Abstract
A solution of steady-state Darcy’s flow in heterogeneous porous media is developed by means of the Dual Reciprocity Boundary Element Method (DRBEM). The governing equation is reduced to a Poisson-type equation involving a nonlinear non-homogeneous term. The Dual Reciprocity Method (DRM) is used for converting the resulting domain integral into equivalent boundary integrals. The present formulation is general as it allows the solution of Darcy’s flow with any hydraulic conductivity variation. Numerical examples are provided to demonstrate the validity of the procedure.
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References
C.A. Brebbia, J.C.F. Telles and L.C. Wrobel, Boundary Element Techniques: Theory and Applications in Engineering, Springer-Verlag, Berlin, 1984.
C.A. Brebbia and J. Dominguez, Boundary Elements. An Introductory Course, Computational Mechanics Publications, Southampton, and McGraw-Hill, New York, 1989.
R. Butterfield and G.R. Tomlin, ‘Integral techniques for solving zoned anisotropic continuum problems’, Proc. Int. Conf. on Variational Methods in Engineering, Vol. 2, Southampton, UK, 1972.
O.E. Lafe, J.A. Liggett and P.L-F. Liu, ‘BIEM solutions to combinations of leaky, layered, confined, unconfined, nonisotropic aquifers’, Water Resour. Res., Vol. 17, pp. 1431–1444, 1981.
G.P. Lennon, ‘Boundary element analysis of flow in heterogeneous porous media’, Proc. ASCE/HYD Specialty Conf., Hydraul. Div., ASCE, Cour d’Alene, Idaho, 1984.
R. Rangogni, ‘Numerical solution of the generalized Laplace equation by coupling the boundary element method and the perturbation method’, Appl. Math. Modelling, Vol. 10, pp. 266–270, 1986.
O.E. Lafe and A.H-D. Cheng, ‘A perturbation boundary element code for steady state groundwater flow in heterogeneous aquifers’, Water Resour. Res., Vol. 23, pp. 1079–1084, 1987.
O.E. Lafe, O. Owoputi and A.H-D. Cheng, ‘Two perturbation boundary element codes for steady groundwater flow in heterogeneous aquifers’, Computational Methods in Water Resources, Vol. 1, pp. 83–88, Computational Mechanics Publications, Southampton, and Elsevier, Amsterdam, 1988.
D.L. Clements, ‘A boundary integral equation method for the numerical solution of a second order elliptic equation with variable coefficients’, J. Austral. Math. Soc., Series B, Vol. 22, pp. 218–228, 1980.
A.H-D. Cheng, ‘Darcy’s flow with variable permeability: A boundary integral solution’, Water Resour. Res., Vol. 20, pp. 980–984, 1984.
A.H-D. Cheng, ‘Heterogeneities in flows through porous media by the boundary element method’, Topics in Boundary Element Research, Vol. 4, pp. 129–144, Springer-Verlag, Berlin, 1987.
D. Nardini and C.A. Brebbia, ‘Boundary integral formulation of mass matrices for dynamic analysis’, Topics in Boundary Element Research, Vol. 2, pp. 191–208, Springer-Verlag, Berlin, 1985.
P.W. Partridge, C.A. Brebbia and L.C. Wrobel, The Dual Reciprocity Boundary Element Method, Computational Mechanics Publications, Southampton, and Elsevier, London, 1991.
J. Bear, Hydraulics of Groundwater, McGraw-Hill, New York, 1979.
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© 1992 Computational Mechanics Publications
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El Harrouni, K., Ouazar, D., Wrobel, L.C., Brebbia, C.A. (1992). Dual Reciprocity Boundary Element Method for Heterogeneous Porous 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_10
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DOI: https://doi.org/10.1007/978-94-011-2872-8_10
Publisher Name: Springer, Dordrecht
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