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Volume 13, Issue 4
High-Order Well-Balanced Finite Volume WENO Schemes with Conservative Variables Decomposition for Shallow Water Equations

Jiaojiao Li, Gang Li, Shouguo Qian & Jinmei Gao

Adv. Appl. Math. Mech., 13 (2021), pp. 827-849.

Published online: 2021-04

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  • 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.

  • AMS Subject Headings

74S05

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COPYRIGHT: © Global Science Press

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@Article{AAMM-13-827, author = {Li , JiaojiaoLi , GangQian , Shouguo and Gao , Jinmei}, title = {High-Order Well-Balanced Finite Volume WENO Schemes with Conservative Variables Decomposition for Shallow Water Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0138}, url = {http://global-sci.org/intro/article_detail/aamm/18753.html} }
TY - JOUR T1 - High-Order Well-Balanced Finite Volume WENO Schemes with Conservative Variables Decomposition for Shallow Water Equations AU - Li , Jiaojiao AU - Li , Gang AU - Qian , Shouguo AU - Gao , Jinmei JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 827 EP - 849 PY - 2021 DA - 2021/04 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2020-0138 UR - https://global-sci.org/intro/article_detail/aamm/18753.html KW - Shallow water equations, source term, WENO schemes, well-balanced property, hydrostatic reconstruction, conservative variables decomposition. AB -

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.

Jiaojiao Li, Gang Li, Shouguo Qian & Jinmei Gao. (1970). High-Order Well-Balanced Finite Volume WENO Schemes with Conservative Variables Decomposition for Shallow Water Equations. Advances in Applied Mathematics and Mechanics. 13 (4). 827-849. doi:10.4208/aamm.OA-2020-0138
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