二维RayleighBénard对流系统非线性特征的DSMC研究

 应用发端于微观分子动力学的蒙特卡罗直接模拟(DSMC)方法实现了RB(RayleighBénard)对流的数值模拟,并在此基础上得到了与线性稳定性理论分析结果相一致的RB系统第一次分叉的临界瑞利数;通过对大瑞利数下RB系统中心点处温度信号进行功率谱分析,得到RB系统通向混沌的倍周期分叉路径,同时应用现代混沌分析方法研究了RB对流系统的关联维、最大Lyapunov指数等非线性特征。

Nonlinear Characteristic Analysis of Two-Dimensional Rayleigh Bénard Convective System Using Direct Simulation Monte Carlo Method

Rayleigh Bénard(RB) convective system is simulated numerically using Direct Simulation Monte Carlo (DSMC) method which origins from micro-molecular dynamics. On the basis of DSMC simulation results, the critical Rayleigh number is obtained, which is consistent with the linear stability theory. The double periods bifurcate route to chaos in RB system is obtained by spectrum analysis of temperature signal on the center point of RB system; At the same time, the nonlinear characteristics such as conjunction dimensionality and Lyapunov index are obtained by modern chaotic analysis method.