Supersensitivity due to uncertain boundary conditions
Supersensitivity due to uncertain boundary conditions
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DOI：
10.1002/nme.1152
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发表时间：
2004-11
影响因子：
2.9
通讯作者：
D. Xiu;G. Karniadakis
中科院分区：
文献类型：
--
作者：
D. Xiu;G. Karniadakis
研究了边界条件受扰动的粘性Burgers型方程。考虑了两种摄动：确定性摄动和随机摄动。对于确定性的微扰，我们证明了微小的微扰可以导致过渡层位置的O(1)变化。对于随机扰动，我们用不同的方法求解随机Burgers型方程。首先，我们利用广义多项式混沌的一个子集--雅可比多项式混沌进行随机建模。报道了收敛的数值结果(高达七位有效数字)，并且我们观察到过渡层的平均位置具有类似的“随机超敏感性”。随后，我们采用了高达四阶的微扰展开。我们表明，即使在小的随机输入下，由于输出的随机响应较大，摄动法的分辨率也相对较差。我们考虑了两种类型的分布：均匀分布和无尾的截断高斯分布。研究了各种解的统计特性，包括稳态概率密度函数的空间演化。版权所有©2004 John Wiley&Sons，Ltd.
We study the viscous Burgers' equation subject to perturbations on the boundary conditions. Two kinds of perturbations are considered: deterministic and random. For deterministic perturbations, we show that small perturbations can result in O(1) changes in the location of the transition layer. For random perturbations, we solve the stochastic Burgers' equation using different approaches. First, we employ the Jacobi‐polynomial‐chaos, which is a subset of the generalized polynomial chaos for stochastic modeling. Converged numerical results are reported (up to seven significant digits), and we observe similar ‘stochastic supersensitivity’ for the mean location of the transition layer. Subsequently, we employ up to fourth‐order perturbation expansions. We show that even with small random inputs, the resolution of the perturbation method is relatively poor due to the larger stochastic responses in the output. Two types of distributions are considered: uniform distribution and a ‘truncated’ Gaussian distribution with no tails. Various solution statistics, including the spatial evolution of probability density function at steady state, are studied. Copyright © 2004 John Wiley & Sons, Ltd.