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A Similarity Technique for Solving Two-Layer Shallow-Water Equations

¹ Department of Engineering Physics and Mathematics, Faculty of Engineering, Zagazig University, Zagazig, Egypt
² Department of Engineering Physics and Mathematics, Faculty of Engineering, Zagazig University, Zagazig, Egypt
³ Department of Engineering Physics and Mathematics, Faculty of Engineering, Zagazig University, Zagazig, Egypt
⁴ Department of Engineering Physics and Mathematics, Faculty of Engineering, Zagazig University, Zagazig, Egypt

Applied Mathematics·Volume 03 (2012)·Pages 315–321·Published 27 April 2012·DOI10.4236/am.2012.34047

Abstract

This paper is devoted to the analysis of the two-layer shallow-water equations representing gravity currents. A similarity technique which is the characteristic function method is applied for this study. The application of the characteristic function method makes it possible to obtain the similarity forms depending on a group of infinitesimal transformations. Thus, the number of independent variables is reduced by one and the governing partial differential equations with the auxiliary conditions reduce to a system of ordinary differential equations with the appropriate auxiliary conditions. Numeric solutions are presented and discussed.

KeywordsThe Characteristic Function MethodThe Two-Layer Shallow-Water EquationsGravity Currents

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A Similarity Technique for Solving Two-Layer Shallow-Water Equations

Abstract

References (19)