A new convergence criterion for the modified Picard iteration method to solve the variably saturated flow equation

Journal of Hydrology

Volumn 178, Issue 1-4, 1996, Pages 69-91

  Huang, K ^a   Mohanty, B P ^a   Van Genuchten, M Th ^a  

^a U S SALINITY LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE CRITERION; PICARD ITERATION; POROUS MEDIUM; VARIABLY SATURATED MEDIUM; WATER FLOW; WATER RESOURCE;

ALGORITHMS; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; ENVIRONMENTAL IMPACT; HYDROLOGY; ITERATIVE METHODS; MATHEMATICAL MODELS; SATURATION (MATERIALS COMPOSITION); SOILS;

PICARD ITERATION METHOD; RICHARDS EQUATION; SATURATED FLOW EQUATION; TAYLOR SERIES EXPANSION; WATER CONTENT; WATER FLUX DISTRIBUTIONS;

FLOW OF WATER;

FLOW PATTERNS; ITERATIVE TECHNIQUES; PICARD; POROUS MEDIA-FLOW THROUGH; WATER RESOURCES;

EID: 0029657358     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/0022-1694(95)02799-8     Document Type: Article

References (33)

1. Allen, M.B. and Murphy, C.L., 1985. A finite element collocation method for variably saturated flows in porous media. Numer. Methods Partial Differential Equations, 1: 229-239.
2. Allen, M.B. and Murphy, C.L., 1986. A finite element collocation method for variably saturated flow in two space dimensions. Water Resour. Res., 22: 1537-1542.
3. Brutsaert, W.F., 1971. A functional iteration technique for solving the Richards equation applied to two dimensional infiltration problems. Water Resour. Res., 7: 1583-1596.
4. Celia, M.A. and Bining, P., 1992. A mass-conservative numerical solution for two-phase flow in porous media with application to unsaturated flow. Water Resour. Res., 28: 2819-2828.
5. Celia, M.A., Ahuja, L.R. and Pinder, G.F., 1987. Orthogonal collocation and alternating-direction procedures for unsaturated flow problems. Adv. Water Resour., 10: 178-187.
6. Celia, M.A., Bouloutas, E.T. and Zarba, R.L., 1990. A general mass-conservative numerical solution for the unsaturated flow equation. Water Resour. Res., 26: 1483-1496.
7. Cooley, R.L., 1983. Some new procedures for numerical solution of variably saturated flow problems. Water Resour. Res., 19: 1271-1285.
8. Davis, L.A. and Neuman, S.P., 1983. Documentation and user's guide: UNSAT2 - variable saturated flow model. NUREG/CR-3390, US Nuclear Regulatory Comm., Washington, DC.
9. El-Kadi, A.I. and Ling, G., 1993. The Courant and Peclet number criteria for the numerical solution of the Richards equation. Water Resour. Res., 29: 3485-3494.
10. Gottardi, G. and Venutelli, M., 1992. Moving finite element model for one-dimensional infiltration in unsaturated soil. Water Resour. Res., 28: 3259-3267.
11. Hills, R.G., Porro, I., Hudson, D.B. and Wierenga, P.J., 1989. Modeling one-dimensional infiltration into very dry soils 1. Model development and evaluation. Water Resour. Res., 25: 1259-1269.
12. Hopmans, J.W. and Stricker, J.N.M., 1989. Stochastic analysis of soil water regime in a watershed. J. Hydrol., 105: 57-84.
13. Huyakorn, P.S. and Pinder, G.F., 1983. Computational Methods in Subsurface Flow. Academic Press, Orlando, FL.
14. Huyakorn, P.F. and Wadsworth, T.D., 1985. FLAMINGO: a three-dimensional finite element code for analyzing water flow and solute transport in saturated-unsaturated porous media. GeoTrans, Inc., Herndon, VA.
15. Huyakorn, P.S., Thomas, S.D., Mercer, J.W. and Lester, B.H., 1983. SATURN: a finite element model for simulating saturated-unsaturated flow and radionuclide transport. Electric Power Research Institute, Palo Alto, CA.
16. Huyakorn, P.S., Kool, J.B. and Robertson, J.B., 1989. VAM2D - variably saturated analysis model in two dimensions (Version 5.0 with hysteresis and chain decay transport): documentation and user guide. NUREG/CR-5352, HGL89-01, Nuclear Regulatory Comm., Washington, DC.
17. Huang, K., Zhang, R. and van Genuchten, M.Th., 1994. An Eulerian-Lagrangian approach with an adaptively corrected method of characteristics to simulate variably saturated flow. Water Resour. Res., 30(2): 499-507.
18. Kaluarachchi, J.J. and Parker, J.C., 1989. An efficient finite element method for modeling multiphase flow. Water Resour. Res., 25: 43-54.
19. Kirkland, M.R., Hills, R.G. and Wierenga, P.J., 1992. Algorithms for solving Richards equation for variably saturated soils. Water Resour. Res., 28: 2049-2058.
20. Kool, J.B. and van Genuchten, M.Th., 1991. HYDRUS: one-dimensional variably saturated flow and transport model, including hysteresis and root water uptake. Res. Rep. 124, US Salinity Laboratory, USDA, ARS, Riverside, CA.
21. McCord, J.T., 1991. Application of second-type boundaries in unsaturated flow modeling. Water Resour. Res., 27: 3257-3260.
22. Milly, P.C.D., 1985. A mass-conservative procedure for time-stepping in models of unsaturated flow. Adv. Water Resour., 8: 32-36.
23. Neuman, S.P., 1973. Saturated-unsaturated flow seepage by finite element. Proc. ASCE, J. Hydraul. Div., 99(HY12).
24. Pan, L. and Wierenga, P.J., 1995. A transformed pressure head-based approach to solve Richards' equation for variably saturated soils. Water Resour. Res., 31: 925-931.
25. Rathfelder, K. and Abriola, L.M., 1994. Mass conservative numerical solutions of the head-based Richards equation. Water Resour. Res., 30: 2579-2586.
26. Ray, C. and Mohanty, B.P., 1992. Some numerical investigations of the Richards equation. ASAE Paper 92-2586. ASAE, St. Joseph, MI.
27. Richards, L.A., 1931. Capillary conduction of liquids in porous mediums. Physics, 1: 318-333.
28. Ross, P.J., 1990. Efficient numerical methods for infiltration using Richards equation. Water Resour. Res., 26: 279-290.
29. Ross, P.J. and Bristow, K.L., 1990. Simulating water movement in layered and gradational soils using the Kirchhoff transform. Soil Sci. Soc. Am. J., 54: 1519-1524.
30. Šimu̇nek, J., Vogel, T. and van Genuchten, M.Th., 1994. The SWMS_2D code for simulating water flow and solute transport in two-dimensional variably saturated media. Res. Rep. 132, US Salinity Laboratory, USDA, ARS, Riverside, CA.
31. Van Genuchten, M.Th., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J., 44: 892-898.
32. Vogel, T., Huang, K., Zhang, R. and van Genuchten, M.Th., 1995. The HYDRUS (Version 5.0) code for simulating one-dimensional water flow, solute transport, and heat movement in variably-saturated media. Res. Rep. 135, US Salinity Laboratory, USDA, ARS, Riverside, CA.
33. Zaidel, J. and Russo, D., 1992. Estimation of finite difference interblock conductivities for simulation of infiltration into initially dry soils. Water Resour. Res., 28: 2285-2295.