@Article{AAMM-13-4,
author = {Li, Jiaojiao and Li, Gang and Shouguo, Qian and Jinmei, Gao},
title = {High-Order Well-Balanced Finite Volume WENO Schemes with Conservative Variables Decomposition for Shallow Water Equations},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2021},
volume = {13},
number = {4},
pages = {827--849},
abstract = {<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>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2020-0138},
url = {https://global-sci.com/article/72992/high-order-well-balanced-finite-volume-weno-schemes-with-conservative-variables-decomposition-for-shallow-water-equations}
}