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SIAMREV
2016

A Newton-Galerkin Method for Fluid Flow Exhibiting Uncertain Periodic Dynamics

3 years 5 months ago
A Newton-Galerkin Method for Fluid Flow Exhibiting Uncertain Periodic Dynamics
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 wellknown 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 the phase-drift of the stochastic trajectories, keeping the necessary PC order low. Based on the rescaled governing equations...
Michael Schick, Vincent Heuveline, O. P. Le Ma&ici
Added 09 Apr 2016
Updated 09 Apr 2016
Type Journal
Year 2016
Where SIAMREV
Authors Michael Schick, Vincent Heuveline, O. P. Le Maître
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