小波变换在湍流数值研究中的应用

小波变换具有时空双局部性特点,恰好适应了湍流特性。本文主要阐述了小波在湍流数值计算中的两大研究进展:一个是利用连续小波(高斯小波)可使L ap lace算子降阶的特性来求解N-S方程;另一个是正交小波与有限元法相结合的方法——相干涡模拟。指出它们的优缺点及其存在的问题,并对小波在湍流计算中的应用前景作了展望。

Application of wavelet analysis in numerical study of turbulence

The wavelet transform are localized in both temporal and spatial spaces,which adopt to the characteristics of turbulence.Wavelet analysis has been applied and developed in turbulent numerical study since 1990's.In this paper,two aspects in turbulence numerical simulation are described,which one is made use of continuous wavelets,Gaussian wavelets to obtain the solutions of N-S equations by degrading the Laplace operator into one-order operator,and the other is orthonormal wavelet was combined with finite element method: coherent vortex simulation(CVS).The advances and defects of the numerical application of wavelets in turbulence are discussed,the presented problems are pointed out and the prospect is predicted based on present numerical study.