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首页> 外文期刊>International Journal of Heat and Mass Transfer >Generalized polynomial chaos for the convection diffusion equation with uncertainty
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Generalized polynomial chaos for the convection diffusion equation with uncertainty

机译：不确定对流扩散方程的广义多项式混沌。

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摘要

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.
机译：本文提出了几种数值算法来求解具有随机扩散率和周期边界条件的对流扩散方程。基于广义多项式混沌展开和Galerkin投影，将随机对流扩散方程变成一组耦合的确定性方程。然后将隐式-显式方案和全隐式方案分别用于时间离散化，而傅立叶谱法用于空间离散化。我们重点研究随机输入不同分布的两种数值方案。数值结果表明，均匀随机输入是特殊的，随着多项式混沌展开式的增长，解的统计误差在达到最小值后将迅速增大。对于二维模型问题，隐式-显式方案不能很好地工作。此外，还通过蒙特卡洛方法进行了数值模拟，以证明所提算法的有效性和鲁棒性。

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