非嵌入式多项式混沌方法在拉氏计算中的应用

UNCERTAINTY QUANTIFICATION FOR LAGRANGIAN COMPUTATION USING NON-INTRUSIVE POLYNOMIAL CHAOS

论文介绍了多项式混沌方法的数学理论基础,包括正交多项式以及混沌多项式展开.给出了非嵌入混沌多项式进行不确定度量化分析的主要过程.同时结合经典拉氏计算格式,给出了二次人为粘性在Sod问题中的不确定度量化,计算结果表明非嵌入混沌方法可为现有遗产程序进行不确定度量化分析.

This paper introduces the mathematical theory for the method of polynomial chaos,including the expansion of orthogonal polynomials and polynomial chaos.We give the main procedure of uncertainty quantification with non-intrusive polynomial chaos.Meanwhile,together with the classical Lagrangian scheme,we show the uncertainty quantification of the second artificial viscosity in Sod problem.Our result shows that the method of non-intrusive polynomial chaos can provide the uncertainty quantification for the inherited programs.