Abstract
A boundary integral equation method for steady unsaturated flow in non-homogeneous porous media is presented. Steady unsaturated flow in porous media is described by the steady form of the so-called Richards equation, a highly nonlinear Fokker-Planck equation. By applying a Kirchhoff transformation and employing an exponential model for the relation between capillary pressure and hydraulic conductivity, the flow equation is rendered linear in each subdomain of a piece-wise homogeneous material. Unfortunately, the transformation results in nonlinear conditions along material interfaces, giving rise to a jump in the potential along these boundaries. An algorithm developed to solve the nonhomogeneous flow problem is described and verified by comparison to analytical and numerical solutions. The code is applied to examine the moisture distribution in a layered porous medium due to infiltration from a strip source, a model for infiltration from shallow ponds and washes in arid regions.
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References
Martinez, M. J. and McTigue, D. F. ‘The Distribution of Moisture Beneath a Two-Dimensional Surface Source’ Water Resources Research, Vol. 27, pp. 1193–1206, 1991.
Bear, J. Dynamics of Fluids in Porous Media American Elsevier, New York, 1972.
Philip, J. R. ‘Theory of Infiltration’ Advances in Hydroscience Vol. 5, pp. 215–296, 1969.
Philip, J. R. ‘The Scattering Analog for Infiltration in Porous Media’ Reviews of Geophysics Vol. 27, pp. 431–448, 1989.
Pullan, A. J. ‘The Quasilinear Approximation for Unsaturated Porous Media Flow’ Water Resources Research Vol. 26, pp. 1219–1234, 1990.
Carslaw, H. S. and Jaeger, J. C. Conduction of Heat in Solids 2nd. Ed., Oxford University Press, Oxford, 1978.
Rizzo, F. J. and Shippy, D. J. ‘A Formulation and Solution Procedure for the General Nonhomogeneous Elastic Inclusion Problem’ International Journal of Solids and Structures, Vol. 4, pp. 1161–1179, 1968.
Brebbia, C. A. and Walker, S. Boundary Element Techniques in Engineering Newnes-Butterworths, London and Boston, 1980.
Martinez, M. J. and Udell, K. S. ‘Axisymmetric Creeping Motion of Drops Through Circular Tubes’ Journal of Fluid Mechanics Vol. 210, pp. 565–591, 1990.
Haskell, K. H., Vandevender, W. H., and Walton, L. E., ‘The SLATEC common mathematics subprogram library: SNLA implementation’ Technical Report SAND80–2792, Sandia National Laboratories, Albuquerque, New Mexico, 1980.
Martinez, M. J., and McTigue, D. F., ‘A Boundary Integral Equation Method for Steady Two-Dimension al Flow in Partially Saturated Media’ Technical Report, SAND90-0253, Sandia National Laboratories, Albuquerque, New Mexico, July, 1991.
Eaton, R. R. and Hopkins, P. L. ‘LLUVIA-II: A Program for Two-Dimensional, Transient Flow Through Partially Saturated Porous Media’ Technical Report, SAND90-2416, Sandia National Laboratories, Albuquerque, New Mexico, to appear.
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© 1992 Computational Mechanics Publications
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Martinez, M.J. (1992). A Boundary Integral Method for Steady Unsaturated Flow in Nonhomogeneous Media. In: Brebbia, C.A., Ingber, M.S. (eds) Boundary Element Technology VII. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2872-8_11
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DOI: https://doi.org/10.1007/978-94-011-2872-8_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-85166-782-6
Online ISBN: 978-94-011-2872-8
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