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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

DOI: 10.4208/aamm.OA-2021-0117

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 = {Cheng , MingyangTang , LingyanChen , Yaming and Song , Songhe}, 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.

Cheng , MingyangTang , LingyanChen , Yaming and Song , Songhe. (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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