A generalized analytical solution for a nonlinear infiltration equation using the exp-Function method

Scientia Iranica

Volumn 18, Issue 1 A, 2011, Pages 36-46

  Asgari, A ^a   Bagheripour, M H ^b   Mollazadeh, M ^b  

^a TARBIAT MODARES UNIVERSITY   (Iran)

^b SHAHID BAHONAR UNIVERSITY OF KERMAN   (Iran)

Author keywords

Analytical solutions; Exp function method; Nonlinear infiltration equation; Richard's equation

Indexed keywords

ALGEBRA; GEOTECHNICAL ENGINEERING; INFILTRATION; POROUS MATERIALS; SOIL MOISTURE; SOLUTE TRANSPORT;

EXP-FUNCTION METHOD; GENERALIZED SOLUTION; NONLINEAR INFILTRATION EQUATION; PARTIAL DIFFERENTIAL; RICHARD'S EQUATION; SYMBOLIC COMPUTATION; UNSATURATED INFILTRATIONS; UNSATURATED POROUS MEDIUM;

NONLINEAR EQUATIONS;

COMPLEXITY; GEOTECHNICAL ENGINEERING; INFILTRATION; NONLINEARITY; NUMERICAL MODEL; POROUS MEDIUM; RICHARDS EQUATION; SOIL WATER; WATER CONTENT;

ACER;

EID: 79952941348     PISSN: 10263098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.scient.2011.03.005     Document Type: Article

References (45)

1. Mays, L.W., Water Resources Engineering, John Wiley & sons Inc., USA (2005).
2. Richards, L.A. "Capillary conduction of liquids through porous medium", Physics, 1, pp. 318-33 (1931).
3. Haverkamp, R., Vauclin, M., Tourna, J., Wierenga, P. and Vachaud, G. "Comparison of numerical simulation models for one dimensional infiltration", Soil Sci. Soc. Am., 41, pp. 285-294 (1977).
4. Paniconi, C., Ferraris, S., Putti, M., Pini, G. and Gambolati, G. "Three dimensional numerical codes for simulating groundwater contamination: FLOW3D, flow in saturated and unsaturated porous media", Pollut Model, Boston, CMP (1994).
5. Simunek, J., Sejna, M. and Van Genuchten, M.T. "HYDRUS-2-D: simulating water flow and solute transport in two-dimensional variably saturated media", USA Technical Report IGWMC, Golden Co. (1999).
6. Parlange, J.Y. "On solving the flow equation in unsaturated soils by optimization: horizontal infiltration", Soil Sci. Soc. Am. Proc., 39, pp. 415-418 (1975).
7. Parlange, J.Y., Barry, D.A., Parlange, M.B., Hogarth, W.L., Haverkamp, R. and Ross, P.J. "New approximate analytical technique to solve Richards equation for arbitrary surface boundary conditions", Water Resour Res., 33, pp. 903-906 (1975).
8. Parlange, J.Y., Haverkamp, R., Rand, R.H., Rendon, L. and Schmitz, G.H. "Water movement in soils: The role of analytical solutions in future developments in soil science research, Soil Science Society of America Spec. Publ., Madison, Wis., pp. 11-21 (1987).
9. Parlange, M.B., Prasad, S.N., Parlange, J.Y. and Romkens, M.J.M. "Extension of the Heaslet-Alksne technique to arbitrary soil water diffusivities", Water Resour Res., 28, pp. 2793-2797 (1992).
10. Parlange, J.Y., Hogarth, W.B., Barry, D.A., Parlange, M.B., Haverkamp, R. and Ross, P.J. "Analytical approximation to the solution of Richards' equation with applications to infiltration, ponding and time compression approximation", Adv. Water Resour., 23, pp. 189-194 (1999).
11. Rashidi, M.M., Domairry, G. and Dinarvand, S. "Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method", Communications in Nonlinear Science and Numerical Simulation (2007).
12. Serrano, S.E. and Adomian, G. "New contribution to the solution of transport equation in porous media", Math. Comput. Model, 24, pp. 15-25 (1996).
13. Serrano, S.E. "Analytical decomposition of the nonlinear unsaturated flow equation", Water Resour Res., 31, pp. 2733-2742 (1998).
14. Serrano, S.E. "Modeling infiltration with approximate solutions to Richard's equation", Hydro Eng., 9, pp. 421-432 (1999).
15. Pamuk, S. "Solution of the porous media equation by Adomian's decomposition method", Phys. Lett. A, 344, pp. 184-188 (2005).
16. Nasseri, M., Babolian, E., Daneshbod, Y. and Seyyedian, H. "An analytic solution of nonlinear infiltration equation using modified Adomian decomposition method", Computers and Geotechnics (in press), DOI 10.1016/j.compgeo.2008.05.0022008.
17. Wazwaz, A.M. "Traveling wave solutions for generalized forms of Burgers, Burgers-KdV and BurgersHuxley equations", Appl. Math. Comput., 169, pp. 639-656 (2005).
18. Nasseri, M., Shaghaghian, M.R., Daneshbod, Y. and Seyyedian, H. "An analytic solution of water transport in unsaturated porous media", Journal of Porous Media, 11, pp. 591-601 (2008).
19. Brooks, R.H. and Corey, A.T. "Hydraulic properties of porous media", Hydrology Paper, 3, Colorado State University, Fort Collins, 24 p. (1964).
20. Corey, A.T., Mechanics of Immiscible Fluids in Porous Media, Highlands Ranch Co., Water Resource Publications (1994).
21. He, J.H. and Wu, X.H. "Exp-function method for nonlinear wave equations", Chaos, Solitons & Fractals, 30, pp. 700-708 (2006).
22. He, J.H. and Abdou, M.A. "New periodic solutions for nonlinear evolution equations using exp-function method", Chaos Solitons & Fractals, 34, pp. 1421-1429 (2007).
23. Zhang, S. "Application of exp-function method to Riccati equation and new exact solutions with three arbitrary functions of Broer-Kaup-Kupershmidt equations", Physics Letters A, 372, pp. 1873-1880 (2008).
24. Ganji, D.D., Asgari, A. and Ganji, Z.Z. "Expfunction based solution of nonlinear Radhakrishnan, Kundu and Laskshmanan (RKL) equation", Acta. Appl. Math., DOI 10.1007/sl0440-008-9252-0.
25. Ganji, Z.Z., Ganji, D.D. and Asgari, A. "Finding general and explicit solutions of high nonlinear equations by the exp-function method", Comput. Math, with Appli., 58, pp. 2124-2130 (2009)
26. He, J.H. "Variational iteration method: A kind of nonlinear analytical technique: some examples", Int. J. Non-linear Mech., 34(4), pp. 699-708 (1999).
27. Jalilian, Y. "A variational iteration method for solving systems of partial differential equations and for numerical simulation of the reaction-diffusion brusselator model", Scientia Iranica, 15(2), pp. 223-229 (2008).
28. He, J.H. "Homotopy perturbation method: A new nonlinear analytical technique", Appl. Math. Comput., 135, pp. 73-79 (2003).
29. He, J.H. and Zhang, L.N. "Generalized solitary solution and compacton-like solution of the JaulentMiodek equations using the exp-function method", Phys. Lett. A, 372, pp. 1044-1047 (2008).
30. Ebaid, A. "Exact solitary wave solutions for some nonlinear evolution equations via exp-function method", Phys. Lett. A, 365(3), pp. 213-219 (2007).
31. Delleur, J.W., The Handbook of Groundwater Engineering, CRC Press, USA (2007).
32. Caputo, J., Caputo, G. and Stepanyants, Y.A. "Front solutions of Richards' equation. PACS: 52.35.Tc shock waves and discontinuities, 47.56.+r flows through porous media 52.35, Mw nonlinear phenomena: waves".
33. Smith, R.E., Infiltration Theory for Hydrologie Applications, USA (2002).
34. Richards, L.A. "Capillary conduction of liquids through porous mediums", Physics, 1, pp. 318-333 (1931).
35. Buckingham, E. Studies on the Movement of Soil Moisture, US. Dept. of Agriculture Bureau of Soils Bull (1907).
36. Philip, J.R., Theory of Infiltration, in Advances in Hydroscience, New York, Academic Press, pp. 215-296 (1969).
37. Carman, P. C. "The determination of the specific surface of powders" J. Soc. Chem. Ind. Trans., 57, p. 225 (1938).
38. Corey, A.T., Mechanics of Immiscible Fluids in Porous Media, Colorado Co., Water Resource Publication (1986).
39. Witelski, T.P. "Perturbation analysis for wetting front in Richards' equation", Transport Porous Med., 27, pp. 121-34 (1997).
40. Witelski, T.P. "Motion of wetting fronts moving into partially pre-wet soil", Adv. Water Resour., 28, pp. 1131-1141 (2005).
41. Basha, H.A. "Burgers' equation: a general nonlinear solution of infiltration and redistribution", Water Resour Res., 38, pp. 291-299 (2002).
42. Broadbridge, P. and Rogers, C. "Exact solution for vertical drainage and redistribution in soils", Eng. Math., 24, pp. 25-43 (1990).
43. Whitam, G.B., Linear and Nonlinear Waves, New York, Wiley (1974).
44. Wu, X.H. and He, J.H. "Solitary solutions, periodic solutions and compacton-like solutions using the expfunction method", Comput. Math., 54, pp. 966-986 (2007).
45. Yaghobi Moghaddam, M., Asgari, A. and Yazdani, H. "Exact travelling wave solutions for the generalized nonlinear Schrödinger (GNLS) equation with a source by extended tanh-coth, sine-cosine and expfunction methods", Appli. Math. Computa., 210, pp. 422-435 (2009).