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.