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

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

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
• Public URL: https://durham-repository.worktribe.com/output/1280783