TY - JOUR
T1 - Improved Sixth-Order WENO Finite Difference Schemes for Hyperbolic Conservation Laws
AU - Wang , Cai-Feng
AU - Don , Wai-Sun
AU - Li , Jia-Le
AU - Wang , Bao-Shan
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1591
EP - 1624
PY - 2025
DA - 2025/09
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2024-0037
UR - https://global-sci.org/intro/article_detail/aamm/24488.html
KW - Ai-WENO, critical points, global smoothness indicator, low dissipation, positivity-preserving, long-time simulation.
AB - <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>