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Transport in Porous Media

, Volume 18, Issue 1, pp 15–36 | Cite as

An integral equation formulation for the unconfined flow of groundwater with variable inlet conditions

  • Z. -X. Chen
  • G. S. Bodvarsson
  • P. A. Witherspoon
  • Y. C. Yortsos
Article

Abstract

We combine an integral equation formulation with a hodograph transformation to solve self-similar problems describing the unconfined flow of groundwater with variable inlet conditions. A class of new semi-analytical solutions is obtained for both rectilinear and radial flow geometries. The solutions are in general agreement with those derived by Barenblatt, although there are some discrepancies for the case of radial flow. The formulation presented provides additional analytical insight, and for computational purposes is simpler than Barenblatt's. In addition, the method proposed can be successfully used for the solution of a host of other nonlinear problems that admit self-similarity.

Key words

Analytical solution unconflned flow groundwater 

Nomenclature

a

parameter defined in (3) [L/T]

f

relative total discharge function for the case of constant head

g

gravitational constant [L/T2]

h

hydraulic head [L]

H

dimensionless hydraulic head

k

permeability [L2]

K

hydraulic conductivity [L/T]

Q

total discharge per unit width [L2/T]

R

relative total discharge function

r

radial distance [L]

t

time [T]

v

dimensionless total discharge

V

cumulative volume [L3]

w

total discharge per unit head

x

distance [L]

α

exponent of time variation of inlet head

λ

dimensionless constant defined in (9)

Μ

viscosity [M/TL]

ξ

similarity variable

ρ

density [M/L3]

Φ

porosity

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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Z. -X. Chen
    • 1
  • G. S. Bodvarsson
    • 1
  • P. A. Witherspoon
    • 1
  • Y. C. Yortsos
    • 2
  1. 1.Lawrence Berkeley LaboratoryUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of Chemical EngineeringUniversity of Southern CaliforniaLos AngelesUSA

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