A Newton-Galerkin Method for Fluid Flow Exhibiting Uncertain Periodic Dynamics
A Newton-Galerkin Method for Fluid Flow Exhibiting Uncertain Periodic Dynamics
复制标题
具有不确定周期动力学的流体流动的牛顿-伽辽金方法
DOI：
10.1137/130908919
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Heuveline V
中科院分区：
文献类型：
--
作者：
Schick M;Le Maitre OP;Heuveline V
稳定极限环的确定对于量化动力系统的特性具有重要作用。在实践中，模型参数的准确知识很少，导致参数的不确定性，这可以建模为随机变量的输入。这使得极限环本身变得随机，几乎必然产生具有随机周期的时间周期解。本文基于多项式混沌谱随机有限元方法，提出了一种新的计算稳定随机极限环的数值方法。我们能够克服PC的困难，其众所周知的收敛故障的长期整合。为此，我们引入了一个随机时间尺度，它把随机周期作为一个额外的随机变量，并控制thepase-drift的随机轨迹，保持必要的PC阶低。基于重新标度的控制方程，我们的目标是确定一个初始条件和一个周期，使轨迹关闭后完成一个随机循环。此外，我们验证了数值方法的计算旋涡脱落的圆形区域周围的流动与随机流入边界条件作为基准问题。结果进行了验证，通过比较，纯粹的确定性参考问题，并表现出高精度的机器精度捕捉的极限环的随机变化。
The determination of stable limit-cycles plays an important role in quantifying the characteristics of dynamical systems. In practice, exact knowledge of model parameters is rarely available leading to parameter uncertainties, which can be modeled as an input of random variables. This has the effect that the limit-cycles become stochastic themselves, resulting in almost surely time-periodic solutions with a stochastic period. In this paper we introduce a novel numerical method for the computation of stable stochastic limit-cycles based on the spectral stochastic finite element method using polynomial chaos (PC). We are able to overcome the difficulties of PC regarding its well-known convergence breakdown for long term integration. To this end, we introduce a stochastic time scaling which treats the stochastic period as an additional random variable and controls thephase-driftof the stochastic trajectories, keeping the necessary PC order low. Based on the rescaled governing equations, we aim at determining an initial condition and a period such that the trajectories close after completion of one stochastic cycle. Furthermore, we verify the numerical method by computation of a vortex shedding of a flow around a circular domain with stochastic inflow boundary conditions as a benchmark problem. The results are verified by comparison to purely deterministic reference problems and demonstrate high accuracy up to machine precision in capturing the stochastic variations of the limit-cycle.
DOI：
10.1137/090777797
发表时间：
2010
期刊：
SIAM J. Matrix Anal. Appl.
影响因子：
--
作者：
C. Powell;E. Ullmann
通讯作者：
E. Ullmann
HiFlow3：硬件感知并行有限元包
DOI：
10.1007/978-3-642-31476-6_12
发表时间：
2011
期刊：
Computer Science - Research and Development
影响因子：
--
作者：
H. Anzt;W. Augustin;Martin Baumann;T. Gengenbach;Tobias Hahn;Andreas Helfrich;V. Heuveline;E. Ketelaer;D. Lukarski;A. Nestler;S. Ritterbusch;Staffan Ronnås;M. Schick;Mareike Schmidtobreick;C. Subramanian;Jan;Florian Wilhelm;Martin Wlotzka
通讯作者：
Martin Wlotzka
DOI：
10.1615/int.j.uncertaintyquantification.2012004727
发表时间：
2014
影响因子：
1.7
作者：
V. Heuveline;M. Schick
通讯作者：
M. Schick