Asian Science

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Mathematical Modeling of Two-Dimensional Unconfined Flow in Aquifers


Affiliations
1 Department of Mathematics, Shivaji Arts, Commerce and Science College, Kannad, Aurangabad (M.S.), India
2 Department of Mathematics, Deogiri College, Aurangabad (M.S.), India
     

   Subscribe/Renew Journal


Derivation of general equation for two-dimensional aquifer flow is given. In this derivation we perform a volume balance instead of a mass balance and obtained analytical solutions of two-dimensional saturated flow under various condition. We also constructed transient unconfined groundwater flow equation by combining continuity equation with the Darcy law and provide an analytical solution.

Keywords

Aquifer, Analytical Solution, Unconfined, Two-Dimensional, Transmissivity, Isotropic.
Subscription Login to verify subscription
User
Notifications
Font Size


  • Bath, M. (1968). Mathematical aspects of seismology. In: Developments in solid earth physics, 4. Elsevier.

  • Boulton, N.S. (1954). The drawdown of the water table under nonsteady conditions near a pumped well in an unconfined formation. Proc. Instn Civ. Engrs, 3 (3) : 564-567.

  • Boulton, N.S. (1965). The discharge to a well in an extensive unconfined aquifer with constant pumping level. J. Hydrol., 3 : 124-130.

  • Brutsaert, W.F., Bretenback, E.A. and Sunda, D.K. (1971). Computer analysis of full surface well flow. J. Irrig. Drain. Div. ASCE, 97 : 405-420.

  • Carslaw, H.S. and Jaeger, J. C. (1959). Conduction of heat in solids, 2nd Ed., Oxford University Press, Ely House, LANDON, UNITED KINGDOM.

  • Charles, R. Fitts (2002). Groundwater science, Academic Press, An Imprint of Elsevier, 84 Theobalds Road, Landon WCIX 8RR, U.K.

  • Crank, J. (1975). Mathematical diffusion, Clarendon Press Oxford 1975. De Wiest, R.J.M. (1969) Flow through porous media. Academic Press.

  • Dupuit, J. (1863). Estudes thèoriques et pratiques sur le mouvement des eaux dans les canaux dècouverts et à travers les terrains permèables, 2nd Ed., Dunod, Paris, 304-304pp.

  • Forchheimer, P. (1886). Ueber die ergiebigkeit von brunnenanlagen und sickerschlitzen. Z. Architekt. Ing. Ver. Hannover, 32 : 539–563.

  • Gambolati, G. (1976). Transient free surface flow to a well:An analysis of theoretical solutions. Wat. Resour. Res., 2 : 27-39.

  • Jacob Bear (1979). Hydraulics of groundwater, McGraw-Hill Series in Water Resources and Environmental Engineering, NEW YORK, U.S.A.

  • James, W. (1980).Mercer and charles R. Faust, ground water, 18 (3) May-June 1980.

  • Kirkham, D. (1967). Explanation of paradoxes in DupuitForchheimer Seepage Theory. DOI: 10.1029/WR003i002 p00609.

  • Necati ozisic, M. (1993). Heat conduction, 2nd Ed., A WileyInterscience Publication, John Wiley & Sons, Inc. NEWYORK, U.S.A.

  • Nguyen, V.U. and Raudkivi, A.J. (1983). Analytical solution for transient two-dimensional unconfined groundwater flow, hydrological sciences, J.-des Sci. Hydrologiques, 28 : 2-6.

  • Polubarinova-Kochina, P.Y.A. (1962) Theory of underground water movement. Princeton University Press.

  • Raudkivi, A.J. and Callander, R.A. (1976). Analysis of groundwater flow. Arnold.

  • Raudkivi, A.J. (1979). Hydrology. Pergamon Press, Oxford, U.K.

  • Singh, R.N. (2013). Advection diffusion equation models in near-surface geophysical and environmental sciences J. Indian Geophys. Union, 17 (2) : 117-127.

  • Streltsova, J.D. (1975). Unsteady unconfined flow into a surface reservoir. J. Hydrol., 27 : 95-110.

  • Szabo, B.A. and McGaig, I.W. (1968). A mathematical model for transient free surface flow in non homogeneous or anisotropic porous media. Wat. Resour. Bull., 4 (3) : 5.

  • Thiem, G. (1906). Hydrologische methoden [Hydrological methods]. PhD Thesis, University of Stuttgart, Stuttgart, Germany.

  • Tsai, W.F. and Chen, C.J. (1996). Closure of unsteady finiteanalytic method for solute transport in ground-water flow, J. Engg. Mechanics, American Society of Civil Engineers, 122 : 589-589.

  • Vauclin, M., Vachaud, G. and Khanji, J. ( 1975). Two dimensional numerical analysis of transient water transfer in saturated-unsaturated soils. In: G.C. Vansteenkiste (Editor), Modeling and Simulation of water Resources Systems, North-Holland, Amsterdam, pp. 299-323.

  • Yates, S.R. (1992). An analytical solution for one-dimensional transport in porous media with an exponential dispersion function, Water Resour. Res., 28 : 2149-2154.


Abstract Views: 715

PDF Views: 49




  • Mathematical Modeling of Two-Dimensional Unconfined Flow in Aquifers

Abstract Views: 715  |  PDF Views: 49

Authors

R. V. Waghmare
Department of Mathematics, Shivaji Arts, Commerce and Science College, Kannad, Aurangabad (M.S.), India
S. B. Kiwne
Department of Mathematics, Deogiri College, Aurangabad (M.S.), India

Abstract


Derivation of general equation for two-dimensional aquifer flow is given. In this derivation we perform a volume balance instead of a mass balance and obtained analytical solutions of two-dimensional saturated flow under various condition. We also constructed transient unconfined groundwater flow equation by combining continuity equation with the Darcy law and provide an analytical solution.

Keywords


Aquifer, Analytical Solution, Unconfined, Two-Dimensional, Transmissivity, Isotropic.

References