Modeling Water Table Rise Between Two Canal In Aquifer with Differential Quadrature Method.

Document Type : Research Paper

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Abstract

In many of agricultural land water table is raised because of seepage from canal and surface recharge. This raised is gradually caused some problem appear in land such as waterlogging and salinity, ultimately leading to land degradation. Therefore development of agriculture and economics in that region are endangered. It is necessary before problems appear engineers and researchers consider the variation of the groundwater table.In this article that problem has selected which shows an aquifer lied on a slopping impervious barrier which is discharged by a constant discharge from the surface and two canals with (L) horizontal distance. The initial water table is located horizontally h0 above the either horizontal or slopping bottom. After recharge and canal commencement, water table starts to rise. The rate of rising depends on the rate and duration of recharge and seepage from canal.
In this article, application of DQM in discretization of governing equations for chosen case study and formulation of the problem is presented. For further comparison and find more reliable answer are used three method for discretization of governing equation:1-Explicit Scheme,2-Implicit Scheme,3-Semi Implicit Crank Nicholson Scheme.
This investigation confirm that DQM has vast capability and simplicity to produce accurate results which is satisfactory compatible with Finite Difference numerical model as well as whit analytical solution while is highly efficient in time and low cost of running. The discretization scheme in this method does not establish large sets of simultaneous equation to be solved and is not sensitive to the number of grids in its mesh. There for with a very small number of grids comparing to a very large number of required grids in Finite Difference scheme produce very accurate results close to analytical solution results and create exactly the same results as Finite Difference scheme produce.

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References

Mustafa, S. (1987).Water table rise a semiconfined aquifer due to surface onfiltration and canal recharge. J.of Hydrology. 95(3),269-276.
Rai, S.N., Singh, R.N.(1992) .Water table fluctuations in an aquifer system owing to time-varying surface infiltration and canal recharge. J. of Hydrology. 136(1),381–387.[A1] 
Sewa, R., Jaiswal, C.S., Chauhan, H.S..(1994).Transient water table rise with canal seepage and recharge. J.of Hydrology. 163(3), 197–202.
Manglik, A., Rai, S. N., Singh, R. N..(1994). Water table fluctuation in response to transient recharge from a rectangular basin. J. Water Resource Management. 8(1),1-10.[A2] 
Manglik, A., Rai, S. N., Singh, R. N. .(1997). Response of an unconfined aquifer induced by time varying recharge from a rectangular basin. J. Water Resource Management . 11(3),185–196.
Upadhyaya , A. , Chauhan, H.S..(2001). Water table fluctuations due to canal seepage and time varying recharge. J. of Hydrology. 244 (1),1–8.
Upadhyaya , A. , Chauhan, H.S..(2002).Water Table Rise in Sloping Aquifer due to Canal Seepage and Constant Recharge. J. of Irrigation and Drainage Engineering. 2002, 128(3),160-167.
Bellman, R. ,Casti, J..(1971).Differential quadrature and long term integration. J. Math. Anal.Appl. 34(2),235–238.
Chen, R.P. , Zhou, W.H. , Wang, H.Z. , Chen, Y.M..(200). One - dimensional nonlinear consolidation of multi-layered soil by differential quadrature method. J. Computers and Geotechnics. 32(5) .358-369.
Hashemi ,M.R., Abedini ,M.J., Malekzadeh ,P.(2007). A Differential quadrature analysis of unsteady open channel flow. J. Appleid Math. Model. 31(8),1594–1608.
Hashemi ,M.R., Abedini ,M.J., Malekzadeh, P. (2006). Numerical modeling oflong waves in shallow water using incremental differential quadrature method . J.Ocean engineering.33(13) 1749-1764.
Robati, A. ,Barani, G.A. (2009). Modeling of water surface profile in subterranean channel by differential quadrature method (DQM). J. Appleid Math. Model.33(3),1295–1305.
Ozisik, M. N. (1980)  Heat conduction. New York .Wiley.[A3] 
Shu,C. ,Richards, B.E.(1990) High resolution of natural convection in square cavity by generalized differential quadrature. Proc of 3rd Conf on Adv in Numer. Methods in Eng. Theoryand App., Sewansea, UK, pp 978–985.
Shu, C.(2000) Differential Quadrature and its Application in Engineering.", London, Springer.
Jain, M. K., Iyenger, S. R. K., Jain, R. K.(1994) Computationalmethods for partial differential equations.New Delhi, Wiley.
 
 
 
Iranian Journal of Soil and Water Research
Volume 47, Issue 2
August 2016
Pages 307-317

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