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

Zhu, Fangfang; Dodd, Nicholas


Fangfang Zhu

Professor of Coastal Dynamics


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.


Zhu, F., & Dodd, N. (2019). Quasi-exact solution of the Riemann problem for generalised dam-break over a mobile initially flat bed. Journal of Engineering Mathematics, 115(1), 99–119.

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
Keywords General Engineering; General Mathematics
Public URL
Publisher URL
Additional Information Received: 5 June 2018; Accepted: 12 February 2019; First Online: 6 March 2019


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