@Article{AAMM-15-5,
author = {Zixuan, Zhang and Yidao, Dong and Zhang, Huaibao and Zheng, Shichao and Xiaogang, Deng},
title = {A Scale-Invariant Fifth Order WCNS Scheme for Hyperbolic Conservation Laws},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {5},
pages = {1256--1289},
abstract = {<p style="text-align: justify;">In this article, a robust, effective, and scale-invariant weighted compact nonlinear scheme (WCNS) is proposed by introducing descaling techniques to the nonlinear weights of the WCNS-Z/D schemes. The new scheme achieves an essentially
non-oscillatory approximation of a discontinuous function (ENO-property), a scale-invariant property with an arbitrary scale of a function (Si-property), and an optimal
order of accuracy with smooth function regardless of the critical point (Cp-property).
The classical WCNS-Z/D schemes do not satisfy Si-property intrinsically, which is
caused by a loss of sub-stencils’ adaptivity in the nonlinear interpolation of a discontinuous function when scaled by a small scale factor. A new nonlinear weight is
devised by using an average of the function values and the descaling function, providing the new WCNS schemes (WCNS-Zm/Dm) with many attractive properties. The
ENO-property, Si-property and Cp-property of the new WCNS schemes are validated
numerically. Results show that the WCNS-Zm/Dm schemes satisfy the ENO-property
and Si-property, while only the WCNS-Dm scheme satisfies the Cp-property. In addition, the Gaussian wave problem is solved by using successively refined grids to
verify that the optimal order of accuracy of the new schemes can be achieved. Several
one-dimensional shock tube problems, and two-dimensional double Mach reflection
(DMR) problem and the Riemann IVP problem are simulated to illustrate the ENO-property and Si-property of the scale-invariant WCNS-Zm/Dm schemes.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0196},
url = {https://global-sci.com/article/72873/a-scale-invariant-fifth-order-wcns-scheme-for-hyperbolic-conservation-laws}
}