Solutions of Boussinesq Equation in Semiinfinite Flow Region
Publication: Journal of Irrigation and Drainage Engineering
Volume 124, Issue 5
Abstract
In a semiinfinite flow region, prediction of the water table profile due to an abrupt rise or drop in the canal or drain water level in the cases of recharging and discharging aquifers has been done for times equal to 1.0, 2.0, 3.0, 4.0, and 5.0 days by employing a numerical solution and five analytical solutions. Comparison of the water table profile predicted by the proposed numerical solution with the existing analytical solutions (based on L2 and Tchebycheff norms) shows that the performance of Polubarinova-Kochina's 1948 solution is the best, followed by Lockington's 1997 solution, Verigin's 1949 solution, Polubarinova-Kochina's 1949 solution, and Edelman's 1947 solution for both recharging and discharging aquifers. However, for the example considered in this study, for practical purposes, any of these solutions except the Edelman solution may be adopted for predicting water table heights, because the maximum relative percentage difference in water table heights predicted by these analytical solutions and the proposed numerical solution is not more than ±1.5%.
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References
1.
Aravin, V. I., and Numerov, S. N. (1965). Theory of fluid flow in undeformable porous media. Israel Program for Scientific Translations, Daniel Davey and Co., New York, N.Y.
2.
Bear, J. (1979). Hydraulics of ground water. McGraw-Hill, New York, N.Y.
3.
Boussinesq, J. (1904). “Recherches theoriques sur l'ecoulement des nappes d'eau infiltree's dans le sol et sur le debit des sources.”Journal de Math, Pures et Appl., Series 5, Tome X (in French).
4.
Carslaw, H. S., and Jaeger, J. C. (1959). Conduction of heat in solids. 2nd Ed., Oxford at the Clarendon Press, London, U.K.
5.
Du Fort, H. C., and Frankel, S. P.(1953). “Stability conditions in the numerical treatment of parabolic differential equations.”Math. Tables Aids Comp., 7, 135–152.
6.
Edelman, F. (1947). “Over de berekening van ground water stromingen,” PhD thesis, University of Delft, Delft, The Netherlands (in Dutch).
7.
Hantush, M. S. (1964). “Hydraulics of wells.”Advances in hydroscience, Vol. 1, Ven Te Chow, ed., Academic Press, New York, N.Y., 305.
8.
Lockington, D. A.(1997). “Response of unconfined aquifer to sudden change in boundary head.”J. Irrig. and Drain. Engrg., ASCE, 123(1), 24–27.
9.
Polubarinova-Kochina, P. (1948). “On a non-linear partial differential equation, occurring in seepage theory.”Doklady Akademii Nauk, 36(6).
10.
Polubarinova-Kochina, P. (1949). “On unsteady flow of ground water seeping from reservoirs.”Prikladnaya Mathematika i Makhanika, 13(2).
11.
Polubarinova-Kochina, P. (1962). Theory of ground water movement. J. M. R. de Wiest, translator, Princeton University Press, Princeton, N.J.
12.
Prenter, P. M. (1975). Spline and variational methods. John Wiley & Sons, New York, N.Y., 6–11.
13.
Verigin, N. N. (1949). “On unsteady flow of ground water near reservoirs.”Doklady Akademii Nauk, 66(6).
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Copyright © 1998 American Society of Civil Engineers.
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Published online: Sep 1, 1998
Published in print: Sep 1998
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