TY - JOUR
T1 - A Fourth Order WENO Scheme for Hyperbolic Conservation Laws
AU - Cheng , Xiaohan
AU - Feng , Jianhu
AU - Zheng , Supei
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 992
EP - 1007
PY - 2020
DA - 2020/06
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0097
UR - https://global-sci.org/intro/article_detail/aamm/16937.html
KW - Hyperbolic conservation laws, WENO scheme, nonlinear weights, Euler equations.
AB - <p style="text-align: justify;">In this work, a fourth order weighted essentially non-oscillatory (WENO) scheme is developed for hyperbolic conservation laws. The new reconstruction is a convex combination of three linear reconstructions. To keep high order accuracy in smooth regions and maintain non-oscillatory near discontinuities, the nonlinear weights are carefully designed. The main advantage of the proposed scheme is that the scheme achieves one order of improvement in accuracy in smooth regions compared with the classical third order scheme when using the same spatial nodes. Several benchmark examples are presented to verify the scheme&#39;s fourth order accuracy and capacity of dealing with problems containing complicated structures.</p>