Lie group analysis of nonlinear inviscid flows with a free surface under gravity

Funding Sponsor

American University in Cairo

Author's Department

Mathematics & Actuarial Science Department

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https://doi.org/10.1016/j.cam.2013.07.051

Document Type

Research Article

Publication Title

Journal of Computational and Applied Mathematics

Publication Date

1-1-2014

doi

10.1016/j.cam.2013.07.051

Abstract

We applied the Lie group method in studying nonlinear inviscid flows with a free surface under gravity. This method reduces the number of independent variables by one. Therefore, for a system of partial differential equations with three independent variables we applied the method twice to yield a system represented by ordinary differential equations with appropriate corresponding conditions. We obtained analytical solutions for this system. Solutions for the free surface and the velocity components are obtained in closed form. The results are illustrated graphically for different parameters. © 2013 Elsevier B.V. All rights reserved.

First Page

17

Last Page

29

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