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A new numerical treatment of moving wet/dry fronts in dam-break flows

Al-Ghosoun, Alia; Herty, Michael; Seaid, Mohammed

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Authors

Alia Al-Ghosoun

Michael Herty



Abstract

The aim of this paper is to present a new finite volume method for moving wet/dry fronts in shallow water flows. The method consists on reformulating the shallow water equations in a moving wetted domain where the wet/dry interface is located using the speed of the water flow. A set of parametrized coordinates is introduced and the underlying equations are transformed to a new hyperbolic system with advection terms to be solved in fixed domains. A well-balanced finite volume method is developed to approximate numerical solutions of the parametrized system. We derive a well-balanced approximation of the source terms and prove that the proposed method is well-balanced for the shallow water flows in the presence of moving wet/dry fronts over non-flat topography. Several numerical results confirm the reliability and accuracy of the new method.

Citation

Al-Ghosoun, A., Herty, M., & Seaid, M. (2018). A new numerical treatment of moving wet/dry fronts in dam-break flows. Journal of Applied Mathematics and Computing, 59(1-2), 489-516. https://doi.org/10.1007/s12190-018-1189-5

Journal Article Type Article
Online Publication Date May 19, 2018
Publication Date Feb 28, 2018
Deposit Date Oct 29, 2019
Publicly Available Date Nov 13, 2019
Journal Journal of Applied Mathematics and Computing
Print ISSN 1598-5865
Electronic ISSN 1865-2085
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 59
Issue 1-2
Pages 489-516
DOI https://doi.org/10.1007/s12190-018-1189-5

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