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基于嵌入式多项式混沌展开法的随机边界下流动与传热问题不确定性量化
引用本文:姜昌伟,刘星,石尔,李韬海,江怡.基于嵌入式多项式混沌展开法的随机边界下流动与传热问题不确定性量化[J].应用数学和力学,2021,42(5):481-491.
作者姓名:姜昌伟  刘星  石尔  李韬海  江怡
作者单位:长沙理工大学 能源与动力工程学院, 长沙 410114
基金项目:国家自然科学基金(11572056);湖南省自然科学基金(2018JJ3533)
摘    要:提出了一种嵌入式多项式混沌展开(polynomial chaos expansion, PCE)的随机边界条件下流动与传热问题不确定性量化方法及有限元程序框架.该方法利用Karhunen-Loeve展开表达随机输入边界条件,以及嵌入式多项式混沌展开法表达输出随机场;同时利用谱分解技术将控制方程转化为一组确定性控制方程,并对每个多项式混沌进行求解得到其统计特征.与Monte-Carlo法相比,该方法能够准确高效地预测随机边界条件下流动与传热问题的不确定性特征,同时可以节省大量计算资源.

关 键 词:不确定性量化    嵌入式多项式混沌展开    随机边界条件    流动与传热    随机有限元
收稿时间:2020-07-22

Uncertainty Quantification of Flow and Heat Transfer Problems With Stochastic Boundary Conditions Based on the Intrusive Polynomial Chaos Expansion Method
Affiliation:College of Energy and Power Engineering, Changsha University of Science & Technology, Changsha 410114, P.R.China
Abstract:An intrusive polynomial chaos expansion method and a finite element program framework were proposed to quantify the uncertainty of flow and heat transfer problems under stochastic boundary conditions. In this method, the Karhunen-Loeve expansion was used to express the stochastic boundary condition, and the polynomial chaos expansion method was used to express the output random field. At the same time, the control equation was transformed into a set of deterministic equations with the spectral decomposition technology, and each polynomial chaos was solved to obtain the statistical characteristics of the numerical solution. Compared with the Monte Carlo method, this method can accurately and efficiently predict the uncertainty characteristics of flow and heat transfer problems under stochastic boundary conditions, and can save a lot of computing resources.
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