In this article, we describe horizontal groundwater flow due to a uniform flow at infinity around a cylindrical or elliptical inhomogeneity, where the permeability inside the inhomogeneity is anisotropic and different from the isotropic domain outside the inhomogeneity. The orientation of the uniform flow with respect to the orientation of the ellipse is arbitrary as well as the orientation of the anisotropy inside the ellipse. We derive an expression for the ratio of the flow through the ellipse with respect to the flow in the homogeneous case.
Batu V.: Applied Flow and Solute Transport Modeling in Aquifers: Fundamental Principles and Analytical and Numerical Methods. Taylor & Francis, Boca Raton, FL (2006)
Bear J.: Dynamics of Fluids in Porous Media. American Elsevier, New York (1972)
Carslaw H.S., Jaeger J.C.: Conduction of Heat in Solids, 2nd edn. Oxford University Press, Oxford (1959)
Dagan G.: Flow and Transport in Porous Formations. Springer-Verlag, Berlin (1989)
Dagan G., Lessoff S.C.: Solute transport in heterogeneous formations of bimodal conductivity distribution 1. Theory Water Resour. Res. 37(3), 465–472 (2001)
Dagan G., Fiori A., Janković I.: Flow and transport in highly heterogeneous formations: 1. Conceptual framework and validity of first-order approximations. Water Resour. Res. 39(9), 1268 (2003). doi:10.1029/2002WR001717
Janković I., Fiori A., Dagan G.: Effective conductivity of an isotropic heterogeneous medium of lognormal conductivity distributions. Multiscale Model. Simul. 1(1), 40–56 (2003a)
Janković I., Fiori A., Dagan G.: Flow and transport in highly heterogeneous formations: 3. Numerical simulations and comparison with theoretical results. Water Resour. Res. 39(9), 1270 (2003b). doi:10.1029/2002WR001721
Mityushev V.: Conductivity of a two-dimensional composite containing elliptical inclusions. Proc. R. Soc. A 465(2110), 2991–3010 (2009). doi:10.1098/rspa.2009.0219
Obdam A.N.M., Veling E.J.M.: Elliptical inhomogeneities in groundwater flow—an analytical description. J. Hydrol. 95, 87–96 (1987)
Phillips O.M.: Flow and Reactions in Permeable Rocks. Cambridge University Press, Cambridge (1991)
Strack, O.D.L.: Groundwater Mechanics. Prentice Hall, Englewood Cliffs (1989)
Suribhatla R., Bakker M., Bandilla K., Janković I.: Steady two-dimensional groundwater flow through many elliptical inhomogeneities. Water Resour. Res. 40, W04202 (2004). doi:10.1029/2003WR002718
Zimmerman R.: Effective conductivity of a two-dimensional medium containing elliptical inhomogeneities. Proc. R. Soc. Lond. A 452(1950), 1713–1727 (1996). doi:10.1098/rspa.1996.0091
The author thanks Christophe Frippiat (Louvain-la-Neuve, Belgium) for suggesting this problem.
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Veling, E.J.M. About the Porous Media Flow Through Circular and Elliptical Anisotropic Inhomogeneities. Transp Porous Med 91, 717–732 (2012). https://doi.org/10.1007/s11242-011-9868-9
- Analytical solution
- Groundwater flow
- Cylindrical inhomogeneity
- Elliptical inhomogeneity