar]
  3. J. Bear, Dynamics of fluids in porous media. American Elsevier, New York, USA (1972). [Google Scholar]
  4. J. Bear and Y. Bachmat, Introduction to Modeling of Transport Phenomena in Porous Media. Kluwer Academic Publishers, Dordrecht, Boston, London (1991). [Google Scholar]
  5. A. Bourgeat, M. Kern, S. Schumacher and J. Talandier, The COUPLEX test cases: Nuclear waste disposal simulation: Simulation of transport around a nuclear waste disposal site. Computat. Geosci. 8 (2004) 83–98. [CrossRef] [Google Scholar]
  6. M.A. Celia, T.F. Russell, I. Herrera and R.E. Ewing, An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation. Adv. Wat. Res. 13 (1990) 187–206. [CrossRef] [Google Scholar]
  7. G.R. Eykolt, Analytical solution for networks of irreversible first-order reactions. Wat. Res. 33 (1999) 814–826. [CrossRef] [Google Scholar]
  8. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods, in Handbook of Numerical Analysis 7, Amsterdam, North Holland (2000) 713–1020. [Google Scholar]
  9. R. Eymard, T. Gallouët and R. Herbin, Finite volume approximation of elliptic problems and convergence of an approximate gradient, in Handbook of Numerical Analysis 37, Appl. Numer. Math. (2001) 31–53. [Google Scholar]
  10. R. Eymard, T. Gallouët and R. Herbin, Error estimates for approximate solutions of a nonlinear convection-diffusion problem. Adv. Differ. Equ. 7 (2002) 419–440. [Google Scholar]
  11. I. Farago and J. Geiser, Iterative operator-splitting methods for linear problems. International J. Computat. Sci. Eng. 3 (2007) 255–263. [Google Scholar]
  12. E. Fein, Test-example for a waste-disposal and parameters for a decay-chain. Private communications, Braunschweig, Germany (2000). [Google Scholar]
  13. E. Fein, Physical Model and Mathematical Description. Private communications, Braunschweig, Germany (2001). [Google Scholar]
  14. E. Fein, T. Kühle and U. Noseck, Development of a software-package for three dimensional models to simulate contaminated transport problems. Technical Concepts, Braunschweig, Germany (2001). [Google Scholar]
  15. P. Frolkovič, Flux-based method of characteristics for contaminant transport in flowing groundwater. Comput. Vis. Sci. 5 (2002) 73–83. [CrossRef] [MathSciNet] [Google Scholar]
  16. P. Frolkovič and H. De Schepper, Numerical modeling of convection dominated transport coupled with density driven flow in porous media. Adv. Wat. Res. 24 (2001) 63–72. [Google Scholar]
  17. P. Frolkovič and J. Geiser, Numerical Simulation of Radionuclides Transport in Double Porosity Media with Sorption, in Proceedings of Algorithmy 2000, Conference of Scientific Computing (2000) 28–36. [Google Scholar]
  18. J. Geiser, Gekoppelte Diskretisierungsverfahren für Systeme von Konvektions-Dispersions-Diffusions-Reaktionsgleichungen. Doktor-Arbeit, Universität Heidelberg, Germany (2004). [Google Scholar]
  19. M.T. Genuchten, Convective-dispersive transport of solutes involved in sequential first-order decay reactions. Comput. Geosci. 11 (1985) 129–147. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  20. S.K. Godunov, A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics. Mat. Sb. 47 (1959) 271–290. [MathSciNet] [Google Scholar]
  21. E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Springer Series in Computational Mathematics 31. Springer Verlag Berlin, Heidelberg, New York (2002). [Google Scholar]
  22. A. Harten, B. Enguist, S. Osher and S. Charkravarthy, Uniformly high order esssentially non-oscillatory schemes I. SIAM J. Numer. Anal. 24 (1987) 279–309. [CrossRef] [MathSciNet] [Google Scholar]
  23. A. Harten, B. Enguist, S. Osher and S. Charkravarthy, Uniformly high order esssentially non-oscillatory schemes III. J. Computat. Phys. 71 (1987) 231–303. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  24. W.H. Hundsdorfer, Numerical Solution of Advection-Diffusion-Reaction Equations. Technical Report NM-N9603, CWI (1996). [Google Scholar]
  25. W. Hundsdorfer and J.G. Verwer, Numerical Solution of Time-dependent Advection-Diffusion-Reaction Equations, Springer Series in Computational Mathematics 33. Springer Verlag (2003). [Google Scholar]
  26. X.-D. Liu, S. Osher and T. Chan, Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115 (1994) 200–212. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  27. R.J. LeVeque, Numerical Methods for Conservation Laws, Lectures in Mathematics. Birkhäuser Verlag Basel, Boston, Berlin (1992). [Google Scholar]
  28. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics. Cambridge University Press (2002). [Google Scholar]
  29. R.I. McLachlan, R.G.W. Quispel, Splitting methods. Acta Numer. 11 (2002) 341–434. [CrossRef] [MathSciNet] [Google Scholar]
  30. K.W. Morton, On the analysis of finite volume methods for evolutionary problems. SIAM J. Numer. Anal. 35 (1998) 2195–2222. [CrossRef] [MathSciNet] [Google Scholar]
  31. P.J. Roache, A flux-based modified method of characteristics. Int. J. Numer. Methods Fluids 12 (1992) 1259–1275. [CrossRef] [Google Scholar]
  32. A.E. Scheidegger, General theory of dispersion in porous media. J. Geophysical Research 66 (1961) 32–73. [Google Scholar]
  33. C.-W. Shu, High order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD. Internat. J. Comput. Fluid Dynamics 17 (2003) 107–118. [CrossRef] [Google Scholar]
  34. T. Sonar, On the design of an upwind scheme for compressible flow on general triangulation. Numer. Anal. 4 (1993) 135–148. [Google Scholar]
  35. B. Sportisse, An analysis of operator-splitting techniques in the stiff case. J. Comput. Phys. 161 (2000) 140–168. [CrossRef] [MathSciNet] [Google Scholar]
  36. G. Strang, On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5 (1968) 506–517. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  37. Y. Sun, J.N. Petersen and T.P. Clement, Analytical solutions for multiple species reactive transport in multiple dimensions. J. Contam. Hydrol. 35 (1999) 429–440. [CrossRef] [Google Scholar]
  38. V. Thomee, Galerkin Finite Element Methods for Parabolic Problems, Lecture Notes in Mathematics 1054. Springer Verlag, Berlin, Heidelberg (1984). [Google Scholar]
  39. J.G. Verwer and B. Sportisse, A note on operator-splitting in a stiff linear case. MAS-R9830, ISSN (1998) 1386–3703. [Google Scholar]
  40. Z. Zlatev, Computer Treatment of Large Air Pollution Models. Kluwer Academic Publishers (1995). [Google Scholar]

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