中文摘要：

本文介绍了多元多项式混沌方法,采用此方法对随机层流Navier-Stokes方程进行求解,模拟了同时存在多个不确定因素影响的二维方腔驱动流。研究了当上下边界驱动速度和流体黏性系数为服从高斯分布的随机变量时所引起的流动结构的不确定性,着重分析了流场速度的统计特性,并与蒙特卡洛方法的计算结果进行了对比,对多项式混沌方法的结果进行了验证和确认。研究结果表明多项式混沌方法可以准确高效地模拟多个不确定性在流场中的传播,与蒙特卡洛方法相比体现出明显的优势。

英文摘要：

The present paper introduces the mathematic background of multidimensional intrusive polynomial chaos（MIPC） method.The MIPC method was implemented for the compressible stochastic Navier-Stokes equations to simulate the non-deterministic behavior of a cavity flow under the influence of multiple uncertainties.The driven velocities and fluid viscosity were supposed to the uncertain variables with respect to Gaussian probability distributions.The results show the accuracy and efficiency of MIPC method on the simulation of propagation of uncertainties in the flow field, which were validated by Monte Carlo simulations.