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

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 velocitie...

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Main Authors: Zhu, Fangfang, Dodd, Nicholas
Format: Article
Language:English
Published: Springer Netherlands 2019
Subjects:
Online Access:https://eprints.nottingham.ac.uk/56412/
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author Zhu, Fangfang
Dodd, Nicholas
author_facet Zhu, Fangfang
Dodd, Nicholas
author_sort Zhu, Fangfang
building Nottingham Research Data Repository
collection Online Access
description 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 Lax [CBMS-Regional Conference Series in Applied Mathematics, SIAM, 1973]. 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 waves (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 locations, 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.
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spelling nottingham-564122020-03-06T04:30:12Z https://eprints.nottingham.ac.uk/56412/ Quasi-exact solution of the Riemann problem for generalised dam-break over a mobile initially flat bed Zhu, Fangfang Dodd, Nicholas 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 Lax [CBMS-Regional Conference Series in Applied Mathematics, SIAM, 1973]. 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 waves (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 locations, 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. Springer Netherlands 2019-03-06 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/56412/1/Quasi-exact%20solution%20of%20the%20Riemann%20problem%20for%20generalised%20dam-break%20over%20a%20mobile%20initially%20flat%20bed.pdf Zhu, Fangfang and Dodd, Nicholas (2019) Quasi-exact solution of the Riemann problem for generalised dam-break over a mobile initially flat bed. Journal of Engineering Mathematics . ISSN 0022-0833 Dam-break; Mobile bed; Quasi-exact solution; Shallow water equations; Simple wave https://link.springer.com/article/10.1007/s10665-019-09994-6 doi:10.1007/s10665-019-09994-6 doi:10.1007/s10665-019-09994-6
spellingShingle Dam-break; Mobile bed; Quasi-exact solution; Shallow water equations; Simple wave
Zhu, Fangfang
Dodd, Nicholas
Quasi-exact solution of the Riemann problem for generalised dam-break over a mobile initially flat bed
title Quasi-exact solution of the Riemann problem for generalised dam-break over a mobile initially flat bed
title_full Quasi-exact solution of the Riemann problem for generalised dam-break over a mobile initially flat bed
title_fullStr Quasi-exact solution of the Riemann problem for generalised dam-break over a mobile initially flat bed
title_full_unstemmed Quasi-exact solution of the Riemann problem for generalised dam-break over a mobile initially flat bed
title_short Quasi-exact solution of the Riemann problem for generalised dam-break over a mobile initially flat bed
title_sort quasi-exact solution of the riemann problem for generalised dam-break over a mobile initially flat bed
topic Dam-break; Mobile bed; Quasi-exact solution; Shallow water equations; Simple wave
url https://eprints.nottingham.ac.uk/56412/
https://eprints.nottingham.ac.uk/56412/
https://eprints.nottingham.ac.uk/56412/