TY - JOUR
T1 - A New Finite Difference Well-Balanced Mapped Unequal-Sized WENO Scheme for Solving Shallow Water Equations
AU - Li , Liang
AU - Wang , Zhenming
AU - Zhu , Jun
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1176
EP - 1193
PY - 2024
DA - 2024/07
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0228
UR - https://global-sci.org/intro/article_detail/aamm/23290.html
KW - Shallow water equations, exact C-property, mapping function, well-balanced unequalsized WENO (WBMUS-WENO) scheme.
AB - <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>