Numerical modelling of mass transport in hydrogeologic environments: Performance comparison of the Laplace Transform Galerkin and Arnoldi modal reduction schemes

Advances in Water Resources

Volumn 21, Issue 3, 1998, Pages 217-235

  Farrell, D A ^a   Woodbury, A D ^a   Sudicky, E A ^a  

^a NONE

Author keywords

Arnoldi model reduction method; Laplace Transform Galerkin method; Mass transport; Numerical modelling

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; GEOLOGY; HYDRAULIC CONDUCTIVITY; LAPLACE TRANSFORMS; MASS TRANSFER;

ARNOLDI MODAL REDUCTION METHOD; HYDROGEOLOGIC ENVIRONMENTS; LAPLACE TRANSFORM GALERKIN METHOD;

HYDROLOGY;

HYDROGEOLOGY; MASS TRANSFER; MATHEMATICAL MODELING;

ARNODLI MODAL REDUCTION; HYDROGEOLOGY; LAPLACE TRANSFORM GALERKIN METHOD; MASS TRANSFER; MASS TRANSPORT; MODELLING; POROUS MEDIUM; SOLUTE TRANSPORT;

EID: 0032033262     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0309-1708(96)00042-5     Document Type: Article

References (39)

1. Ababou, R., McLaughlin, D., Gelhar, L. W. & Tompson, A. F. B., Numerical simulation of three dimensional saturated flow in randomly heterogeneous porous media. Transport in Porous Media, 4 (1989) 549-65.
2. Bear, J., Dynamics of Fluids in Porous Media. Elsevier, New York, 1972.
3. Behie, G. A. & Forsyth, P. A., Incomplete factorization methods for fully implicit simulation of enhanced oil recovery. SIAM J. Sci. Stat. Comput., 5(3) (1984) 543-61.
4. Beljin, M., Testing and validation of models for simulating solute transport in groundwater: Code intercomparison and evaluation of validation methodology, I.G.W.M.C., GWMI 88-11, 1988.
5. Burr, D. T., Sudicky, E. A. & Naff, R. L., Nonreactive and reactive solute transport in three-dimensional heterogeneous porous media: Mean displacement, plume spreading, and uncertainty. Water Resour. Res., 30(3) (1994) 791-815.
6. Celia, M. A. & Gray, W. G., Numerical Methods for Differential Equations: Fundamental Concepts for Scientific and Engineering Applications. Prentice Hall, Englewood Cliffs, New Jersey, 436 pp., 1992.
7. Chin, D. A. & Wang, T., An investigation of the validity of first-order stochastic dispersion theories in isotropic porous media. Water Resour. Res., 28(6) (1992) 1531-42.
8. Clifton, P. M. & Neuman, S. P., Effects of kriging and inverse modelling on conditional simulation of the Avra Valley aquifer in Southern Arizona. Water Resour. Res., 18(4) (1982) 1215-34.
9. Crump, K. S., Numerical inversion of Laplace transforms using a Fourier series approximation. J. Assoc. Comput. Mach., 23(1) (1976) 89-96.
10. Daus, A. D., Frind, E. O. & Sudicky, E. A., Comparative error analysis in finite element formulations of the advection-dispersion equation. Adv. Water Resour., 8 (1983) 86-95.
11. de Hoog, F. R., Knight, J. H. & Stokes, A. N., An improved method for numerical inversion of Laplace transform. SIAM J. Sci. Stat. Comput., 3(3) (1982) 357-66.
12. Delhomme, J. P., Spatial variability and uncertainty in groundwater flow parameters: A geostatistical approach. Water Resour. Res., 15(2) (1979) 269-80.
13. Dongarra, J. J., Linpack: User's Guide, Philidelphia: Society for Industrial and Applied Mathematics, 320 pp., 1979.
14. Freeze, R. A., A stochastic-conceptual analysis of one-dimensional groundwater flow in nonuniform homogeneous media. Water Resourc. Res., 11(5) (1975) 725-41.
15. Freeze, R. A. & Cherry, J. A., Groundwater. Prentice Hall, Englewood Cliffs, New Jersey, 1979.
16. Freyberg, D. L., A natural gradient experiment on solute transport in a sand aquifer; 2. Spatial moments and the advection and dispersion of nonreactive tracers. Water Resour. Res., 22(13) (1986) 2031-46.
17. Frind, E. O. & Hokkanen, G. E., Simulation of the Borden plume using the alternating direction Galerkin technique. Water Resour. Res., 23(5) (1987) 918-30.
18. Gelhar, L. W., Stochastic Subsurface Hydrology. Prentice Hall, Englewood Cliffs, New Jersey, 1993.
19. Huyakorn, P. S., Kretschek, A. G., Broome, R. W., Mercer, J. W. & Lester, B. H., Testing and validation of models for simulating solute transport in groundwater, HRI Rep. 35, Holcomb Res. Inst., Indianpolis, Ind., 1984.
20. Huyakorn, P. S. & Pinder, G. F., Computational Methods in Subsurface Flow. Academic Press, Inc. (London) Ltd, 473 pp., 1983.
21. Mantoglou, A., Digital simulation of multivariate two-and three-dimensional stochastic processes with a spectral turning bands method. Math. Geol., 19(2) (1987) 129-49.
22. Mantoglou, A. & Wilson, J. L., The turning bands method for the simulation of random fields using line generation by a spectral method. Water Resour. Res., 10(4) (1982) 1379-94.
23. Meija, J. & Rodriguez-Iturbe, I., On the synthesis of random fields from the spectrum: An application to the generation of hydrologic spatial processes. Water Resour. Res., 10(4) (1974) 705-11.
24. Mendoza, C. A., ORTHOFEM User's Guide Version 1.02, Waterloo Centre for Groundwater Research, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1.
25. Nour-Omid, B., Dunbar, W. S. & Woodbury, A. D., Lanczos and Arnoldi methods for solution of convection-diffusion equations. Comput. Methods Appl. Mech. Eng., 88 (1991) 75-95.
26. Ogata, A., Theory of dispersion in a granular medium, U.S. Geol. Surv. Prof. Paper 411-1, 1970.
27. Robin, M. J. L., Migration of reactive solutes in three-dimensional heterogeneous porous media, Ph.D. thesis, 124 pp., Dept. of Earth Sci., Univ. of Waterloo, Waterloo, Ont., Canada, 1991.
28. Robin, M. J. L., Gutjahr, A. L., Sudicky, E. A. & Wilson, J. L., Cross-correlated random field generator with direct Fourier transform method. Water Resour. Res., 29(7) (1993) 2385-97.
29. Ruan, F. & McLaughlin, D., An efficient multivariate random field generator using the Fast Fourier Transform, Eos Trans. AGU, 76(17), Spring Meeting Suppl., S57, 1995.
30. Saad, Y. & Schultz, M. H., GMRES: A generalized minimal residual algorithm for solving rionsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7 (1986) 856-69.
31. Sudicky, E. A., A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process. Water Resour. Res., 22(13) (1986) 2069-82.
32. Sudicky, E. A., The Laplace Transform Galerkin technique: A time-continuous finite element theory and application to mass transport in groundwater. Water Resour. Res., 25(8) (1989) 1833-46.
33. Sudicky, E. A. & McLaren, R. G., The Laplace Transform Galerkin technique for large-scale simulation of mass transport is discretely fractured porous formations. Water Resour. Res., 28(2) (1992) 499-514.
34. Sudicky, E. A., Cherry, J. A. & Frind, E. O., Migration of contaminants in groundwater at a landfill: A case study; 4. A natural gradient dispersion test. J. Hydrol., 63 (1983) 81-108.
35. Therrien, R., Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media, Ph.D. thesis, 116 pp., Dept. of Earth Sci., Univ. of Waterloo, Waterloo, Ont., Canada, 1992.
36. Tompson, A. F. B., Ababou, R. & Gelhar, L. W., Implementation of the three-dimensional turning bands random field generator. Water Resour. Res., 25(10) (1989) 2227-43.
37. Tompson, A. F. B. & Gelhar, L. W., Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media. Water Resour. Res., 26(10) (1990) 2541-62.
38. Woodbury, A. D., Dunbar, W. S. & Nour-Omid, B., Application of the Arnoldi algorithm to the solution of the advection-dispersion equation. Water Resour. Res., 26(10) (1990) 2579-90.
39. Xu, L. & Brusseau, M. L., A combined Laplace transform and streamline upwind approach for nonideal transport of solutes in porous media. Water Resour. Res., 31(10) (1995) 2483-9.