@Article{AAMM-15-1515,
author = {Guo , WeiChen , ZimingQian , ShouguoLi , Gang and Niu , Qiang},
title = {A New Well-Balanced Finite Volume CWENO Scheme for Shallow Water Equations over Bottom Topography},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {6},
pages = {1515--1539},
abstract = {<p style="text-align: justify;">In this article, we develop a new well-balanced finite volume central
weighted essentially non-oscillatory (CWENO) scheme for one- and two-dimensional
shallow water equations over uneven bottom. The well-balanced property is of
paramount importance in practical applications, where many studied phenomena can
be regarded as small perturbations to the steady state. To achieve the well-balanced
property, we construct numerical fluxes by means of a decomposition algorithm based
on a novel equilibrium preserving reconstruction procedure and we avoid applying
the traditional hydrostatic reconstruction technique accordingly. This decomposition
algorithm also helps us realize a simple source term discretization. Both rigorous theoretical analysis and extensive numerical examples all verify that the proposed scheme
maintains the well-balanced property exactly. Furthermore, extensive numerical results strongly suggest that the resulting scheme can accurately capture small perturbations to the steady state and keep the genuine high-order accuracy for smooth solutions
at the same time.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0131},
url = {http://global-sci.org/intro/article_detail/aamm/22050.html}
}