An improved WENO-Z scheme

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• 作者：F. Acker^a ; ^{acker@labma.ufrj.br" class="auth_mail" title="E-mail the corresponding author} ; R. B. de R. Borges^a ; ^b ; ^{rafael.borges@ime.uerj.br" class="auth_mail" title="E-mail the corresponding author} ; B. Costa^a ; ^{bcosta@labma.ufrj.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：WENO schemes ; Smoothness indicators ; High-order methods ; High resolution shock capturing schemes ; Hyperbolic conservation laws
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：313
• 期：Complete
• 页码：726-753
• 全文大小：4221 K

文摘

In this article, we show that for a WENO scheme to improve the numerical resolution of smooth waves, increasing to some extent the contribution of the substencils where the solution is less smooth is much more important than improving the accuracy at critical points. WENO-Z, for instance, achieved less dissipative results than classical WENO through the use of a high-order global smoothness measurement, τ, which increased the weights of less-smooth substencils. This time, we present a way of further increasing the relevance of less-smooth substencils by adding a new term to the WENO-Z weights that uses information which is already available in its formula. The improved scheme attains much better resolution at the smooth parts of the solution, while keeping the same numerical stability of the original WENO-Z at shocks and discontinuities.