Articles | Volume 20, issue 7
https://doi.org/10.5194/hess-20-2669-2016
https://doi.org/10.5194/hess-20-2669-2016
Research article
 | 
08 Jul 2016
Research article |  | 08 Jul 2016

A comparison of the modern Lie scaling method to classical scaling techniques

James Polsinelli and M. Levent Kavvas

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Cited articles

Barenblatt, G. I.: Scaling, self-similarity, and intermediate asymptotics, Cambridge University Press, New York, NY, 1996.
Bear, J.: Dynamics of fluids in porous media, American Elsevier, New York, 1972.
Bear, J. and Buchlin, J.-M. (Eds.): Modelling and Applications of Transport Phenomena in Porous Media, in: Theory and Applications of Transport in Porous Media, Kluwer Academic Publishers, Dordrecht; Boston, 5, XII, 381 pp., https://doi.org/10.1007/978-94-011-2632-8, 1991.
Bertrand, J.: Sur l'homogeneite dans les formules de physique, Comptes Rendus, 86, 916–920, 1878.
Bluman, G. W. and Anco, S. C.: Symmetry and Integration Methods for Differential Equations, in: Applied Mathematical Sciences, Springer-Verlag, New York, 154, X, 422 pp., https://doi.org/10.1007/b97380, 2002.
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Short summary
This article summarizes the theory and demonstrates the technique of a new scaling method known as the Lie scaling. In the course of applying the method to two example problems, classical notions of dynamical and kinematic scaling are incorporated. The two example problems are a 2-D unconfined groundwater problem in a heterogeneous soil and a 1-D contaminant transport problem. The article concludes with comments on the relative strengths and weaknesses of Lie scaling and classical scaling.