Three-layer approximation of two-layer shallow water equations

Abstract

Two-layer shallow water equations describe flows that consist of two layers of inviscid fluid of different (constant) densities flowing over bottom topography. Unlike the single-layer shallow water system, the two-layer one is only conditionally hyperbolic: the system loses its hyperbolicity because of the momentum exchange terms between the layers and as a result its solutions may develop instabilities. We study a three-layer approximation of the two-layer shallow water equations by introducing an intermediate layer of a small depth. We examine the hyperbolicity range of the three-layer model and demonstrate that while it still may lose hyperbolicity, the three-layer approximation may improve stability properties of the two-layer shallow water system.

Keywords:

two-layer shallow water equations, central-upwind scheme, well-balanced scheme, conditional hyperbolicity

How to Cite

Chertock, A., Kurganov, A., Kurganov, A., Qu, Z., & Wu, T. (2013). Three-layer approximation of two-layer shallow water equations. Mathematical Modelling and Analysis, 18(5), 675-693. https://doi.org/10.3846/13926292.2013.869269

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December 1, 2013
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2013-12-01

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How to Cite

Chertock, A., Kurganov, A., Kurganov, A., Qu, Z., & Wu, T. (2013). Three-layer approximation of two-layer shallow water equations. Mathematical Modelling and Analysis, 18(5), 675-693. https://doi.org/10.3846/13926292.2013.869269

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