Generalized polynomial chaos for the convection diffusion equation with uncertainty
Generalized polynomial chaos for the convection diffusion equation with uncertainty
复制标题
不确定性对流扩散方程的广义多项式混沌
DOI：
10.1016/j.ijheatmasstransfer.2016.02.006
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发表时间：
2016
影响因子：
5.2
通讯作者：
Gui Dongwei
中科院分区：
文献类型：
--
作者：
Li Ning;Zhao Jianping;Feng Xinlong;Gui Dongwei
本文提出了几种求解具有随机扩散系数和周期边界条件的对流扩散方程的数值算法。基于广义多项式混沌展开和Galerkin投影，将随机对流扩散方程转化为一组耦合的确定性方程。然后分别采用隐-显格式和全隐格式进行时间离散，空间离散采用傅立叶谱方法。重点研究了两类具有不同随机输入分布的数值格式。数值结果表明，均匀随机输入的特殊性在于解的统计误差在达到最小值后会随着多项式混沌展开的增长而迅速增大。隐-显格式对二维模型问题的计算效果不好。此外，数值模拟的Monte Carlo方法也表明，所提出的算法的效率和鲁棒性。
In this paper, several numerical algorithms are presented for solving the convection diffusion equation with random diffusivity and periodic boundary conditions. Based on the generalized polynomial chaos expansion and Galerkin projection, the stochastic convection diffusion equation is turned into a set of coupled deterministic equations. Then the implicit–explicit scheme and the fully implicit scheme are employed to temporal discretization respectively, while the Fourier spectral method is used for spatial discretization. We place emphasis on the study of the two kinds of numerical schemes with different distribution of random inputs. Numerical results show that the Uniform random inputs is special, it is that the statistical error of solution will increase rapidly after reaches the minimum as the polynomial chaos expansion growth. And the implicit–explicit scheme doesn’t work well for the two-dimensional model problems. Moreover, numerical simulations by Monte Carlo method are also shown to demonstrate the efficiency and robustness of the proposed algorithms.