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Journal of Scientific Computing

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01-06-2015

Well-Balanced Central Schemes on Overlapping Cells with Constant Subtraction Techniques for the Saint-Venant Shallow Water System

Authors: Suo Yang, Alexander Kurganov, Yingjie Liu

Published in: Journal of Scientific Computing | Issue 3/2015

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Abstract

We develop well-balanced finite-volume central schemes on overlapping cells for the Saint-Venant shallow water system and its variants. The main challenge in deriving the schemes is related to the fact that the Saint-Venant system contains a geometric source term due to nonflat bottom topography and therefore a delicate balance between the flux gradients and source terms has to be preserved. We propose a constant subtraction technique, which helps one to ensure a well-balanced property of the schemes, while maintaining arbitrary high-order of accuracy. Hierarchical reconstruction limiting procedure is applied to eliminate spurious oscillations without using characteristic decomposition. Extensive one- and two-dimensional numerical simulations are conducted to verify the well-balanced property, high-order of accuracy, and non-oscillatory high-resolution for both smooth and nonsmooth solutions.

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Title: Well-Balanced Central Schemes on Overlapping Cells with Constant Subtraction Techniques for the Saint-Venant Shallow Water System
Authors: Suo Yang
Alexander Kurganov
Yingjie Liu
Publication date: 01-06-2015
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2015
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9908-z

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