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Volume 14, Issue 5
A Well-Balanced Weighted Compact Nonlinear Scheme for Pre-Balanced Shallow Water Equations

Mingyang Cheng, Lingyan Tang, Yaming Chen & Songhe Song

Adv. Appl. Math. Mech., 14 (2022), pp. 1181-1200.

Published online: 2022-06

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  • Abstract

It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical errors. In this paper, a well-balanced weighted compact nonlinear scheme (WCNS) is proposed for shallow water equations in pre-balanced forms. The scheme is proved to be well-balanced provided that the source term is treated appropriately as the advection term. Some numerical examples in one- and two-dimensions are also presented to demonstrate the well-balanced property, high order accuracy and good shock capturing capability of the proposed scheme.

  • Keywords

Shallow water equation, weighted compact nonlinear scheme, well-balanced property, shock capturing property.

  • AMS Subject Headings

65N12, 76M20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-1181, author = {Mingyang and Cheng and and 23528 and and Mingyang Cheng and Lingyan and Tang and and 23529 and and Lingyan Tang and Yaming and Chen and and 23530 and and Yaming Chen and Songhe and Song and and 23531 and and Songhe Song}, title = {A Well-Balanced Weighted Compact Nonlinear Scheme for Pre-Balanced Shallow Water Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {5}, pages = {1181--1200}, abstract = {

It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical errors. In this paper, a well-balanced weighted compact nonlinear scheme (WCNS) is proposed for shallow water equations in pre-balanced forms. The scheme is proved to be well-balanced provided that the source term is treated appropriately as the advection term. Some numerical examples in one- and two-dimensions are also presented to demonstrate the well-balanced property, high order accuracy and good shock capturing capability of the proposed scheme.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0117}, url = {http://global-sci.org/intro/article_detail/aamm/20557.html} }
TY - JOUR T1 - A Well-Balanced Weighted Compact Nonlinear Scheme for Pre-Balanced Shallow Water Equations AU - Cheng , Mingyang AU - Tang , Lingyan AU - Chen , Yaming AU - Song , Songhe JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1181 EP - 1200 PY - 2022 DA - 2022/06 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2021-0117 UR - https://global-sci.org/intro/article_detail/aamm/20557.html KW - Shallow water equation, weighted compact nonlinear scheme, well-balanced property, shock capturing property. AB -

It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical errors. In this paper, a well-balanced weighted compact nonlinear scheme (WCNS) is proposed for shallow water equations in pre-balanced forms. The scheme is proved to be well-balanced provided that the source term is treated appropriately as the advection term. Some numerical examples in one- and two-dimensions are also presented to demonstrate the well-balanced property, high order accuracy and good shock capturing capability of the proposed scheme.

Mingyang Cheng, Lingyan Tang, Yaming Chen & Songhe Song. (2022). A Well-Balanced Weighted Compact Nonlinear Scheme for Pre-Balanced Shallow Water Equations. Advances in Applied Mathematics and Mechanics. 14 (5). 1181-1200. doi:10.4208/aamm.OA-2021-0117
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