@Article{AAMM-16-5,
author = {Liang, Li and Zhenming, Wang and Zhu, Jun},
title = {A New Finite Difference Well-Balanced Mapped Unequal-Sized WENO Scheme for Solving Shallow Water Equations},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2024},
volume = {16},
number = {5},
pages = {1176--1196},
abstract = {<p style="text-align: justify;">In this paper, we propose a newly designed fifth-order finite difference
well-balanced mapped unequal-sized weighted essentially non-oscillatory (WBMUS-WENO) scheme for simulating the shallow water systems on multi-dimensional structured meshes. We design new non-linear weights and a new mapping function, so
that the WBMUS-WENO scheme can maintain fifth-order accuracy with a small $ε$ even
nearby the extreme points in smooth regions. The truncation errors of the scheme is
smaller and it has better convergence in simulating some steady-state problems. Unlike the traditional well-balanced WENO-XS scheme [29], this new WBMUS-WENO
scheme uses three unequal-sized stencils, denotes the linear weights to be any positive numbers on condition that their summation is one. By incorporating a quartic
polynomial on the whole big stencil into WENO reconstruction, the WBMUS-WENO
scheme is simple and efficient. Extensive examples are performed to testify the exact C-property, absolute convergence property, and good representations of this new
WBMUS-WENO scheme.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0228},
url = {https://global-sci.com/article/90884/a-new-finite-difference-well-balanced-mapped-unequal-sized-weno-scheme-for-solving-shallow-water-equations}
}