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Eliminating discharge imbalances in predicting shallow water flows with shocks

Liang, D (2010) Eliminating discharge imbalances in predicting shallow water flows with shocks. The Hong Kong Institution of Engineers Transactions, 17. pp. 55-60. ISSN 1023-697X

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Abstract

The shallow water equations are widely used in modelling environmental flows. Being a hyperbolic system of differential equations, they admit shocks that represent hydraulic jumps and bores. Although the water surface can be solved satisfactorily with the modern shock-capturing schemes, the predicted flow rate often suffers from imbalances where shocks occur, eg the mass conservation is violated by failing to maintain a constant discharge rate at every cross-section in a steady open channel flow. A total-variation-diminishing Lax-Wendroff scheme is developed, and used to demonstrate how to achieve an exact flux balance. The performance of the proposed methods is inspected through some test cases, which include 1- and 2-dimensional, flat and irregular bed scenarios. The proposed methods are shown to preserve the mass exactly, and can be easily extended to other shock-capturing models.

Item Type: Article
Uncontrolled Keywords: Shallow Water, Supercritical Flow, Total Variation Diminishing, Shock-capturing, Lax-Wendroff Scheme
Subjects: UNSPECIFIED
Divisions: Div A > Fluid Mechanics
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 12:35
Last Modified: 10 Mar 2014 16:31
DOI:

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