Flux-based methods of characteristics for coupled transport equations in porous media

Computing and Visualization in Science

Volumn 6, Issue 4, 2004, Pages 173-184

  Frolkovič, Peter ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE VOLUME METHOD; GROUNDWATER; MATHEMATICAL MODELS; POROUS MATERIALS;

ADVECTION DOMINATED TRANSPORT; COUPLED TRANSPORT EQUATIONS; HIGH RESOLUTION; LARGE SYSTEM; NUMERICAL SOLUTION; RADIOACTIVE CONTAMINANTS; RETARDATION FACTORS; TIME STEP;

ELECTRIC ARCS;

EID: 33748131967     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s00791-004-0126-3     Document Type: Article

References (26)

1. 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. Comput. Visualization Sci. 1(1), 27-40 (1997)
2. Bastian, P., Lang, S.: Couplex benchmark computations with UG. Technical Report 2002-31, IWR, Universität Heidelberg 2002
3. 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(1), 103-114 (1996)
4. Cai, Z., Mandel, J., Mc Cormick, S.: The finite volume element method for diffusion equations on general triangulations. SIAM J. Numer. Anal. 28(2), 392-402 (1991)
5. Prabhakar Clement, T.: Generalized solution to multispecies transport equations coupled with a first-order reaction network. Water Resources Research 37(1), 157-163 (January 2001)
6. Frolkovič, P.: Maximum principle and local mass balance for numerical solutions of transport equation coupled with variable density flow. Acta Mathematica Universitatis Comenianae 67(1), 137-157 (1998)
7. Frolkovič, P.: Discretization. In: Fein, E. (ed.), D3F -ein Programmpaket zur Modellierung von Dichteströmungen. Braunschweig, 1999. GRS-139, ISBN 3-923875-97-5, (see also http://www.iwr.uniheidelelberg. de/Peter.Frolkovic)
8. Frolkovič, P.: Flux-based method of characteristics for contaminant transport in flowing groundwater. Comput. Visualization Sci. 5(2), 73-83 (2002)
9. Frolkovič, P.: Flux-based methods of characteristics for transport problems in groundwater flow induced by sources and sinks. In: Hassanizadeh, S.M., Schotting, R.J., Gray,W.G., Pinder, G.F. (eds.), Comput. Meth. Water Resources 2, pp. 979-986, Elsevier 2002
10. Frolkovič, P., Geiser, J.: Numerical simulations of radionuclides transport in double porosity media with sorption. In: Handlovičova, A., et al. (eds.), Algoritmy 2000, pp. 28-36, Slovak University of Technology, Bratislava 2000
11. Frolkovič, P., Geiser, J.: Discretization methods with discrete minimum and maximum property for convection dominated transport in porous media. In: Dimov, I., et al. (eds.), Numer. Meth. Appl., Lecture Notes in Computer Science 2542, pp. 445-453, Berlin Heidelberg: Springer-Verlag 2003
12. Frolkovič, P., Mikula, K.: Flux-based level set method: a finite volume method for evolving interfaces. Preprint 15, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, September 2003
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(7), 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(1), 11-26 (1998)
15. Ikeda, T.: Maximum principle in finite element models for convectiondiffusion phenomena. North-Holland, Amsterdam, New York, Oxford 1983
16. Johannsen, K.: Aligned 3D-finite-volumes for convection- diffusionproblems. In: Vilsmeier, R., Benkhaldoun, F., (eds.), Finite Volumes for Complex Applications, pp. 291-300, Paris: Hermes 1996
17. Kačur, J., Frolkovič, P.: Semi-Analytical solutions for contaminant transport with nonlinear sorption in 1D. Preprint 24, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Oktober 2002
18. LeVeque, R.J.: Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press 2002
19. Malengier, B.: Dimensional splitting techniques for the flux based method of characteristics, in preparation
20. Ohlberger, M.: Higher order finite volume methods on selfadaptive grids for convection dominated reactive transport problems in porous media. Preprint 02-25, Mathematische Fakultät Freiburg 2002
21. Patankar, S.V.: Numerical heat transfer and fluid flow. Hemisphere Publishing Corporation 1980
22. Roache, P.J.: A flux-based modified method of characteristics. Int. J. Numer. Meth. Fluids 12, 1259-1275 (1992)
23. Russell, T.: Numerical dispersion in Eulerian-Lagrangian methods. In: Hassanizadeh, S.M., Schotting, R.J., Gray, W.G., Pinder, G.F. (eds.), Comput. Meth. In Water Resources 2, pp. 963-970, Elsevier 2002
24. Russell, T.: Private communication. November 2002
25. Russell, T.F., Celia, M.A.: An overview of research on Eulerian-Lagrangian localized adjoint methods (ELLAM). Advances in Water Resources 25, 1215-1231 (2002)
26. Sonar, T.: On the design of an upwind scheme for compressible flow on general triangulations. Numer. Algorithms 4, 135-149 (1993)