Abstract
The COUPLEX1 Test case (Bourgeat et al., 2003) is devoted to the comparison of numerical schemes on a convection–diffusion–reaction problem. We first show that the results of the simulation can be mainly predicted by a simple analysis of the data. A finite volume scheme, with three different treatments of the convective term, is then shown to deliver accurate and stable results under a low computational cost.
Similar content being viewed by others
References
A. Bourgeat, M. Kern, S. Schumacher and J. Talandier, The Couplex test cases: Nuclear waste dis-posal simulation, Comput. Geosci. (2004), this issue.
Y. Coudière, T. Gallouët and R. Herbin, Discrete Sobolev inequalities and L p error estimates for finite volume solutions of convection diffusion equations, M2AN, Math. Model. Numer. Anal. 35 (2001) 767–778.
V. Dolejsi, M. Feistauer and C. Schwab, On discontinuous Galerkin methods for nonlinear convection–diffusion problems and compressible flow, Math. Bohem. 127 (2002) 163–179.
R. Eymard, T. Gallouët and R. Herbin, Convergence of finite volume schemes for semilinear convection diffusion equations, Numer. Math. 82 (1999) 91–116.
R. Eymard, T. Gallouët and R. Herbin, Finite volume methods, in: Handbook of Numerical Analysis Vol. VII, eds. P.G. Ciarlet and J.L. Lions (2000) pp. 723–1020.
R. Eymard, T. Gallouët and R. Herbin, Error estimate for approximate solutions of a nonlinear convection–diffusion problem, Adv. Differ. Equations 7 (2002) 419–440.
J. Fuhrmann and H. Langmach, Stability and existence of solutions of time-implicit finite volume schemes for viscous nonlinear conservation laws, Appl. Numer. Math. 37 (2001) 201–230.
R. Herbin, An error estimate for a finite volume scheme for a diffusion–convection problem on a triangular mesh, Numer. Methods Partial Differ. Equations 11 (1995) 165–173.
H. Hoteit, J. Erhel, R. Mosé, B. Philippe and Ph. Ackerer, Numerical reliability for mixed methods applied to flow problems in porous media, Comput. Geosci. 6 (2002) 161–194.
R.D. Lazarov, I.D. Mishev and P.S. Vassilevski, Finite volume methods for convection–diffusion prob-lems, SIAM J. Numer. Anal. 33 (1996) 31–55.
M. Ohlberger, A posteriori error estimates for vertex centered finite volume approximations of convection–diffusion–reaction equations, M2AN, Math. Model. Numer. Anal. 35 (2001) 355–387.
J.-M. Thomas and D. Trujillo, Mixed finite volume methods, Internat. J. Numer. Methods Engrg. 46 (1999) 1351–1366.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chénier, E., Eymard, R. & Nicolas, X. A Finite Volume Scheme for the Transport of Radionucleides in Porous Media. Computational Geosciences 8, 163–172 (2004). https://doi.org/10.1023/B:COMG.0000035077.63408.71
Issue Date:
DOI: https://doi.org/10.1023/B:COMG.0000035077.63408.71