非线性系统随机过程对初始条件的敏感性  

Sensitivity of Nonlinear System to the Random Initial Condition

作　　者：任孝安[1] 吴文权[1] 

机构地区：[1]上海理工大学能源与动力过程学院,上海200093

出　　处：《工程热物理学报》2014年第2期252-255,共4页Journal of Engineering Thermophysics

基　　金：国家自然科学基金资助项目(No.50976071)

摘　　要：将作者所提出的基于混沌展开的动态自适应小波随机数值模拟方法进一步发展应用于对非线性随机对流-扩散Burgers方程的数值分析。不仅进一步显示了其各求解分量拥有独立的自适应小波网格特点,同时也为随机系统对干扰的敏感性分析:敏感区及其随时间的演变,提供了一个直接可应用的有效方法。数值实验的结果进一步验证了非线性系统对初始条件的敏感性,并初步揭示了输入扰动向高梯度区演变的规律。We extend the dynamically adaptive wavelet method based on polynomial chaos for linear stochastic computations to the numerical solution of nonlinear stochastic convection-diffusion Burgers equation. We show further that our approach allows all scales of each solution component to be refined independently of the rest, and at the same time introduce a directly applicable effective means for the initial value sensitivity analysis of stochastic nonlinear system （sensitive area and its evolution with time）. Our numerical experiments confirm the sensitivity of the nonlinear system to the small perturbation in the initial condition, and preliminary results reveal the sensitive area gradually shifting towards high gradient region.

关 键 词：随机过程 非线性对流扩散方程 初始条件敏感性 动态自适应小波方法 多项式混沌展开 

分 类 号：O422[理学—声学]