Numerical methods for reactive transport on rectangular and streamline-oriented grids

Advances in Water Resources

Volumn 22, Issue 7, 1999, Pages 711-728

  Cirpka, Olaf A ^b   Frind, Emil O ^a   Helmig, Rainer ^c  

^a UNIVERSITY OF WATERLOO   (Canada)

^b Stanford University   (United States)

^c TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

Artificial diffusion; Finite volume schemes; Grid orientation; Transport modeling

Indexed keywords

AQUIFERS; COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; FINITE VOLUME METHOD; MASS TRANSFER; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; TRANSPORT PROPERTIES;

ADVECTION-DOMINATED REACTIVE TRANSPORT;

GROUNDWATER FLOW;

ADVECTION; FINITE VOLUME TECHNIQUE; FLOW MODELING; MATHEMATICAL METHOD;

ADVECTION; DIFFUSION; FINITE VOLUME METHOD; FLOW MODELING; NUMERICAL METHOD;

EID: 0033617511     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0309-1708(98)00051-7     Document Type: Article

References (35)

1. Arbogast, T., Wheeler, M. F. and Yotov, I. Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences. SIAM J. Numer. Anal., 1997, 34, 828-852.
2. Arbogast, T., Dawson, C. N., Keenan, P. T., Wheeler, M. F. and Yotov, I. Enhanced cell-centered finite differences for elliptic equations on general geometry. SIAM J. Sci. Comput., 1998, 19, 404-425.
3. Boris, J. P. and Book, D. L. Flux corrected transport: I. SHASTA, a fluid transport algorithm that works. J. Comput. Phys., 1973, 11, 38-69.
4. Brenan, K. E., Campbell, S. L. and Petzold, L. R. Numerical solution of initial-value problems in differential-algebraic equations. Elsevier, New York, 1989.
5. Brown, P. N., Hindmarsh, A. C. and Petzold, L. R. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput., 1994, 15, 1467-1488.
6. Casper, J. and Atkins, H. L. A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems. J. Comput. Phys., 1993, 106, 62-76.
7. Cirpka, O., Frind, E. O. and Helmig, R. Numerical simulation of biodegradation controlled by transverse mixing. J. Contam. Hydrol., submitted.
8. Cirpka, O., Frind, E. O. and Helmig, R. Streamline-oriented grid-generation of transport modelling in two-dimensional domains including wells. Advances Water Res., 1999, 22(7), 697-710.
9. Cirpka, O. and Helmig, R. Comparison of approaches for coupling of chemistry to transport in groundwater systems. In Helmig, R., Jäger, W., Kinzelbach, W., Knabner, P. and Wittum, G., editors. Modeling and Computation in Environmental Sciences, number 59 in Notes on Numerical Fluid Mechanics, Braunschweig, Vieweg Verlag, 1997, pp. 102-120.
10. Colella, P. Multidimensional upwind methods for hyperbolic conservation laws. J. Comput. Phys., 1990, 87, 171-200.
11. Deutsch, C. V. and Journel, A. G. GSLIB: Geostatistical software library and user's guide. Oxford University Press, New York, 1992.
12. Fabriol, R., Sauty, J.-P. and Ouzounian, G. Coupling geochemistry with a particle tracking transport model. J. Contam. Hydrol., 1993, 13, 117-129.
13. Frind, E. O. The principal direction technique: A new approach to groundwater contaminant transport modelling. In: K. Holz, U. Meissner, W. Zielke, C. Brebia, G. Pinder and W. Gray, editors. Proceedings of the fourth international conference on Finite Elements in water resources. Springer, New York, 1982, pp. 13-25.
14. Frind, E. O. and Pinder, G. F. The principal direction technique for solution of the advection-dispersion equation. In: Scientific Computing, North-Holland, New York, 1982, pp. 305-313.
15. Godunov, S. K. A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics. Math. Sb., 1959, 47, 271-303.
16. Harten, A. and Osher, S. Uniformly high-order accurate nonoscillatory schemes: I. SIAM J. Num. Anal., 1987, 24, 279-309.
17. MacNab Jr W. W. and Narasimhan, T. N. Modeling reactive transport of organic compounds in groundwater using a partial redox disequilibrium approach. Water Resour. Res., 1994, 30, 2619-2635.
18. Kinzelbach, W., Schäfer, W. and Herzer, J. Numerical modeling of natural and enhanced denitrification processes in aquifers. Water Resour. Res., 1991, 27, 1123-1135.
19. Lax, P. D. and Wendroff, B. Systems of conservation laws. Comm. Pure Appl. Math., 1960, 13, 217-237.
20. Lensing, H. H. Numerische Modellierung Mikrobieller Abbauprozesse im Grundwasser. Ph.D. Thesis, Universität Karlsruhe - Fakultät für Bauingenieur- und Vermessungswesen, Institut für Hydrologie und Wasserwirtschaft. Karlsruhe, Germany, 1995.
21. LeVeque, R. J. High resolution finite volume methods on arbitrary grids via wave propagation. J. Comput. Phys., 1988, 78, 36-63.
22. LeVeque, R. J. Numerical methods for conservation laws. Birkhäuser Verlag, Basel, 1992.
23. LeVeque, R. J. CLAWPACK User Notes. Applied Mathematics, University of Washington, Seattle, WA, 1995. http://www.amath.washington.edu/∼rjl/clawpack.html.
24. LeVeque, R. J. High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal., 1996, 33, 627-665.
25. Löhner, R., Peraire, K. M. J. and Vahdati, M. Finite-element flux-corrected transport (FEM-FCT) for the Euler and Navier-Stokes equation. Int. J. Num. Meth. Fl., 1987, 7, 1093-1109.
26. Parrott, A. K. and Christie, M. A. FCT applied to the 2-D Finite Element solution of tracer transport by single phase flow in a porous medium. In: K. W. Morton and M. J. Braines, editors. Numerical methods for fluid dynamics. Oxford University Press, Oxford, 1986, pp. 609-620.
27. Petzold, L. R. A description of DASSL: A differential/ algebraic system solver. Technical Report SAND 82-8637, SANDIA Nat. Lab., 1982.
28. Rice, J. G. and Schnipke, R. J. A monotone streamline upwind finite element method for convection-dominated flows. Comput. Meth. Appl. Mech. Eng., 1985, 48, 313-327.
29. Roe, P. L. Some contributions to the modeling of discontinuous flows. Lect. Notes Appl. Math., 1985, 22, 163-193.
30. Roe, P. L. and Sidilkover, D. Optimum positive linear schemes for advection in two and three dimensions. SIAM J. Numer. Anal., 1992, 29, 1542-1568.
31. Sweby, P. K. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal., 1984, 21, 2206-2223.
32. van Leer, B. Towards the ultimate conservative difference scheme: I. The quest of monotonicity. Springer Lecture Notes in Physics, 1973, 18, 163-168.
33. Walter, A. L., Frind, E. O., Blowes, D. W. Ptacek, C. J. and Molson, J. W. Modeling of multicomponent reactive transport in groundwater: 1. Model development and evaluation. Water Resour. Res., 1994, 30, 3137-3148.
34. Yen, G. and Chang, J. An exact peak capturing and oscillation-free scheme to solve advective-dispersion transport equations. Water Resour. Res., 1992, 28, 2973-2951.
35. Zalesak, S. T. Fully multidimensional Flux-Corrected Transport algorithm for fluids. J. Comput. Phys., 1979, 31, 335-362.