TY - JOUR
T1 - A New Well-Balanced Finite Volume CWENO Scheme for Shallow Water Equations over Bottom Topography
AU - Guo , Wei
AU - Chen , Ziming
AU - Qian , Shouguo
AU - Li , Gang
AU - Niu , Qiang
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1515
EP - 1539
PY - 2023
DA - 2023/10
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2022-0131
UR - https://global-sci.org/intro/article_detail/aamm/22050.html
KW - Shallow water equations, source term, CWENO scheme, decomposition algorithm, well-balanced property.
AB - <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>