Dynamic responses and flow field characteristic of stochastic Burgers equation

Abstract

Turbulent flow is a highly irregular motion which is usually described as stochastic process in engineering analysis and design, and Burgers equation as a turbulence model has been widely used in various fields. In order to obtain the probability density function of physical quantities in the stochastic Burgers equation and more flow field characteristic information, we propose the direct probability integral method (DPIM), and solve the viscous Burgers equation with random initial conditions of Gaussian white noise. Firstly, the basic theory of Burgers equation and the numerical method for computing Burgers equation, namely predictor-corrector method, are introduced. Secondly, the hybrid spectral representation and random function approach is utilized to accurately simulate the stochastic process of Gaussian white noise by using only two random variables. Finally, the stochastic Burgers equation is calculated via DPIM, and the probability density functions of different position responses at different times are achieved, which are compared with those results by Monte Carlo simulation. It is indicated the probability density functions of flow velocity obtained by the two methods are in good agreement, and DPIM is more efficient. With the increase of time, the velocity response of Burgers equation gradually decreases due to the influence of viscosity coefficient in its diffusion term.