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Journal of Scientific Computing

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12-11-2016

Entropy-TVD Scheme for the Shallow Water Equations in One Dimension

Authors: Rongsan Chen, Min Zou, Li Xiao

Published in: Journal of Scientific Computing | Issue 2/2017

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Abstract

The Entropy-TVD scheme was developed for the non-linear scalar conservation laws in Chen and Mao (J Sci Comput 47:150–169, 2011). The scheme with step reconstruction simultaneously computes the two numerical entities, the numerical solution and the numerical entropy, and numerical examples show that the scheme provides a super-convergence rate. In this paper, we extend an Entropy-TVD scheme to the shallow water equations in one dimension. We prove that the scheme satisfies the entropy condition. Numerical tests show that the Entropy-TVD scheme has better resolution than the standard Godunov scheme.

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Title: Entropy-TVD Scheme for the Shallow Water Equations in One Dimension
Authors: Rongsan Chen
Min Zou
Li Xiao
Publication date: 12-11-2016
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2/2017
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0322-6

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