Flux-based method of characteristics for contaminant transport in flowing groundwater

Computing and Visualization in Science

Volumn 5, Issue 2, 2002, Pages 73-83

  Frolkovič, Peter ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; FINITE VOLUME METHOD; GROUNDWATER;

COMPUTATIONAL GRIDS; CONTAMINANT TRANSPORT; EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD; METHOD OF CHARACTERISTICS; NUMERICAL DISPERSIONS; NUMERICAL RESULTS; ONE-DIMENSIONAL PROBLEM; TRANSPORT PROBLEMS;

NUMERICAL METHODS;

EID: 0037668672     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s00791-002-0089-1     Document Type: Article

References (26)

1. Aizinger, V., Dawson, C., Cockburn, B., Castillo, P.: The local discontinuous Galerkin method for contaminant transport. Advances in Water Resources 24, 73-87 (2001)
2. Angermann, L.: An introduction to finite volume methods for linear elliptic equations of second order. Techn. Ber., Vol. 164, Institut für Angewandte Mathematik, Universität Erlangen, 1995
3. Angermann, L.: An upwind scheme of finite volume type with reduced crosswind diffusion. Techn. Ber., Vol. 165, Institut für Angewandte Mathematik, Universität Erlangen, 1995
4. Arbogast, T., Wheeler, M.F.: A characteristics-mixed finite element method for advection-dominated transport problems. SIAM J. Numer. Anal. 32, 404-424 (1995)
5. Bastian, P., Birken, K., Eckstein, K., Johannsen, K., Lang, S., Neuss, N., Rentz-Reichert, H.: UG -A flexible software toolbox for solving partial differential equations. Comp. Visual. Sci. 1, 27-40 (1997)
6. Bear, J., Verruijt, A.: Modeling Groundwater Flow and Pollution. Dordrecht, Boston, Lancaster, Tokyo: D. Reidel Publishing Company 1987
7. Binning, P., Celia, M.A.: A finite volume Eulerian-Lagrangian localized adjoint method for solution of the contaminant transport equations in two-dimensional multiphase flow systems. Water Resources Research 32, 103-114 (1996)
8. Celia, M.A., Russell, T.F., Herrera, I., Ewing, R.E.: An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation. Advances in Water Resources 13, 187-206 (1990)
9. Chilakapati, A.: A characteristic-conservative model for Darcian advection. Advances in Water Resources 22, 597-609 (1999)
10. Frolkovič, P., Geiser, J.: Numerical simulations of radionuclides transport in double porosity media with sorption. In: Handlovičová , A., Komorníková, M., Mikula, K., ?Sevčovič, D. (Eds.): Algoritmy 2000, pp. 28-36. Bratislava: Slovak University of Technology 2000
11. Frolkovič, P., De Schepper, H.: Numerical modelling of convection dominated transport coupled with density driven flow in porous media. Advances in Water Resources 24, 63-72 (2001)
12. Hackbusch, W.: On first and second order box schemes. Computing 41, 277-296 (1989)
13. Healy, R.W., Russel, T.F.: A finite-volume Eulerian-Lagrangian localized adjoint method for solution of the advection-dispersion equation. Water Resources Research 29, 2399-2413 (1993)
14. Healy, R.W., Russell, T.F.: Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method. Advances in Water Resources 21, 11-26 (1998)
15. Ikeda, T.: Maximum principle in finite element models for convectiondiffusion phenomena. Amsterdam, New York, Oxford: North-Holland 1983
16. Jianguo, H., Shitong, X.: On the finite volume element method for general self-Adjoint elliptic problems. SIAM J. Numer. Anal. 35, 1762-1774 (1998)
17. Johannsen, K.: Aligned 3D-finite-volumes for convection- diffusionproblems. In: Benkhaldoun F, Vilsmeier R. (Eds.): Finite Volumes for Complex Applications, pp. 291-300. Paris: Hermès 1996
18. Lanser, D., Verwer, J.G.: Analysis of operator splitting for advectiondiffusion-reaction problems from air pollution modelling. J. Comput. Appl. Math. 111, 201-216 (1999)
19. Leonard, B.P., Lock, A.P., MacVean, M.K.: The NIRVANA scheme applied to one-dimensional advection. Int. J. Numer. Methods Heat Fluid Flow 5, 341-377 (1995)
20. Leonard, B.P., Lock, A.P., MacVean, M.K.: Conservative explicit unrestricted-Time-step multidimensional constancy-preserving advection method. Monthly Weather Review 124, 2588-2606 (1996)
21. Lin, S.J., Rood, R.B.: Multidimensional flux-form semi-Lagrangian transport schemes. Monthly Weather Review 124, 2046-2070 (1996)
22. Manson, J.R., Wallis, S.G.: An accurate numerical algorithm for advective transport. Communications in Numerical Methods in Engineering 11, 1039-1045 (1995)
23. Roache, P.J.: A flux-based modified method of characteristics. Int. J. Numer. Methods Fluids 12, 1259-1275 (1992)
24. Roache, P.J.: Fundamentals of computational fluid dynamics. Albuquerque: Hermosa 1998
25. Wang, H., Dahle, H.K., Ewing, R.E., Espedal, M.S., Sharpley, R.C., Man, S.: An ELLAM scheme for advection-diffusion equations in two dimensions. SIAM J. Sci. Comput. 20, 2160-2194 (1999)
26. Frolkovič, P.: Flux-based methods of characteristics for transport problems in groundwater flows induced by sources and skins. In: Hassanizadeh, S.M., Schotting, R.J., Gray, W.G., Pinder, G.F. (Eds.): Computational methods in water resources, pp. 979-986. Elsevier 2002