小波自适应方法模拟二维涡旋演化

计算物理 ›› 2009, Vol. 26 ›› Issue (6): 842-848.

小波自适应方法模拟二维涡旋演化

宗智^1,2, 赵勇¹, 邹文楠³, 高云¹

1. 大连理工大学运载工程与力学学部船舶工程学院, 辽宁大连 116024;
2. 大连理工大学工业装备结构分析国家重点实验室, 辽宁大连 116024;
3. 南昌大学工程力学研究所, 江西南昌 330031

收稿日期:2008-06-13 修回日期:2008-12-03 出版日期:2009-11-25 发布日期:2009-11-25
作者简介:宗智(1964-),男,教授,博士,从事计算力学研究.

Numerical Simulation of Two-dimensional Vortexes with Adaptive Wavelet Method

ZONG Zhi^1,2, ZHAO Yong¹, ZOU Wennan³, GAO Yun¹

1. Department of Naval Architecture, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology 116024, China;
2. State Key Laboratory of Structural Analysis and Industrial Equipment, Dalian University of Technology, Dalian 116024, China;
3. Institute of Engineering Mechanics, Nanchang University, Nanchang 330031, China

Received:2008-06-13 Revised:2008-12-03 Online:2009-11-25 Published:2009-11-25

摘要/Abstract

摘要： 以涡量方程为控制方程,模拟初始状态涡量分布为高斯分布三个涡旋演化过程.提出一个关联实际流动的小波系数临界值,小波系数分为临界值以上及以下部分,进而涡量可分成尺度系数项、小波系数突出项和小波系数平凡项三部分.只采用尺度系数项和小波系数突出项近似涡量,既可以节约计算量,还可以自动追踪绝大部分的拟涡能.数值结果表明,用不到10%的小波系数,可控制99%以上的拟涡能.

关键词: 小波自适应, 涡量方程, 涡旋合并, 拟序结构, 临界值

Abstract: Taking vorticity equation as a controlling equation, we simulate three vortexes developing progress with initial condition of Gaussian probability vorticity distribution. The wavelet expression of vorticity contains scaling coefficient term and wavelet coefficient tenn. The latter can be divided into a significant wavelet coefficient term and a trivial wavelet coefficient term reference to a given critical value. The critical value contains practical flow information. The vorticity is reconstructed only with scaling coefficients and significant wavelet coefficients. It saves computing time and capture most part of entrophy. Numerical results show that scaling coefficients together with significant wavelet coefficients is less than 10% of total wavelet coefficients, but they contains more than 99% of total enstrophy.

Key words: wavelet adaptivity, vorticity equation, vortex emerge, coherent structure, critical value

中图分类号:

宗智, 赵勇, 邹文楠, 高云. 小波自适应方法模拟二维涡旋演化[J]. 计算物理, 2009, 26(6): 842-848.

ZONG Zhi, ZHAO Yong, ZOU Wennan, GAO Yun. Numerical Simulation of Two-dimensional Vortexes with Adaptive Wavelet Method[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(6): 842-848.