EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

改进的五阶WENO-Z-格式

骆信 吴颂平

骆信, 吴颂平. 改进的五阶WENO-Z-格式[J]. 力学学报, 2019, 51(6): 1927-1939. doi: 10.6052/0459-1879-19-249
引用本文: 骆信, 吴颂平. 改进的五阶WENO-Z-格式[J]. 力学学报, 2019, 51(6): 1927-1939. doi: 10.6052/0459-1879-19-249
Luo Xin, Wu Songping. AN IMPROVED FIFTH-ORDER WENO-Z+ SCHEME[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1927-1939. doi: 10.6052/0459-1879-19-249
Citation: Luo Xin, Wu Songping. AN IMPROVED FIFTH-ORDER WENO-Z+ SCHEME[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1927-1939. doi: 10.6052/0459-1879-19-249

改进的五阶WENO-Z-格式

doi: 10.6052/0459-1879-19-249
基金项目: 1) 国家自然科学基金资助项目(91530325)
详细信息
    通讯作者:

    吴颂平

  • 中图分类号: V211.3

AN IMPROVED FIFTH-ORDER WENO-Z+ SCHEME

  • 摘要: WENO-Z$+\!$格式的性能提升依赖于新增项的作用,该项的作用是在WENO-Z格式的基础上进一步增大欠光滑子模板上的权重. 系数$\lambda$被设置用来调控该项的作用, 以避免负耗散. 本文指出了WENO-Z$+\!$格式的缺陷,其所采用$\lambda $的取值方式既不能充分发挥格式的潜力, 也未完全消除负耗散;提出$\lambda $的值应随当地流场数据变化,方能充分发挥新增项在降低数值耗散、提高分辨率上的潜力. 基于此,本文重新设计了$\lambda $的计算公式,该公式能自适应地调控新增项的作用: 只在欠光滑子模板上的权重容易过度增大的地方削弱该项的作用,以避免负耗散; 在其他地方则充分发挥新增项的作用,最大限度增大欠光滑子模板上的权重, 提高格式的分辨率.将使用该系数公式的新格式命名为WENO-Z++, 并对其数值性能进行了系统的研究.理论分析表明, 新格式在间断处具有基本无振荡(essentially non-oscillatory,ENO)特性和更低的数值耗散. 对近似色散关系(approximate dispersion relation,ADR)的研究表明,新格式有效地避免了因过度增大欠光滑子模板上的权重而带来的负耗散,其频谱特性也得到了显著提升.本文还推导了使新格式在极值点处也能保持最优阶的精度的参数设置.一系列求解Euler方程的数值试验表明,新格式的激波捕捉能力和对复杂流场结构的分辨率都显著优于原WENO-Z$+\!$格式.}

     

  • 1 Fu L, Tang Q. High-order low-dissipation targeted ENO schemes for ideal magnetohydrodynamics. Journal of Scientific Computing, 2019,80:692-716
    2 Nonomura T, Fujii K. Characteristic finite-difference WENO scheme for multicomponent compressible fluid analysis: Overestimated quasi-conservative formulation maintaining equilibriums of velocity, pressure, and temperature. Journal of Computational Physics, 2017,340:358-388
    3 Huang ZY, Lin G, Ardekani AM. A mixed upwind/central WENO scheme for incompressible two-phase flows. Journal of Computational Physics, 2019,387:455-480
    4 Liu HP, Gao ZX, Jiang CW, et al. Numerical study of combustion effects on the development of supersonic turbulent mixing layer flows with WENO schemes. Computers and Fluids, 2019,189:82-93
    5 童福林, 李新亮, 唐志共 . 激波与转捩边界层干扰非定常特性数值分析. 力学学报, 2017, 49:(1):93-104
    5 ( Tong Fulin, Li Xinliang, Tang Zhigong, Numerical analysis of unsteady motion in shock wave/transitional boundary layer interaction. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(1):93-104 (in Chinese))
    6 童福林, 李欣, 于长平 等. 高超声速激波湍流边界层干扰直接数值模拟研究. 力学学报, 2018,50(2):197-208
    6 ( Tong Fulin, Li Xin, Yu Changping, et al. Direct numerical simulation of hypersonic shock wave and turbulent boundary layer interactions. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(2):197-208 (in Chinese))
    7 洪正, 叶正寅 . 各向同性湍流通过正激波的演化特征研究. 力学学报, 2018,50(6):1356-1367
    7 ( Hong Zheng, Ye Zhengyin, Study on evolution characteristics of isotropic turbulence passing through a normal shock wave. ChineseJournal of Theoretical and Applied Mechanics, 2018,50(6):1356-1367 (in Chinese))
    8 Yu PX, Bai JQ, Yang H, et al. Interface flux reconstruction method based on optimized weight essentially non-oscillatory scheme. Chinese Journal of Aeronautics, 2018,31(5):1020-1029
    9 Sirajuddin D, Hitchon WNG. A truly forward semi-Lagrangian WENO scheme for the Vlasov-Poisson system. Journal of Computational Physics, 2019,392:619-665
    10 Lefèvre V, Garnica A, Lopez-Pamies O. A WENO finite-difference scheme for a new class of Hamilton-Jacobi equations in nonlinear solid mechanics. Computer Methods in Applied Mechanics and Engineering, 2019,349:17-44
    11 Kumar S, Singh P. High order WENO finite volume approximation for population density neuron model. Applied Mathematics and Computation, 2019,356:173-189
    12 Wang D, Byambaakhuu T. High-order Lax-Friedrichs WENO fast sweeping methods for the $S_{N}$ neutron transport equation. Nuclear Science and Engineering, 2019,193(9):982-990
    13 Harten A, Engquist B, Osher S, et al. Uniformly high order accurate essentially non-oscillatory schemes, III. Journal of Computational Physics, 1987,71(2):231-303
    14 Liu XD, Osher S, Chan T. Weighted essentially non-oscillatory schemes. Journal of Computational Physics, 1994,115(1):200-212
    15 Jiang GS, Shu CW. Efficient implementation of weighted ENO schemes. Journal of Computational Physics, 1996,126(1):202-228
    16 Henrick AK, Aslam TD, Powers JM. Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points. Journal of Computational Physics, 2005,207(2):542-567
    17 Borges R, Carmona M, Costa B, et al. An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws. Journal of Computational Physics, 2008,227(6):3191-3211
    18 Ha Y, Kim CH, Lee YJ, et al. An improved weighted essentially non-oscillatory scheme with a new smoothness indicator. Journal of Computational Physics, 2013,232(1):68-86
    19 Kim CH, Ha YS, Yoon JH. Modified non-linear weights for fifth-order weighted essentially non-oscillatory schemes. Journal of Scientific Computing, 2016,67:299-323
    20 Fan P, Shen YQ, Tian BL, et al. A new smoothness indicator for improving the weighted essentially non-oscillatory scheme. Journal of Computational Physics, 2014,269:329-354
    21 Yan ZG, Liu HY, Mao ML, et al. New nonlinear weights for improving accuracy and resolution of weighted compact nonlinear scheme. Computers and Fluids, 2016,127:226-240
    22 Yamaleev NK, Carpenter MH. Third-order energy stable WENO scheme. Journal of Computational Physics, 2009,228(8):3025-3047.
    23 Yamaleev NK, Carpenter MH. A systematic methodology for constructing high-order energy stable WENO schemes. Journal of Computational Physics, 2009,228(11):4248-4272
    24 Baeza A, Bürger R, Mulet P, et al. On the efficient computation of smoothness indicators for a class of WENO reconstructions. Journal of Scientific Computing, 2019,80:1240-1263
    25 Bhise AA, Gande NR, Samala R, et al. An efficient hybrid WENO scheme with a problem independent discontinuity locator. International Journal for Numerical Methods in Fluids, 2019,91:1-28
    26 Zhang SH, Zhu J, Shu CW. A brief review on the convergence to steady state solutions of Euler equations with high-order WENO schemes. Advances in Aerodynamics, 2019,1:16
    27 Aràndiga F, Baeza A, Belda AM, et al. Analysis of WENO schemes for full and global accuracy. SIAM Journal on Numerical Analysis, 2011,49(2):893-915
    28 Don WS, Borges R. Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes. Journal of Computational Physics, 2013,250:347-372
    29 Acker F, Borges RBDR, Costa B. An improved WENO-Z scheme. Journal of Computational Physics, 2016,313:726-753
    30 Borges RBDR. Recent results on the improved WENO-Z+ scheme// Bittencourt ML eds. Lecture Notes in Computational Science and Engineering 119, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 Rio de Janeiro, Brazil 2016, New York: Springer International Publishing, 2017: 547559
    31 Xu WZ, Wu WG. An improved third-order WENO-Z scheme. Journal of Scientific Computing, 2018,75:1808-1841
    32 Pirozzoli S. On the spectral properties of shock-capturing schemes. Journal of Computational Physics, 2006,219(2):489-497
    33 Shu CW, Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes, II. Journal of Computational Physics, 1989,83(1):32-78
    34 Titarev VA, Toro EF. Finite-volume WENO schemes for three-dimensional conservation laws. Journal of Computational Physics, 2004,201(1):238-260
    35 Lax PD. Weak solutions of nonlinear hyperbolic equations and their numerical computation. Communications on Pure and Applied Mathematics, 1954,7(1):159-193
    36 Lax PD, Liu XD. Solution of two-dimensional Riemann problems of gas dynamics by positive schemes. SIAM Journal on Scientific Computing, 1998,19(2):319-340
    37 Woodward P, Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. Journal of Computational Physics, 1984,54(1):115-173
    38 Shi J, Zhang YT, Shu CW. Resolution of high order WENO schemes for complicated flow structures. Journal of Computational Physics, 2003,186(2):690-696
  • 加载中
计量
  • 文章访问数:  1225
  • HTML全文浏览量:  129
  • PDF下载量:  184
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-09-04
  • 刊出日期:  2019-11-18

目录

    /

    返回文章
    返回