A modified fifth-order WENOZ method for hyperbolic conservation laws

Hu, Fuxing1; Wang, Rong2; Chen, Xueyong3

2016-09

10.1016/j.cam.2016.02.027

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   影响因子和分区

0377-0427

1879-1778

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 WENO epsilon here, Arandiga 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. (C) 2016 Elsevier B.V. All rights reserved.

WENO schemes High-order schemes Hyperbolic conservation laws Smoothness indicators

SCI ; EI

英语

其他

Foundation for Distinguished Young Talents in Higher Education of Guangdong, China[2013LYM_0089]

Mathematics

Mathematics, Applied

WOS:000375177500005

ELSEVIER SCIENCE BV

20161102110743

Physical properties

Numerical Methods:921.6 ; Physical Properties of Gases, Liquids and Solids:931.2

MATHEMATICS

Web of Science

1.Huizhou Univ, Dept Math, Huizhou 516007, Guangdong, Peoples R China
2.South Univ Sci & Technol China, Dept Gen Educ, Shenzhen 518055, Guangdong, Peoples R China
3.Xuchang Univ, Fac Math & Stat, Xuchang 461000, Henan, Peoples R China

Hu, Fuxing,Wang, Rong,Chen, Xueyong. A modified fifth-order WENOZ method for hyperbolic conservation laws[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2016,303:56-68.

Hu, Fuxing,Wang, Rong,&Chen, Xueyong.(2016).A modified fifth-order WENOZ method for hyperbolic conservation laws.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,303,56-68.

Hu, Fuxing,et al."A modified fifth-order WENOZ method for hyperbolic conservation laws".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 303(2016):56-68.