Modeling Uncertainty In Three-dimensional HeatTransfer Problems
Modeling Uncertainty In Three-dimensional HeatTransfer Problems
复制标题
三维传热问题中的不确定性建模
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
G. Karniadakis
中科院分区：
文献类型：
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作者：
X. Wan;D. Xiu;G. Karniadakis
我们提出了一种广义多项式混沌方法来解决边界条件、扩散系数和强迫项不确定的稳态和非稳态传热问题。随机输入和输出通过采用 Askey 方案中的正交多项式泛函来表示，作为 Wiener [1] 原始多项式混沌思想的推广。应用随机空间中的伽辽金投影来推导弱形式方程，并采用并行谱/hp 元素方法来求解所得的确定性方程组。这里首次展示了随机维数为 38、大约 1.5 亿个未知数的三维域中的模拟。
We present a generalized polynomial chaos method to solve the steady and unsteady heat transfer problems with uncertainty in boundary conditions, diffusivity coefficient and forcing terms. The stochastic inputs and outputs are represented spectrally by employing the orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener [1]. A Galerkin projection in random space is applied to derive the equations in weak form, and a parallel spectral/hp element method is employed to solve the resulting set of deterministic equations. Simulations in three-dimensional domains with stochastic dimension 38 and about 150 million unknowns are presented here for the first time.