Quasi-exact solution of the Riemann problem for generalised dam-break over a mobile initially flat bed

Zhu, Fangfang; Dodd, Nicholas

Abstract

This paper investigates dam-break problems with flows on one or two sides of zero or nonzero velocities over a mobile initially flat bed, and quasi-exact solutions are presented by solving the Riemann problems using the simple wave theory. The flow structures after dam collapse for nonzero velocities are much richer than those for zero velocities on both sides, although they are also a combination of waves of different characteristic families, which are consistent with [7]. The wave can be a rarefaction, a shock, or a combination of a rarefaction and a semi-characteristic shock. The semi-characteristic shock is related to the morphodynamic characteristics. The relationship between morphodynamic and hydrodynamic characteristics is illustrated, along with types of wave (shock, rarefaction or a combination of these), and sediment convergence and type of characteristic. It is shown that the types of waves that may occur in the Riemann solution, and, in some cases, their possible approximate location, can be determined prior to the construction of the Riemann solution itself. The Riemann solution presented here can be used to study shock-shock interactions.

• Journal Article Type: Article
• Acceptance Date: Feb 14, 2019
• Online Publication Date: Mar 6, 2019
• Publication Date: 2019-04
• Deposit Date: Feb 15, 2019
• Publicly Available Date: Mar 7, 2020
• Journal: Journal of Engineering Mathematics
• Print ISSN: 0022-0833
• Electronic ISSN: 1573-2703
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 115
• Issue: 1
• Pages: 99–119
• DOI: https://doi.org/10.1007/s10665-019-09994-6
• Keywords: General Engineering; General Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/1551108
• Publisher URL: https://link.springer.com/article/10.1007/s10665-019-09994-6
• Additional Information: Received: 5 June 2018; Accepted: 12 February 2019; First Online: 6 March 2019