The Application Of Wavelet Analysis In Fluid Equations

The wavelet analysis is the development and perfection of the Fourier analysis.Wavelet analysis theory is also a arisen science which was applied extensively toevery domain. Being a time-frequency analysis tool in 1980s', Wavelet transform hassucceeded to be applied to the signal and image processing domain and been thecriterion of JPEG 2000 by it's advantages Since the development of the waveletanalysis is the basis to solve some practical problems, and then, it develops into aradioactive multi-disciplined theory, now it has become a hot field in the researchinternationally. The study of solving partial differential equations has played animportant role in the development of mechanics. At present, One of the primarymethods to solve partial differential equations is numerical method. based onMultiresolution Analysis, scale functions and wavelet functions have good analysisand computation characteristic which are been made the best of to discrete thedifferential equations. Then some algebra equations can be acquired. The applicationof wavelet analysis in Numerical Simulation of turbulence is No 3-D Numericalsimulation of turbulent flowfield. The research for the laminar flows has focused onits 1 -D numerical Simulation. Then representative numerical Simulations are solvingBurgers differential equation The purpose, method, results, conclusions and new viewof this paper is as follow:The purpose of this paper:Make the excellent numerical Simulation result enter into multivariate fluidcalculation.The method of this paper:We use wavelet bases formed by tensor products, Euler method was used in timediscretization. This paper researches the problem using the Von Neumann method.We study the convergence property of iteration matrices generated by the waveletmethod and Study on ill-conditioned problems of matrices generated by the waveletmethod.The results of this paper: carrying out the nine numerical Simulations for fluid Equation, the stability theory is mainly by 2-D and 3-D linear stability theory has been formed. Carrying out 1-D , 2-D and 3-D Stability Analysis of iteration matrices and ill-conditioned problems of matrices for the safeguard of numerical calculation.The conclusions of this paper:The wavelet analysis is an advanced and valuable numerical simulation method for multivariate fluid calculation and for Steady Navier-Stokes Equations. The task of constructing linear stability theory can be realized. 1-D, 2-D and 3-D Stability Analysis for the safeguard of numerical calculation forms the base of the application of fluid numerical simulation.The new view of this paper:The wavelet theory shows its potential in fluid numerical simulation when it was compared with finite-difference method. With the in-depth development of the wavelet theory, the wavelet analysis may probably be one of fastest-growing, the most prospect and the most powerful numerical simulation technique.