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Solving Two-Mode Shallow Water Equations Using Finite Volume Methods

Solving Two-Mode Shallow Water Equations Using Finite Volume Methods
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Year:    2014

Communications in Computational Physics, Vol. 16 (2014), Iss. 5 : pp. 1323–1354

Abstract

In this paper, we develop and study numerical methods for the two-mode shallow water equations recently proposed in [S. STECHMANN, A. MAJDA, and B. KHOUIDER, Theor. Comput. Fluid Dynamics, 22 (2008), pp. 407–432]. Designing a reliable numerical method for this system is a challenging task due to its conditional hyperbolicity and the presence of nonconservative terms. We present several numerical approaches – two operator splitting methods (based on either Roe-type upwind or central-upwind scheme), a central-upwind scheme and a path-conservative central-upwind scheme – and test their performance in a number of numerical experiments. The obtained results demonstrate that a careful numerical treatment of nonconservative terms is crucial for designing a robust and highly accurate numerical method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.180513.230514a

Communications in Computational Physics, Vol. 16 (2014), Iss. 5 : pp. 1323–1354

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    32

Keywords:   

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