@Article{AAMM-17-1591,
author = {Wang , Cai-FengDon , Wai-SunLi , Jia-Le and Wang , Bao-Shan},
title = {Improved Sixth-Order WENO Finite Difference Schemes for Hyperbolic Conservation Laws},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2025},
volume = {17},
number = {6},
pages = {1591--1624},
abstract = {<p style="text-align: justify;">This article describes developing and improving sixth-order characteristic-wise Weighted Essentially Non-Oscillatory (WENO) finite difference schemes. These
 schemes are specially designed to solve scalar and system hyperbolic conservation
 laws with high accuracy/resolution and robustness. The schemes have been enhanced
 by using a new reference global smoothness indicator, which ensures the optimal order of accuracy for smooth solutions. The schemes also incorporate affine-invariant
 nonlinear Ai-weights that are independent of the scaling of solution and the choice of
 sensitivity parameter. The improved nonlinear weights enhance the essentially non-oscillatory (ENO) capturing of discontinuities and minimize the numerical dissipation, especially for long-time simulations. The study also introduces the positivity-preserving limiter to ensure that the numerical solution of Euler equations is physically
 valid. The effectiveness of improved schemes is demonstrated through one- and two-dimensional benchmark shock-tube problems, such as the Sod, Lax, and Woodward-Colella problems. The improved schemes are compared with other WENO schemes in
 terms of accuracy, resolution, ENO, and robustness.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2024-0037},
url = {http://global-sci.org/intro/article_detail/aamm/24488.html}
}