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中文摘要：
多项式混沌方法是研究不确定性CFD分析的方法之一。本文介绍了嵌入式多项式混沌方法的数学方法，并以一维Burgers方程为例，介绍了多项式混沌与非线性方程的耦合过程。并采用有限差分法求解一维随机Burgers方程，研究由于黏性系数的不确定性引起的方程解的变化。通过与解析解和采用蒙特卡洛法的模拟结果的对比，对模拟结果进行了验证与确认。研究结果表明多项式混沌方法可以有效地模拟不确定性在流场中的传播，并有很高的速度和精度。
英文摘要：
Polynomials chaos （PC） method is one of the non-deterministic analysis methods which are used in CFD. In this paper, the mathematic model of intrusive polynomials chaos method and its application to nonlinear Burger equation were presented. The finite difference method coupled with intrusive polynomials chaos method was implemented for solving one dimension stochastic Burgers equation with uncertainty viscosity coefficient. The unsteady behavior of the solution was validated and verified by comparing with the analytical solution. Analysis and discussion were focused on the uncertainty effect of viscosity on the velocity of flow, which was fllrther validated with Monte Carlo simulation results. Results are shown for the effect of polynomials chaos method on the simulation of propagation of uncertainty in flow field.
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