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一个改进的三阶WENO-Z型格式

王建玲 李小纲 汪文帅

王建玲, 李小纲, 汪文帅. 一个改进的三阶WENO-Z型格式[J]. 应用数学和力学, 2021, 42(4): 394-404. doi: 10.21656/1000-0887.410203
引用本文: 王建玲, 李小纲, 汪文帅. 一个改进的三阶WENO-Z型格式[J]. 应用数学和力学, 2021, 42(4): 394-404. doi: 10.21656/1000-0887.410203
WANG Jianling, LI Xiaogang, WANG Wenshuai. An Improved 3rd-Order WENO-Z Type Scheme[J]. Applied Mathematics and Mechanics, 2021, 42(4): 394-404. doi: 10.21656/1000-0887.410203
Citation: WANG Jianling, LI Xiaogang, WANG Wenshuai. An Improved 3rd-Order WENO-Z Type Scheme[J]. Applied Mathematics and Mechanics, 2021, 42(4): 394-404. doi: 10.21656/1000-0887.410203

一个改进的三阶WENO-Z型格式

doi: 10.21656/1000-0887.410203
基金项目: 国家自然科学基金(42064004)
详细信息
    作者简介:

    王建玲(1981—), 女, 硕士(Email: 78484615@qq.com);李小纲(1983—), 男, 博士(通讯作者. Email: lixiaogang1222@126.com);汪文帅(1980—), 男,博士(Email: wws@nxu.edu.cn).

  • 中图分类号: O302

An Improved 3rd-Order WENO-Z Type Scheme

Funds: The National Natural Science Foundation of China(42064004)
  • 摘要: 在WENO-Z型格式框架下,基于高阶全局光滑因子,在非线性权建立过程中引入参数,通过收敛性分析确定参数取值范围,兼顾精确性与不振荡性,得到参数最佳取值.最终得到一个低耗散、高分辨率的三阶WENO差分格式,该格式在函数一阶极值点处仍保持预期三阶精度.最后通过精确解算例验证了格式在各种类型极值点处精度恢复情况,并通过一、二维Euler方程组经典算例测试了格式的低耗散、高分辨特性.结果表明,该文格式是一个性能优良的激波捕捉格式.
  • [1] HARTEN A. High resolution schemes for hyperbolic conservation laws[J]. Journal of Computational Physics,1983,49(3): 357-393.
    [2] HARTEN A, OSHER S. Uniformly high order accurate essentially non-oscillatory schemes, Ⅰ[J]. Journal on Numerical Analysis,1987,24: 279-309.
    [3] HARTEN A, ENGQUIST B, OSHER S, et al. Uniformly high order accurate essentially non-oscillatory schemes, Ⅲ[J]. Journal of Computational Physics,1987,71(2): 231-303.
    [4] LIU X D, OSHER S, CHAN T. Weighted essentially non-oscillatory schemes[J]. Journal of Computational Physics,1994,115(1): 200-212.
    [5] JIANG G S, SHU C W. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics,1996,126(1):202-228.
    [6] HENRICK A K, ASLAM T D, POWERS J M. Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points[J]. Journal of Computational Physics,2005,207(2): 542-567.
    [7] BORGES R, CARMONA M, COSTA B, et al. An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws[J]. Journal of Computational Physics,2008,227(6): 3191-3211.
    [8] WU X, ZHAO Y. A high-resolution hybrid scheme for hyperbolic conservation laws[J]. International Journal for Numerical Methods in Fluids,2015,78(3):162-187.
    [9] WU X, LIANG J, ZHAO Y. A new smoothness indicator for third-order WENO scheme[J]. International Journal for Numerical Methods in Fluids,2016,81(7):451-459.
    [10] LI X, LI G, GE Y. Improvement of third-order finite difference WENO scheme at critical points[J]. International Journal of Computational Fluid Dynamics,2020,34: 1-13.
    [11] WANG Y, DU Y, ZHAO K, et al. A low-dissipation third-order weighted essentially nonoscillatory scheme with a new reference smoothness indicator[J]. International Journal for Numerical Methods in Fluids,2020,92: 1212-1234.
    [12] GANDE N R, RATHOD Y, RATHAN S. Third-order WENO scheme with a new smoothness indicator[J]. International Journal for Numerical Methods in Fluids,2017,85(2): 90-112.
    [13] XU W, WU W. An improved third-order WENO-Z scheme[J]. Journal of Scientific Computing,2018,75(3): 1808-1841.
    [14] XU W, WU W. Improvement of third-order WENO-Z scheme at critical points[J]. Computers & Mathematics With Applications,2018,75(9): 3431-3452.
    [15] XU W, WU W. An improved third-order weighted essentially non-oscillatory scheme achieving optimal order near critical points[J]. Computer & Fluids,2018,162: 113-125.
    [16] GANDE N R, RATHOD Y, SAMALA R. Improved third-order weighted essentially non-oscillatory scheme[J]. International Journal for Numerical Methods in Fluids,2018,87(7): 329-342.
    [17] BHISE A A, SAMALA R. An efficient hybrid WENO scheme with a problem independent discontinuity locator[J]. International Journal for Numerical Methods in Fluids,2019,91: 1-28.
    [18] LIU S, SHEN Y, CHEN B, et al. Novel local smoothness indicators for improving the third-order WENO scheme[J]. International Journal for Numerical Methods in Fluids,2018,87(2): 51-69.
    [19] LIU S, SHEN Y. Discontinuity-detecting method for a four-point stencil and its application to develop a third-order hybrid-WENO scheme[J]. Journal of Scientific Computing,2019,81(3): 1732-1766.
    [20] 徐维铮, 孔祥韶, 吴卫国. 基于映射函数的三阶WENO改进格式及其应用[J]. 应用数学和力学, 2017,38(10): 1120-1135.(XU Weizheng, KONG Xiangshao, WU Weiguo. An improved 3rd-order WENO scheme based on mapping function and its application[J]. Applied Mathematics and Mechanics,2017,38(10): 1120-1135.(in Chinese))
    [21] 徐维铮, 吴卫国. 三阶WENO-Z格式精度分析及其改进格式[J]. 应用数学和力学, 2018,39(8): 946-960.(XU Weizheng, WU Weiguo. Precision analysis of the 3rd-order WENO-Z scheme and its improved scheme[J]. Applied Mathematics and Mechanics,2018,39(8): 946-960.(in Chinese))
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出版历程
  • 收稿日期:  2020-07-08
  • 修回日期:  2020-10-28
  • 刊出日期:  2021-04-01

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