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Ground water movement due to arbitrary changes in water level

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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.

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Abbreviations

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)

ζ :

similarity variable

τ :

time coordinate in non self-similar description

n :

refers to the value of the function at time τ

ν :

is the number of the iteration

References

  1. Bear J (1972) Dynamics of Fluids in Porous Media. American Elsevier Publishing Company.

  2. Bluman GW and Cole JD (1974) Similarity Methods for Differential Equations. New York: Springer-Verlag.

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  3. Hansen AG (1964) Similarity Analyses of Boundary Value Problems in Engineering. Prentice Hall.

  4. Keller HS (1978) Numerical Methods in Boundary Layer Theory. Annual Review of Fluid Mechanics 10:417–433.

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  5. Na TY (1979) Computational Methods in Engineering Boundary Value Problems. Academic Press Inc.

  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.

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Authors and Affiliations

  1. Syncrude Canada Ltd., Edmonton, Canada

    R. Seshadri (Senior Mechanical Engineer)

  2. Department of Mechanical Engineering, University of Michigan, Dearborn, Michigan, USA

    T. Y. Na (Professor)

Authors
  1. R. Seshadri
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  2. T. Y. Na
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Seshadri, R., Na, T.Y. Ground water movement due to arbitrary changes in water level. Applied Scientific Research 39, 45–53 (1982). https://doi.org/10.1007/BF00384370

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  • DOI: https://doi.org/10.1007/BF00384370

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