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

一种抑制激波计算中数值振荡现象的双重小波收缩方法

赵勇 宗智 王天霖

赵勇, 宗智, 王天霖. 一种抑制激波计算中数值振荡现象的双重小波收缩方法[J]. 应用数学和力学, 2014, 35(6): 620-629. doi: 10.3879/j.issn.1000-0887.2014.06.004
引用本文: 赵勇, 宗智, 王天霖. 一种抑制激波计算中数值振荡现象的双重小波收缩方法[J]. 应用数学和力学, 2014, 35(6): 620-629. doi: 10.3879/j.issn.1000-0887.2014.06.004
ZHAO Yong, ZONG Zhi>, WANG Tian-lin. A Dual Wavelet Shrinkage Procedure for Suppressing Numerical Oscillation in Shock Wave Calculation[J]. Applied Mathematics and Mechanics, 2014, 35(6): 620-629. doi: 10.3879/j.issn.1000-0887.2014.06.004
Citation: ZHAO Yong, ZONG Zhi>, WANG Tian-lin. A Dual Wavelet Shrinkage Procedure for Suppressing Numerical Oscillation in Shock Wave Calculation[J]. Applied Mathematics and Mechanics, 2014, 35(6): 620-629. doi: 10.3879/j.issn.1000-0887.2014.06.004

一种抑制激波计算中数值振荡现象的双重小波收缩方法

doi: 10.3879/j.issn.1000-0887.2014.06.004
基金项目: 国家重点基础研究发展计划(973计划)(2013CB036101);国家自然科学基金(51309040; 51379033; 51379025);中央高校基本科研业务费专项资金(3132014318;01780623)
详细信息
    作者简介:

    赵勇(1981—), 男,江西奉新人,博士(通讯作者. Tel: +86-411-84727985; E-mail: fluid@126.com)

  • 中图分类号: O351

A Dual Wavelet Shrinkage Procedure for Suppressing Numerical Oscillation in Shock Wave Calculation

Funds: The National Basic Research Program of China (973 Program)(2013CB036101); The National Natural Science Foundation of China(51309040; 51379033; 51379025)
  • 摘要: 在激波数值计算中,容易出现数值振荡的问题,振荡激烈时会掩盖真实解,为此提出了许多高精度复杂计算格式或采用人工粘性抑制数值振荡.从信号处理的角度,提出双重小波收缩方法,它能自适应提取激波数值振荡解中的真实物理解.先用局部微分求积法求解浅水波方程和理想流体Euler运动方程中的激波问题,发现其数值振荡现象严重,然后采用双重小波收缩方法对其处理,获得了无数值振荡解,它能准确捕捉激波的位置并且保持激波结构.相比于复杂的Riemann(黎曼)求解格式,借助小波收缩方法,可以采用相对简单的计算格式如微分求积法求解激波问题.
  • [1] Godunov S K. A difference scheme for numerical computation discontinuous solution of hydrodynamic equations[J].Matematicheskii Sbornik,1959,47(3): 271-306.
    [2] Roe P L. Approximate Riemann solvers, parameter vectors, and difference schemes[J].Journal of Computational Physics,1981,43(2): 357-372.
    [3] Toro E F.Riemann Solver and Numerical Methods for Fluid Dynamics [M]. 2nd ed. Berlin: Springer, 1999.
    [4] Harten A. High resolution schemes for hyperbolic conservation laws[J].Journal of Computational Physics,1983,49(3): 357-393.
    [5] Harten A, Engquist B, Osher S, Chakravathy R. Uniformly high order accurate essentially non-oscillatory schemes, Ⅲ[J].Journal of Computational Physics,1987,71(2): 231-303.
    [6] LIU Xu-dong, Osher S, Chan T. Weighted essentially non-oscillatory schemes[J].Journal of Computational Physics,1994,115(1): 200-212.
    [7] JIANG Guang-shan, SHU Chi-wang. Efficient implementation of weighted ENO schemes[J].Journal of Computational Physics,1996,126(1): 202-228.
    [8] Shyy W, Chen M H, Mittal R, Udaykumar H S. On the suppression of numerical oscillations using a non-linear filter[J].Journal of Computational Physics,1992,102(1): 49-62.
    [9] Beylkin G, Coifman R, Daubechies I, Mallat S, Meyer L, Raphael A, Ruskai M B.Wavelets and Their Application [M]. Cambridge, Massachusetts: Jones and Bartlett, 1992.
    [10] Mallat S.A Wavelet Tour of Signal Processing [M]. 2nd ed. Academic Press, 1999.
    [11] ZONG Zhi, Lam K Y. A localized differential quadrature (LDQ) method and its application to the 2D wave equation[J].Computational Mechanics,2002,29(4/5): 382-391.
    [12] Qian S, Wiess J. Wavelets and the numerical solution of partial differential equations[J].Journal of Computational Physics,1993,106(1): 155-175.
    [13] Zong Z, Zhao Y, Zou W N. Numerical solution for differential evolutional equation using adaptive interpolation wavelet method[J].Chinese Journal of Computational Physics,2010,27(1): 65-69.
    [14] Vasilyev O V, Paolucci S, Sen M. A multilevel wavelet collocation method for solving partial differential equations in a finite domain[J].Journal of Computational Physics,1995,120(1): 33-47.
    [15] Vasilyev O V, Paolucci S. A dynamically adaptive multilevel wavelet collocation method for solving partial differential equations in a finite domain[J].Journal of Computational Physics,1996,125(2): 498-512.
    [16] Farge M, Schneider K, Kevlahan N K R. Non-gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis[J].Physics of Fluids,1999,11(8): 2187-2201.
    [17] Farge M, Schneider K. Coherent vortex simulation (CVS), a semi-deterministic turbulence model using wavelets[J].Flow, Turbulence and Combustion,2001,66(4): 393-426.
    [18] Goldstein D E, Vasilyev O V. Stochastic coherent adaptive large eddy simulation method[J].Physics of Fluids,2004,16(7): 2497-2513.
    [19] Schneider K, Kevlahan N K R, Farge M. Comparison of an adaptive wavelet method and nonlinearly filtered pseudospectral methods for two-dimensional turbulence[J].Theoretical and Computational Fluid Dynamics,1997,9(3/4): 191-206.
    [20] 赵勇, 宗智, 邹文楠. 涡旋演化的小波自适应模拟[J]. 应用数学和力学, 2011,32(1): 33-43.(ZHAO Yong, ZONG Zhi, ZOU Wen-nan. Numerical simulation of vortex evolution based on adaptive wavelet method[J].Applied Mathematics and Mechanics,2011,32(1): 33-43.(in Chinese))
    [21] Daubechies I. Orthonormal bases of compactly supported wavelets[J].Communications on Pure and Applied Mathematics,1988,41(7): 909-996.
    [22] Mallat S G. A theory for multiresolution signal decomposition: the wavelet representation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1989,11(7): 674-693.
    [23] Donoho D L, Johnstone I M. Adapting to unknown smoothness via wavelet shrinkage[J].Journal of the American Statistical Association,1995,90(432): 1200-1224.
    [24] Stoker J J.Water Waves [M]. New York: Interscience Publishers, Inc, 1986.
    [25] Delis A I, Katsaounis Th. Relaxation schemes for the shallow water equations[J].International Journal for Numerical Methods in Fluids,2003,41(7): 695-719.
    [26] ZONG Zhi, ZHANG Ying-yan.Advanced Differential Quadrature Methods[M]. Chapman & Hall/CRC, 2009.
  • 加载中
计量
  • 文章访问数:  957
  • HTML全文浏览量:  81
  • PDF下载量:  1348
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-01-21
  • 修回日期:  2014-02-06
  • 刊出日期:  2014-06-11

目录

    /

    返回文章
    返回