Articles | Volume 20, issue 7
Hydrol. Earth Syst. Sci., 20, 2669–2678, 2016
Hydrol. Earth Syst. Sci., 20, 2669–2678, 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.
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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.,, 2002.
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.