A modified fifth-order WENOZ method for hyperbolic conservation laws

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• 作者：Fuxing Hu^a ; ^{fuxing_hoo@163.com" class="auth_mail" title="E-mail the corresponding author} ; Rong Wang^b ; ^{wangr3@sustc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Xueyong Chen^c ; ^{cxyxy@whu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65M06 ; 65M20
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：303
• 期：Complete
• 页码：56-68
• 全文大小：1850 K

文摘

The paper analyses by Taylor series the several fifth-order of accuracy schemes for hyperbolic conservation laws: the classical WENOJS scheme Jiang and Shu (1996), the WENOM scheme Henrick et al. (2005), the WENOZ scheme Borges et al. (2008) and the scheme, called WENOε$\epsilon$ here, Aràndiga et al. (2011). The order of weights of these four schemes agreed to the optimal weights is presented in detail. Then three prerequisites are developed if one intends to improve the WENOJS scheme: the scheme arrives the 5th-order at critical points; the weights of scheme approximate the optimal weights with high-order accuracy when solution is smooth; the scheme should not introduce much oscillations intuitively in the vicinity of discontinuities. According to the prerequisites above, a new WENO scheme (MWENOZ) is devised which is similar to the WENOZ scheme. Finally, the method designed here is demonstrated robustly by applying it to 1D and 2D numerical simulations and its advantage compared with the WENOZ scheme seems more striking in 2D problems.