TY - JOUR
T1 - High-Order Well-Balanced Finite Volume WENO Schemes with Conservative Variables Decomposition for Shallow Water Equations
AU - Li , Jiaojiao
AU - Li , Gang
AU - Qian , Shouguo
AU - Gao , Jinmei
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 827
EP - 849
PY - 2021
DA - 2021/04
SN - 13
DO - http://doi.org/10.4208/aamm.OA-2020-0138
UR - https://global-sci.org/intro/article_detail/aamm/18753.html
KW - Shallow water equations, source term, WENO schemes, well-balanced property, hydrostatic reconstruction, conservative variables decomposition.
AB - <p style="text-align: justify;">This article presents well-balanced finite volume weighted essentially non-oscillatory (WENO) schemes to solve the shallow water equations (SWEs). Well-balanced schemes are characterized by preservation of the steady state&nbsp; exactly at the discrete level. The well-balanced property is of paramount importance in practical applications where many studied phenomena are regarded as small perturbations to equilibrium states. To achieve the well-balanced property, numerical fluxes presented here are constructed by means of a suitable conservative variables decomposition and the hydrostatic reconstruction idea. This decomposition strategy allows us to realize a novel simple source term approximation. Both rigorous theoretical analysis and extensive numerical examples all verify that the resulting schemes maintain the well-balanced property exactly. Furthermore, numerical results strongly imply that the proposed schemes can accurately capture small perturbations to the steady state and keep the genuine high-order accuracy for smooth solutions.</p>