Applied Scientific Research

, Volume 39, Issue 1, pp 45–53 | Cite as

Ground water movement due to arbitrary changes in water level

  • R. Seshadri
  • T. Y. Na
Article

Abstract

The non self-similar boundary value problem of ground water movement due to arbitrary changes in water level is solved. The non self-similar solutions are generated from known similarity solutions using numerical methods.

Nomenclature

K

permeability of the aquifer

h

height of water level above the impermeable surface

V

void ratio

x

space coordinate

t

time

x t h

non-dimensional variables

L

characteristic length

f

dependent variable, defined in equation (5)

q

flow through a unit width, defined in equation (23a)

Greek letters

ζ

similarity variable

τ

time coordinate in non self-similar description

Subscripts

n

refers to the value of the function at time τ

Superscripts

ν

is the number of the iteration

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References

  1. 1.
    Bear J (1972) Dynamics of Fluids in Porous Media. American Elsevier Publishing Company.Google Scholar
  2. 2.
    Bluman GW and Cole JD (1974) Similarity Methods for Differential Equations. New York: Springer-Verlag.Google Scholar
  3. 3.
    Hansen AG (1964) Similarity Analyses of Boundary Value Problems in Engineering. Prentice Hall.Google Scholar
  4. 4.
    Keller HS (1978) Numerical Methods in Boundary Layer Theory. Annual Review of Fluid Mechanics 10:417–433.Google Scholar
  5. 5.
    Na TY (1979) Computational Methods in Engineering Boundary Value Problems. Academic Press Inc.Google Scholar
  6. 6.
    Zel'dovich YaB and Raizer YuP (1967) Physics of Shock Waves and High Temperature Hydrodynamic Phenomena. In Hayes WD and Probstein RF (eds) Vol 2. Academic Press.Google Scholar

Copyright information

© Martinus Nijhoff Publishers 1982

Authors and Affiliations

  • R. Seshadri
    • 1
  • T. Y. Na
    • 2
  1. 1.Syncrude Canada Ltd.EdmontonCanada
  2. 2.Department of Mechanical EngineeringUniversity of MichiganDearbornUSA

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