## 留言板

 引用本文: 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. doi: 10.3879/j.issn.1000-0887.2011.01.004
 Citation: 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.

• 中图分类号: O357

## Numerical Simulation of Vortex Evolution Based on Adaptive Wavelet Method

• 摘要: 该文考察了小波自适应方法用于涡旋运动的演化过程．首先，通过两个初边值问题，说明小波方法具有可精度可控和局部结构自动捕捉的能力．然后，计算了涡旋的合并过程，结果表明，小波方法可以准确高效的应用于流动涡旋的演化预测，进而，讨论了小波方法在湍流数值模拟中的应用．
•  [1] 梅树立, 陆启韶, 张森文, 金俐. 偏微分方程的区间小波自适应精细积分法[J]. 应用数学和力学, 2005, 26(3): 333-340.(MEI Shu-li, LU Qi-shao, ZHANG Sen-wen, JIN Li. Adaptive interval wavelet precise integration method for partial differential equations[J]. Applied Mathematics and Mechanics(English Edition), 2005, 26 (3): 364-371.) [2] Beylkin G, Keiser J. On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases[J]. Journal of Computational Physics , 1997, 132(2): 233-259. [3] 宗智，赵勇，邹文楠. 小波插值方法自适应数值求解时间进化微分方程[J].计算力学学报, 2010, 27(1): 65-69.(ZONG Zhi, ZHAO Yong, ZOU Wen-nan. Numerical solution for differential evolutional equation using adaptive interpolation wavelet method[J]. Journal of Computational Mechanics, 2010, 27(1): 65-69. (in Chinese)) [4] Qian S, Wiess J. Wavelets and the numerical solution of partial differential equations [J]. Journal of Computational Physics, 1993, 106(1):155-175. [5] 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. [6] Farge M, Kaiser S. Coherent vortex simulation (CVS), a semi-deterministic turbulence model using wavelets[J]. Flow, Turbulence and Combustion, 2001, 66(4):393-426. [7] 郭会芬, 邱翔, 刘宇陆.小波变换在湍流数值研究中的应用[J]. 计算力学学报, 2006, 23(1): 58-64.(GUO Hui-fen, QIU Xiang, LIU Yu-lu. Application of wavelet analysis in numerical study of turbulence[J]. Journal of Computational Mechanics, 2006 , 23(1): 58-64. (in Chinese)) [8] 夏振炎, 田砚, 姜楠. 用子波谱分析壁湍流多尺度结构的能量传递[J]. 应用数学和力学, 2009, 30(4):409-416.（XIA Zhen-yan, TIAN Yan, JIANG Nan. Wavelet spectrum analysis on energy transfer of multi-scale structures in wall turbulence[J]. Applied Mathematics and Mechanics(English Edition), 2009, 30(4): 435-443. ） [9] Goldstein D E, Vasilyev O V. Stochastic coherent adaptive large eddy simulation method[J]. Physics of Fluids, 2004, 16(7):2497-2513. [10] Schneider K, Kevlahan N K R, Farge M. Comparison of an adaptive wavelet method and nonlinearly filtered pseudo-spectral methods for two-dimensional turbulence[J]. Theory and Computational Fluid Dynamics, 1997, 9(3): 191-206. [11] Kumar B V R, Mehra M. A time accurate pseudo-wavelet scheme for two-dimensional turbulence[J]. International Journal of Wavelets, Multiresolution and Information Processing, 2005, 3(4):587-599. [12] Farge M.Wavelet transforms and their application to turbulence[J]. Ann Rev Fluid Mech, 1992, 24:395-457.

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##### 出版历程
• 收稿日期:  2010-07-02
• 修回日期:  2010-10-29
• 刊出日期:  2011-01-15

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