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

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.