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 - <p style="text-align: justify;">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.</p>