Volume 12, Issue 4
A Fourth Order WENO Scheme for Hyperbolic Conservation Laws

Xiaohan Cheng, Jianhu Feng & Supei Zheng

Adv. Appl. Math. Mech., 12 (2020), pp. 992-1007.

Published online: 2020-06

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  • Abstract

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's fourth order accuracy and capacity of dealing with problems containing complicated structures.

  • Keywords

Hyperbolic conservation laws, WENO scheme, nonlinear weights, Euler equations.

  • AMS Subject Headings

65M06, 35L65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-12-992, author = {Cheng , Xiaohan and Feng , Jianhu and Zheng , Supei}, title = {A Fourth Order WENO Scheme for Hyperbolic Conservation Laws}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {4}, pages = {992--1007}, abstract = {

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's fourth order accuracy and capacity of dealing with problems containing complicated structures.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0097}, url = {http://global-sci.org/intro/article_detail/aamm/16937.html} }
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 -

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's fourth order accuracy and capacity of dealing with problems containing complicated structures.

Xiaohan Cheng, Jianhu Feng & Supei Zheng. (2020). A Fourth Order WENO Scheme for Hyperbolic Conservation Laws. Advances in Applied Mathematics and Mechanics. 12 (4). 992-1007. doi:10.4208/aamm.OA-2019-0097
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