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Solution of Burger’s Equation in a One-Dimensional Groundwater Recharge by Spreading Using q-Homotopy Analysis Method

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2016

Key Words:

Author Name
Abstract (2. Language): 
The ground water is recharged by spreading of the water in downward direction and the moisture content of soil increases. The mathematical formulation of the phenomena leads to the governing equation, which is a nonlinear partial differential equation in the form of Burger’s equation which has been solved by using q-homotopy analysis method with appropriate initial and boundary conditions. The average diffusivity coefficient over the whole range of moisture content is regarded as constant. It is concluded that the moisture content of soil increases with the depth Z and increasing time T . The numerical solutions of the governing equation have been obtained in the form of tables and graphs by using Mathematica coding. The numerical solution represents moisture content distribution in the vertically downward direction at any depth Z for time T > 0. This type of problems appears particularly in soil mechanics, hydrology, ceramic engineering and petroleum technology.
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REFERENCES

References: 

[1] M. Allen. Numerical modeling of multiphase flow in porous media, Adv. Water Resources,
8, 162-187. 1985.
[2] J. Bear. Dynamics of Fluids in PorousMedia, American Elsevier Publishing Company, Inc.,
New York, 1972.
[3] B. Faybishenko. Nonlinear dynamics in flow through unsaturated fractured porous media,
Status and perspectives, Reviews of Geophysics, 42(2). 2004.
[4] K. Hari Prasad, M. Mohan, and M. Shekhar. Modelling Flow Through Unsaturated Zone:
Sensitivity to Unsaturated Soil Properties, Sadhana, Indian Academy of Sciences, 26(6),
517-528. 2001.
[5] B. John. Two dimensional unsteady flow in unsturated porous media, Proceeding 1st
international conference finite elements in water resources, Princeton University, U.S.A.,
3.3-3.19, 1976.
[6] M. Joshi, N. Desai, andM. N.Mehta. One-dimensional and Unsaturated Fluid flow
through Porous Media, International Journal of Applied Mathematics and Mechanics,
6(18), 66-79. 2010.
[7] A. Klute. A numerical method for solving the flow equation for water in unsaturated
materials, Soil Science, 73(2), 105-116. 1952.
[8] V. Kovalevsky, G. Kruseman, K. Rushton, Series on groundwater: An international guide
for hydrogeological investigations, United Nations Educational, Scientific and Cultural
Organization 7, place de Fontenoy, 75352 Paris 07 SP, IHP-VI(3), 19. 2004.
[9] S. Liao. The proposed homotopy analysis technique for the solution of nonlinear equations,
PhD thesis, Shanghai Jiao Tong University, 1992.
REFERENCES 124
[10] S. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method. Modern Mechanics
and Mathematics, Chapman and Hall/CRC, Boca Raton, Fla, USA, Vol.2, 2004.
[11] R. Meher, M. N. Mehta and S. Meher, Adomian decomposition method for moisture content
in one-dimensional fluid flowthrough unsaturated porous media. International Journal
of Applied Mathematics and Mechanics, 6(7):13-23. 2010.
[12] M. N. Mehta. A singular perturbation solution of one-dimensional flow in unsaturated
porous media with small diffusivity coefficient, Proceeding of the national conference on
Fluid Mechanics and Fluid Power (FMEP ’75), E1-E4. 1975.
[13] M. N. Mehta and T. Patel. A solution of Burger’s equation type one-dimensional Groundwater
Recharge by spreading in Porous Media, The Journal of the Indian Academy of
Mathematics, 28(1), 25-32. 2006.
[14] M. N.Mehta and S. Yadav. Solution of Problemarising during vertical groundwater
recharge by spreading in slightly saturated Porous Media, Journal of Ultra Scientists of
Physical Sciences. 19(3), 541-546. 2007.
[15] R. Philips. Advances in hydro science (edited Ven Te Chow), Academic Press, New York,
6. 1970.
[16] P. Ya Polubarinova-Kochina. Theory of Groundwater Movement, Princeton University
Press, 499-500. 1962.
[17] M. El-Tawil and S. N. Huseen. The q-homotopy analysis method, International Journal
of Applied Mathematics and Mechanics, 8(15), 51-75. 2012.
[18] De Vries and Simmers. Ground water recharge: an overview and challanges, Journal of
Hydrology, 10(1):5-17. 2002.
[19] A. Verma and S. Mishra. A similarity solution of a one dimensional vertical groundwater
recharge through porous media,Revue Roumaine des Sciences Techniques Serie de
Mechanique Appliquee, 18(2), 345-351. 1973.
[20] A. Verma. The Laplace transform solution of one dimensional groundwater recharge by
spreading, Ricevnto il 21 Gennaio, Annals of Geophysics, XXII-1, 25-31. 1969.
[21] A. Verma. A Mathematical Solution of one-dimensional groundwater recharge for a very
deep water table, Proceeding 16th congress ISTAM, Allahbad, 1972.

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