An improved fifth order alternative WENO-Z finite difference scheme for hyperbolic conservation laws

Bao Shan Wang; Peng Li; Zhen Gao; Wai Sun Don

doi:10.1016/j.jcp.2018.07.052

An improved fifth order alternative WENO-Z finite difference scheme for hyperbolic conservation laws

Bao Shan Wang^*
, Peng Li^*
, Zhen Gao^*
, Wai Sun Don^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

98 Citations (Scopus)

Abstract

An alternative formulation of conservative weighted essentially non-oscillatory (WENO) finite difference scheme with the classical WENO-JS weights (Jiang et al. (2013) [6]) has been successfully used for solving hyperbolic conservation laws. However, it fails to achieve the optimal order of accuracy at the critical points of a smooth function. Here, we demonstrate that the WENO-Z weights (Borges et al. (2008) [1]) should be employed to recover the optimal order of accuracy at the critical points. Several one- and two-dimensional benchmark problems show the improved performance in terms of accuracy, resolution and shock capturing.

Original language	English
Pages (from-to)	469-477
Number of pages	9
Journal	Journal of Computational Physics
Volume	374
DOIs	https://doi.org/10.1016/j.jcp.2018.07.052
Publication status	Published - 1 Dec 2018

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SDG 9 Industry, Innovation, and Infrastructure

User-Defined Keywords

Alternative WENO scheme
Hyperbolic conservation laws
WENO weights

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10.1016/j.jcp.2018.07.052

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title = "An improved fifth order alternative WENO-Z finite difference scheme for hyperbolic conservation laws",

abstract = "An alternative formulation of conservative weighted essentially non-oscillatory (WENO) finite difference scheme with the classical WENO-JS weights (Jiang et al. (2013) [6]) has been successfully used for solving hyperbolic conservation laws. However, it fails to achieve the optimal order of accuracy at the critical points of a smooth function. Here, we demonstrate that the WENO-Z weights (Borges et al. (2008) [1]) should be employed to recover the optimal order of accuracy at the critical points. Several one- and two-dimensional benchmark problems show the improved performance in terms of accuracy, resolution and shock capturing.",

keywords = "Alternative WENO scheme, Hyperbolic conservation laws, WENO weights",

author = "Wang, \{Bao Shan\} and Peng Li and Zhen Gao and Don, \{Wai Sun\}",

note = "The authors would like to acknowledge the funding support of this research by the National Science and Technology Major Project (20101010), Shandong Provincial Natural Science Foundation (ZR2017MA016) and Fundamental Research Funds for the Central Universities (201562012). The author (Don) also likes to thank the Ocean University of China for providing the startup funding (201712011) that is used in supporting this work. The author (Li) also likes to thank the Shijiazhuang Tiedao University for providing the startup funding (Z6811021064) that is used in supporting this work. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

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doi = "10.1016/j.jcp.2018.07.052",

language = "English",

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journal = "Journal of Computational Physics",

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T1 - An improved fifth order alternative WENO-Z finite difference scheme for hyperbolic conservation laws

AU - Wang, Bao Shan

AU - Li, Peng

AU - Gao, Zhen

AU - Don, Wai Sun

N1 - The authors would like to acknowledge the funding support of this research by the National Science and Technology Major Project (20101010), Shandong Provincial Natural Science Foundation (ZR2017MA016) and Fundamental Research Funds for the Central Universities (201562012). The author (Don) also likes to thank the Ocean University of China for providing the startup funding (201712011) that is used in supporting this work. The author (Li) also likes to thank the Shijiazhuang Tiedao University for providing the startup funding (Z6811021064) that is used in supporting this work. Publisher Copyright: © 2018 Elsevier Inc.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - An alternative formulation of conservative weighted essentially non-oscillatory (WENO) finite difference scheme with the classical WENO-JS weights (Jiang et al. (2013) [6]) has been successfully used for solving hyperbolic conservation laws. However, it fails to achieve the optimal order of accuracy at the critical points of a smooth function. Here, we demonstrate that the WENO-Z weights (Borges et al. (2008) [1]) should be employed to recover the optimal order of accuracy at the critical points. Several one- and two-dimensional benchmark problems show the improved performance in terms of accuracy, resolution and shock capturing.

AB - An alternative formulation of conservative weighted essentially non-oscillatory (WENO) finite difference scheme with the classical WENO-JS weights (Jiang et al. (2013) [6]) has been successfully used for solving hyperbolic conservation laws. However, it fails to achieve the optimal order of accuracy at the critical points of a smooth function. Here, we demonstrate that the WENO-Z weights (Borges et al. (2008) [1]) should be employed to recover the optimal order of accuracy at the critical points. Several one- and two-dimensional benchmark problems show the improved performance in terms of accuracy, resolution and shock capturing.

KW - Alternative WENO scheme

KW - Hyperbolic conservation laws

KW - WENO weights

UR - https://www.scopus.com/pages/publications/85050989147

UR - https://www.sciencedirect.com/science/article/pii/S0021999118305151?via%3Dihub

U2 - 10.1016/j.jcp.2018.07.052

DO - 10.1016/j.jcp.2018.07.052

M3 - Journal article

AN - SCOPUS:85050989147

SN - 0021-9991

VL - 374

SP - 469

EP - 477

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

An improved fifth order alternative WENO-Z finite difference scheme for hyperbolic conservation laws

Abstract

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