Analytical model of infiltration under constant-concentration boundary conditions

Water Resources Research

Volumn 46, Issue 3, 2010, Pages

  Triadis, D ^a   Broadbridge, P ^b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b LA TROBE UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL MODEL; CLOSED FORM; DEGREE OF SATURATIONS; FORMAL POWER SERIES; FORMAL SERIES; INTEGRABLE MODELS; NUMERICAL INTEGRATIONS; PROGRAMMED ITERATIONS; SOIL WATER; SORPTIVITY; UNSATURATED SOIL;

ALGORITHMS; BOUNDARY CONDITIONS; DELTA FUNCTIONS; DIFFUSION IN LIQUIDS; GEOLOGIC MODELS; MATHEMATICAL MODELS; SEEPAGE; SOIL MOISTURE;

C (PROGRAMMING LANGUAGE);

ALGORITHM; BOUNDARY CONDITION; DIFFUSIVITY; FLOW MODELING; HYDRAULIC CONDUCTIVITY; NUMERICAL METHOD; ONE-DIMENSIONAL MODELING; SATURATION; SOIL WATER; SORPTION; UNSATURATED MEDIUM;

EID: 78751615982     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2009WR008181     Document Type: Article

References (37)

1. Abramowitz, M., and I. A. Stegun (Eds.) (1965), Handbook of Mathematical Functions, Dover, New York.
2. Barry, D. A., J.-Y. Parlange, and R. Haverkamp (1995), Comment on "Falling head ponded infiltration" by J. R. Philip, Water Resour. Res., 31(3), 787-789.
3. Bear, J. (1972), Dynamics of Fluids in Porous Media, Elsevier, New York.
4. Benton, E. R., and G. W. Platzman (1972), Table of solutions of onedimensional Burgers equation, Q. Appl. Math., 30(2), 195-212.
5. Broadbridge, P., and C. Rogers (1990), Exact solutions for vertical drainage and redistribution in soils, J. Eng. Math., 24(1), 25-43. (Pubitemid 20707344)
6. Broadbridge, P., and I. White (1987), Time to ponding: Comparison of analytic, quasi-analytic, and approximate predictions, Water Resour. Res., 23(12), 2302-2310. (Pubitemid 18536165)
7. Broadbridge, P., and I. White (1988), Constant rainfall rate infiltration: A versatile nonlinear model: 1. Analytic solution, Water Resour. Res., 24(1), 145-154. (Pubitemid 18549938)
8. Broadbridge, P., J. H. Knight, and C. Rogers (1988), Constant rate rainfall infiltration in a bounded profile-Solutions of a nonlinear model, Soil Sci. Soc. Am. J., 52(6), 1526-1533. (Pubitemid 19302604)
9. Broadbridge, P., M. P. Edwards, and J. E. Kearton (1996), Closed-form solutions for unsaturated flow under variable flux boundary conditions, Adv. Water Resour., 19(4), 207-213.
10. Broadbridge, P., D. Triadis, and J. M. Hill (2009), Infiltration from supply at constant water content: An integrable model, J. Eng. Math., 64, 193-206.
11. Carslaw, H. S., and J. C. Jaeger (1959), Conduction of Heat in Solids, Clarendon, Oxford, U. K.
12. Childs, E. C. (1969), An Introduction to the Physical Basis of Soil Water Phenomena, John Wiley, London.
13. x occurring in 2-phase flow in porous media, SIAM J. Appl. Math., 42(2), 318-332.
14. Green, W. H., and G. A. Ampt (1911), Studies on soil physics part I-The flow of air and water through soils, J. Agric. Sci., 4, 1-24, part 1.
15. Hillel, D. (1982), Introduction to Soil Physics, Academic, New York.
16. Kingston, J. G., and C. Rogers (1982), Reciprocal Bäcklund transformations of conservation laws, Phys. Lett. A, 92(6), 261-264.
17. Mualem, Y. (1976), A catalogue of the hydraulic properties of unsaturated soils, Tech. Rep. 442, Isr. Inst. of Technol., Haifa, Israel.
18. Parlange, J. Y., I. Lisle, R. D. Braddock, and R. E. Smith (1982), The 3-parameter infiltration equation, Soil Sci., 133(6), 337-341.
19. Philip, J. R. (1957a), The theory of infiltration: 1. The infiltration equation and its solution, Soil Sci., 83, 345-357.
20. Philip, J. R. (1957b), The theory of infiltration: 4. Sorptivity and algebraic infiltration equations, Soil Sci., 84, 257-264.
21. Philip, J. R. (1957c), The theory of infiltration: 2. The profile of infinity, Soil Sci., 83, 435-448.
22. Philip, J. R. (1969), Theory of infiltration, Adv. Hydrosci., 5, 215-296.
23. 1, Water Resour. Res., 26(9), 2023-2027.
24. Philip, J. R. (1995), Falling head ponded infiltration by J. R. Philip: Reply, Water Resour. Res., 31(3), 791-794.
25. Rogers, C., M. P. Stallybrass, and D. L. Clements (1983), On 2 phase filtration under gravity and with boundary infiltration-Application of a Bäcklund transformation, Nonlinear Anal. Theory Methods Appl., 7(1), 785-799. (Pubitemid 14485970)
26. Rosen, G. (1982), Method for the exact solution of a non-linear diffusionconvection equation, Phys. Rev. Lett., 49(25), 1844-1847.
27. Sander, G. C., J. Y. Parlange, V. Kuhnel, W. L. Hogarth, D. Lockington, and J. P. J. Okane (1988), Exact nonlinear solution for constant flux infiltration, J. Hydrol., 97(3-4), 341-346. (Pubitemid 18574444)
28. Ségol, G. (1994), Classic Groundwater Simulations: Proving and Improving Numerical Models, Prentice-Hall, Englewood Cliffs, N. J.
29. Smith, R. E., R. J. Smettem, P. Broadbridge, and D. A. Woolhiser (2002), Infiltration Theory for Hydrologic Applications, Water Resour. Monogr., vol. 15, AGU, Washington, D. C.
30. Stewart, J. M., and P. Broadbridge (1999), Calculation of humidity during evaporation from soil, Adv. Water Resour., 22(5), 495-505. (Pubitemid 29223910)
31. Tao, L. N. (1979), On free boundary problems with arbitrary initial and flux conditions, J. Appl. Math. Phys., 30, 416-426.
32. Warrick, A. W. (2003), Soil Water Dynamics, Oxford Univ. Press, Oxford, U.K.
33. Warrick, A. W., A. Islas, and D. O. Lomen (1991), An analytical solution to Richards' equation for time-varying infiltration, Water Resour. Res., 27(5), 763-766.
34. White, I., and P. Broadbridge (1988), Constant rate rainfall infiltration: A versatile nonlinear model: 2. Applications of solutions, Water Resour. Res., 24(1), 155-162. (Pubitemid 18549939)
35. Wolfram, S. (2003), The Mathematica Book, 5th ed., Wolfram Media, Champaign, Ill.
36. Yates, S. R., M. T. Van Genuchten, A. W. Warrick, and F. J. Leij (1992), Analysis of measured, predicted, and estimated hydraulic conductivity using the RETC computer-program, Soil Sci. Soc. Am. J., 56(2), 347-354. (Pubitemid 23376222)
37. Youngs, E. G. (1995), Developments in the physics of infiltration, Soil Sci. Soc. Am. J., 59(2), 307-313.