Articles | Volume 20, issue 7
Hydrol. Earth Syst. Sci., 20, 2669–2678, 2016
https://doi.org/10.5194/hess-20-2669-2016
Hydrol. Earth Syst. Sci., 20, 2669–2678, 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

Related authors

Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time
M. Levent Kavvas, Tongbi Tu, Ali Ercan, and James Polsinelli
Earth Syst. Dynam., 11, 1–12, https://doi.org/10.5194/esd-11-1-2020,https://doi.org/10.5194/esd-11-1-2020, 2020
Short summary
Variable Saturation Infiltration Model for Highly Vegetated Regions
James Polsinelli and M. Levent Kavvas
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2016-75,https://doi.org/10.5194/hess-2016-75, 2016
Revised manuscript has not been submitted
Short summary

Related subject area

Subject: Groundwater hydrology | Techniques and Approaches: Modelling approaches
Modelling the hydrological interactions between a fissured granite aquifer and a valley mire in the Massif Central, France
Arnaud Duranel, Julian R. Thompson, Helene Burningham, Philippe Durepaire, Stéphane Garambois, Robert Wyns, and Hervé Cubizolle
Hydrol. Earth Syst. Sci., 25, 291–319, https://doi.org/10.5194/hess-25-291-2021,https://doi.org/10.5194/hess-25-291-2021, 2021
Short summary
A new criterion for determining the representative elementary volume of translucent porous media and inner contaminant
Ming Wu, Jianfeng Wu, Jichun Wu, and Bill X. Hu
Hydrol. Earth Syst. Sci., 24, 5903–5917, https://doi.org/10.5194/hess-24-5903-2020,https://doi.org/10.5194/hess-24-5903-2020, 2020
Short summary
Physics-inspired integrated space–time artificial neural networks for regional groundwater flow modeling
Ali Ghaseminejad and Venkatesh Uddameri
Hydrol. Earth Syst. Sci., 24, 5759–5779, https://doi.org/10.5194/hess-24-5759-2020,https://doi.org/10.5194/hess-24-5759-2020, 2020
Short summary
Hydraulic and geochemical impact of occasional saltwater intrusions through a submarine spring in a karst and thermal aquifer (Balaruc peninsula near Montpellier, France)
Marie-Amélie Pétré, Bernard Ladouche, Jean-Luc Seidel, Romain Hemelsdaël, Véronique de Montety, Christelle Batiot-Guilhe, and Claudine Lamotte
Hydrol. Earth Syst. Sci., 24, 5655–5672, https://doi.org/10.5194/hess-24-5655-2020,https://doi.org/10.5194/hess-24-5655-2020, 2020
Short summary
Calibration of a lumped karst system model and application to the Qachqouch karst spring (Lebanon) under climate change conditions
Emmanuel Dubois, Joanna Doummar, Séverin Pistre, and Marie Larocque
Hydrol. Earth Syst. Sci., 24, 4275–4290, https://doi.org/10.5194/hess-24-4275-2020,https://doi.org/10.5194/hess-24-4275-2020, 2020
Short summary

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.
Download
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.