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Momentum Conservative Schemes for Shallow Water Flows

Momentum Conservative Schemes for Shallow Water Flows
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Year:    2014

East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 2 : pp. 152–165

Abstract

We discuss the implementation of the finite volume method on a staggered grid to solve the full shallow water equations with a conservative approximation for the advection term. Stelling & Duinmeijer [15] noted that the advection approximation may be energy-head or momentum conservative, and if suitable which of these to implement depends upon the particular flow being considered. The momentum conservative scheme pursued here is shown to be suitable for 1D problems such as transcritical flow with a shock and dam break over a rectangular bed, and we also found that our simulation of dam break over a dry sloping bed is in good agreement with the exact solution. Further, the results obtained using the generalised momentum conservative approximation for 2D shallow water equations to simulate wave run up on a conical island are in good agreement with benchmark experimental data.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.290913.170314a

East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 2 : pp. 152–165

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Finite volume method staggered grid conservative scheme shallow water equations.

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