An evaluation of temporally adaptive transformation approaches for solving Richards' equation

Advances in Water Resources

Volumn 22, Issue 8, 1999, Pages 831-840

  Williams, Glenn A ^a   Miller, Cass T ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; EQUATIONS OF MOTION; INTEGRATION; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS;

RICHARDS' EQUATION;

GROUNDWATER FLOW;

INFILTRATION; METHODOLOGY; RICHARDS EQUATION;

EID: 0033597588     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0309-1708(98)00048-7     Document Type: Article

References (52)

1. Gray, W. G., Paradoxes and realities in unsaturated flow theory. Water Resour. Res., 1991, 27(8), 1847-1854.
2. Miller, C. T., Christakos, G., Imhoff, P. T., McBride, J. F., Pedit, J. A. and Trangenstein, J. A. Multiphase flow and transport modelling in heterogeneous porous media: challenges and approaches. Adv. Water Resour., 1998, 21(2), 77-120.
3. Hanks, R. J. and Bowers, S. A. Numerical solution of the moisture flow equation for infiltration into layered soils. In Soil. Sci. Soc. Proc., 1962, pp. 530-534.
4. Rubin, J. Theoretical analysis of two-dimensional, transient flow of water in unsaturated and partly unsaturated soils. Soil Sci. Soc. Am. Proc., 1968, 32(5), 607-615.
5. Hornberger, G. M. and Remson, I. Numeric studies of a composite soil moisture ground-water system. J. Hydrol., 1969, 707-712.
6. Cooley, R. L. A finite-difference method for unsteady flow in variably saturated porous media: application to a single pumping well. Water Resour. Res., 1971, 7(10), 1607-1625.
7. Freeze, R. A. Three-dimensional, transient, saturated-unsaturated flow in a groundwater basin. Water Resour. Res., 1971, 7(2), 347-366.
8. Vauclin, M., Khanji, D. and Vauchad, G. Experimental and numerical study of a transient, two-dimensional unsaturated-saturated water table recharge problem. Water Resour. Res., 1979, 15, 1089-1101.
9. Cooley, R. L. Some new procedures for numerical solution of variably saturated flow problems. Water Resour. Res., 1983, 19(5), 1271-1285.
10. Huyakorn, P. S., Thomas, S. D. and Thompson, B. M. Techniques for making finite elements competitive in modeling flow in variably saturated porous media. Water Resour. Res., 1984, 20(8), 1099-1115.
11. Allen, M. B. and Murphy, C. L. A finite element collocation method for variably saturated flow in two space dimensions. Water Resour. Res., 1986, 22(11), 1537-1542.
12. Hills, R. G., Porro, I., Hudson, D. B. and Wierenga, P. J. Modeling one-dimensional infiltration into very dry soils. 1. Model development and evaluation. Water Resour. Res., 1989, 25(6), 1259-1269.
13. Abriola, L. M., Lang, J. R. Self-adaptive finite element solution of the one-dimensional unsaturated flow equation. Int. J. Numer. Methods Fluids, 1990, 10, 227-246.
14. Celia, M. A., Bouloutas, E. T. and Zarba, R. L. A general mass-conservative numerical solution for the unsaturated flow equation. Water Resour. Res., 1990, 26(7), 1483-1496.
15. Li, C. W. A simplified newton method with linear finite elements for transient unsaturated flow. Water Resour. Res., 1993, 29, 965-971.
16. Forsyth, P. A., Wu, Y. S. and Pruess, K. Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media. Adv. Water Resour., 1995, 18, 25-38.
17. Romano, N., Brunone, B. and Santini, A. Numerical analysis of one-dimensional unsaturated flow in layered soils. Adv. Water Resour., 1998, 21, 315-324.
18. Tocci, M. D., Kelley, C. T. and Miller, C. T. Accurate and economical solution of the pressure-head form of Richards' equation by the method of lines. Adv. Water Resour., 1997, 20(1), 1-14.
19. Williams, G. A., Miller, C. T. and Kelley, C. T. Transformation approaches for simulating flow in variably saturated porous media. Water Resour. Res., submitted.
20. Haverkamp, R., Vauclin, M., Touma, J., Wierenga, P. J. and Vachaud, G. A comparison of numerical simulation models for one-dimensional infiltration. Soil Sci. Soc. Am. J., 1977, 41, 285-294.
21. Kirkland, M. R., Hills, R. G. and Wierenga, P. J. Algorithms for solving Richards' equation for variably saturated soils. Water Resour. Res., 1992, 28(8), 2049-2058.
22. Milly, P. C. D. A mass-conservative procedure for time-stepping in models of unsaturated flow. Adv. Water Resour., 1985, 8(3), 32-36.
23. Celia, M. A., Ahuja, L. R. and Pinder, G. F. Orthogonal collocation and alternating-direction procedures for unsaturated flow problems. Adv. Water Resour., 1987, 10, 178-187.
24. Rathfelder, K. and Abriola, L. M. Mass conservative numerical solutions of the head-based Richards' equation. Water Resour. Res., 1994, 30(9), 2579-2586.
25. Baca, R. G., King, I. P. and Norton, W. R. Finite element models for simultaneous heat and transport in unsaturated soils. In Proc. of The Second International Conference on Finite Elements in Water Resources, pp. 1.19-1.35. Pentech, London, 1978.
26. Ross, P. J. Efficient numerical methods for infiltration using Richards' equation. Water Resour. Res., 1990, 26(2), 279-290.
27. Ross, P. J. and Bristow, K. L. Simulating water movement in layered and gradational soils using the Kirchhoff transform. Soil Sci. Soc. Am. J., 1990, 54, 1519-1524.
28. Pan, L. and Wierenga, P. J. A transformed pressure head-based approach to solve Richards' equation for variably saturated soils. Water Resour. Res., 1995, 31(4), 925-931.
29. Narasimhan, T. N. and Witherspoon, P. A. Numerical model for saturated-unsaturated flow in deformable porous media. Water Resour. Res., 1978, 14(7), 1017-1033.
30. Abriola, L. M. Finite element solution of the unsaturated flow equations using hierarchic basis functions. In Proc. Sixth Intl. Conf. Finite Elements in Water Resources, eds. A. sa da Costa et al., Springer, Berlin, 1986.
31. Miller, C. T., Williams, G. A. and Kelley, C. T. Robust solution of Richards' equation for non-uniform porous media. Water Resour. Res., submitted.
32. Yeh, G. T. FEMWATER: A Finite Element Model of Water Flow through Saturated-Unsaturated Porous Media - First Revision. Oak Ridge National Laboratory, Oak Ridge, TN, ORNL-5567/R1 edition.
33. Simunek, J. and van Genuchten, M. Th. The CHAIN-2D code for simulating the two-dimensional movement of water, heat, and multiple solutes in variably-saturated porous media. Technical Report 136, US Salinity Laboratory, USDA/ARS, Riverside, CA, 1994.
34. Simunek, J., Vogel, T. and van Genuchten, M. Th. The SWMS-2D Code for Simulating Water Flow and Solute Transport in Two-Dimensional Variably Saturated Media, Version 1.21. Technical Report 132, US Salinity Laboratory, USDA/ARS, Riverside, CA, 1994.
35. Simunek, J., Huang, K., Sejna, M. and van Genuchten, M. Th. The HYDRUS-1D Software Package for Simulating the One-Dimensional Movement of Water Heat, and Multiple Solutes Variably Saturated Media, Version 1.0. US Salinity Laboratory, USDA/ARS, Riverside, CA, 1997.
36. Ortega, J. M. and Rheinboldt, W. C. Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York, 1970.
37. Kelley, C. T. Iterative Methods for Linear and Nonlinear Equations, vol. 16, SIAM Frontiers in Applied Mathematics. SIAM, Philadelphia, PA, 1995.
38. Dennis, J. E. and Schnabel, R. B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia, PA, 1996.
39. Tocci, M. D., Kelley, C. T., Miller, C. T. and Kees, C. E. Inexact Newton methods and the method of lines for solving Richards' equation in two space dimensions. Comp. Geosciences, submitted.
40. Huyakorn, P. S. and Pinder, G. F. Computational Methods in Subsurface Flow. Academic Press, Orlando, FL, 1983.
41. de Marsily, G. Quantitative Hydrogeology: Groundwater Hydrology for Engineers. Academic Press, San Diego, CA, 1986.
42. van Genuchten, M. Th. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Am. J., 1980, 44, 892-898.
43. Mualem, Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res., 1976, 12, 513-522.
44. Brown, P. N., Hindmarsh, A. C. and Petzold, L. R. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Stat. Comp., 1994, 15, 1467-1488.
45. Brenan, K. E., Campbell, S. L. and Petzold, L. R. The Numerical Solution of Initial Value Problems in Differential-Algebraic Equations, vol. 16, SIAM Frontiers in Applied Mathematics. SIAM, Philadelphia, PA, 1996.
46. Haverkamp, R. and Vauclin, M. A note on estimating finite difference interblock hydraulic conductivity values for transient unsaturated flow problems. Water Resour. Res., 1979, 15(1), 181-187.
47. Warrick, A. W. Numerical approximations of darcian flow through unsaturated soil. Water Resour. Res., 1992, 27(6), 1215-1222.
48. Zaidel, J. and Russo, D. Estimation of finite difference interblock conductivities for simulation of infiltration into initially dry soils. Water Resour. Res., 1992, 28, 2285-2295.
49. Gilmore, P. and Kelley, C. T. IFFCO: Implicit Filtering for Constrained Optimization. Technical Report CRSC-TR93-7, Center for Research in Scientific Computing, North Carolina State University, Raleigh, NC, 1993.
50. Kool, J. B. and Parker, J. C. Development and evaluation of closed-form expressions for hysteretic soil hydraulic properties. Water Resour. Res., 1987, 23(1), 105-114.
51. Soil Conservation Service. Soil Taxonomy. Technical Report US Agricultural Handbook No. 436, Soil Survey Staff, 1975.
52. Carsel, R. F. and Parrish, R. S. Developing joint probability distributions of soil water retention characteristics. Water Resour. Res., 1988, 24, 755-769.