期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 230, 期 5, 页码 1766-1792出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2010.11.028
关键词
Weighted essentially non-oscillatory; WENO-Z; Smoothness indicators; Nonlinear weights
资金
- CNPq [300315/98-8]
- FAPERJ [E-26/111.564/2008]
- FRG [FRG08-09-II-12]
- Hong Kong Baptist Universit
- Hong Kong Research Grants Council [HKBU-092009]
In [10], the authors have designed a new fifth order WENO finite-difference scheme by adding a higher order smoothness indicator which is obtained as a simple and inexpensive linear combination of the already existing low order smoothness indicators. Moreover, this new scheme, dubbed as WENO-Z, has a CPU cost which is equivalent to the one of the classical WENO-JS [2], and smaller than that of the mapped WENO-M, [5], since it involves no mapping of the nonlinear weights. In this article, we take a closer look at Taylor expansions of the Lagrangian polynomials of the WENO substencils and the related inherited symmetries of the classical lower order smoothness indicators to obtain a general formula for the higher order smoothness indicators that allows the extension of the WENO-Z scheme to all (odd) orders of accuracy. We further investigate the improved accuracy of the WENO-Z schemes at critical points of smooth solutions as well as their distinct numerical features as a result of the new sets of nonlinear weights and we show that regarding the numerical dissipation WENO-Z occupies an intermediary position between WENO-JS and WENO-M. Some standard numerical experiments such as the one dimensional Riemann initial values problems for the Euler equations and the Mach 3 shock density-wave interaction and the two dimensional double-Mach shock reflection problems are presented. (C) 2010 Elsevier Inc. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据