High-Order Well-Balanced Finite Volume WENO Schemes with Conservative Variables Decomposition for Shallow Water Equations
Year: 2021
Author: Jiaojiao Li, Gang Li, Shouguo Qian, Jinmei Gao
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 4 : pp. 827–849
Abstract
This article presents well-balanced finite volume weighted essentially non-oscillatory (WENO) schemes to solve the shallow water equations (SWEs). Well-balanced schemes are characterized by preservation of the steady state exactly at the discrete level. The well-balanced property is of paramount importance in practical applications where many studied phenomena are regarded as small perturbations to equilibrium states. To achieve the well-balanced property, numerical fluxes presented here are constructed by means of a suitable conservative variables decomposition and the hydrostatic reconstruction idea. This decomposition strategy allows us to realize a novel simple source term approximation. Both rigorous theoretical analysis and extensive numerical examples all verify that the resulting schemes maintain the well-balanced property exactly. Furthermore, numerical results strongly imply that the proposed schemes can accurately capture small perturbations to the steady state and keep the genuine high-order accuracy for smooth solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0138
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 4 : pp. 827–849
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Shallow water equations source term WENO schemes well-balanced property hydrostatic reconstruction conservative variables decomposition.
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