@Article{AAMM-14-5,
author = {Shengzhu, Cui and Zhanjing, Tao and Zhu, Jun},
title = {A New Fifth-Order Finite Volume Central WENO Scheme for Hyperbolic Conservation Laws on Staggered Meshes},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2022},
volume = {14},
number = {5},
pages = {1059--1086},
abstract = {<p style="text-align: justify;">In this paper, a new fifth-order finite volume central weighted essentially
non-oscillatory (CWENO) scheme is proposed for solving hyperbolic conservation
laws on staggered meshes. The high-order spatial reconstruction procedure using
a convex combination of a fourth degree polynomial with two linear polynomials
(in one dimension) or four linear polynomials (in two dimensions) in a traditional
WENO fashion and a time discretization method using the natural continuous extension (NCE) of the Runge-Kutta method are applied to design this new fifth-order
CWENO scheme. This new finite volume CWENO scheme uses the information defined on the same largest spatial stencil as that of the same order classical CWENO
schemes [37, 46] with the application of smaller number of unequal-sized spatial stencils. Since the new nonlinear weights are adopted, the new finite volume CWENO
scheme could obtain the same order of accuracy and get smaller truncation errors in $L^1$ and $L^∞$ norms in smooth regions, and control the spurious oscillations near strong
shocks or contact discontinuities. The new CWENO scheme has advantages over the
classical CWENO schemes [37, 46] on staggered meshes in its simplicity and easy extension to multi-dimensions. Some one-dimensional and two-dimensional benchmark
numerical examples are provided to illustrate the good performance of this new fifth-order finite volume CWENO scheme.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0095},
url = {https://global-sci.com/article/72932/a-new-fifth-order-finite-volume-central-weno-scheme-for-hyperbolic-conservation-laws-on-staggered-meshes}
}