Uncertainty quantification of limit-cycle oscillations

Beran, Philip S.; Pettit, Chris L.; Millman, Daniel R.

doi:10.1016/j.jcp.2006.03.038

Cited by 105 publications

(49 citation statements)

References 35 publications

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“…In the following sections, a one-dimensional and a two-dimensional uniformly distributed random input ξ will be considered, where v (1) (ξ) and v (2) (ξ) will be defined later according to the numerical examples. For the outflow boundary condition at Γ o ⊂ ∂D socalled do-nothing boundary conditions are applied [12].…”

Section: The Algorithmmentioning

confidence: 99%

“…In [29] a multielement approach was introduced, which is able to postpone the point of convergence breakdown to later simulation times based on a domain decomposition of the probability space. In [2] a similar idea was developed employing a wavelet multiresolution analysis [17,19], which, however, also suffers from the same drawback regarding the long term integration convergence breakdown. Recently, a time-dependent basis for capturing the time evolution of the probability distribution of the solution was introduced in [8,25].…”

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confidence: 99%

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

Schick

Heuveline

2014

SIAM/ASA J. Uncertainty Quantification

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Abstract. 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, 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.

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Section: The Algorithmmentioning

confidence: 99%

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confidence: 99%

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

Schick

Heuveline

2014

SIAM/ASA J. Uncertainty Quantification

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“…12 Other unsteady applications can also be found in literature. 2,13 In this paper, an efficient alternative approach for uncertainty quantification in oscillatory problems is proposed.…”

Section: Introductionmentioning

confidence: 99%

Unsteady Adaptive Stochastic Finite Elements for Aeroelastic Systems with Randomness

Witteveen¹,

Bijl²

2008

49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference &Amp;lt;br> 16th AIAA/ASME/AHS Ada

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It is recognized in the engineering community that there is an increasing need to move towards unsteady simulations in computational fluid dynamics. This trend also dictates an increasing application of uncertainty quantification methods to unsteady problems. In this paper, an Unsteady Adaptive Stochastic Finite Elements method based on interpolation at constant phase (UASFE-cp) is introduced for resolving the effect of random parameters in unsteady simulations. It achieves a constant accuracy in time with a constant number of samples, in contrast with the usually fast increasing number of samples required by other non-intrusive methods. Results for the stochastic bifurcation behavior of an elastically mounted airfoil with nonlinearity in the flow and the structure are presented.

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“…However, such approaches become impractical when each sample realization results from high-fidelity computational fluid and structural dynamics tools. Probabilistic collocation methodologies are promising candidates to get more insights into physical mechanisms of flutter and LCO [1,2] with affordable computational cost [3][4][5]. These studies are generally based on the use of ad hoc inviscid linear aerodynamics, and the stochastic response of the system is governed by the uncertainties associated with the nonlinear structural stiffness coefficients [5,6].…”

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confidence: 99%

Stochastic Investigation of Flows About Airfoils at Transonic Speeds

Chassaing

Lucor

2010

AIAA Journal

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In this study, a deterministic compressible solver is coupled to a nonintrusive stochastic spectral projection method to propagate several aerodynamic uncertainties through a transonic steady flow around a NACA0012 airfoil. The stochastic model is solved in a generalized polynomial chaos framework. This approach combines the advantage of not modifying the existing deterministic solver while maintaining accurate representations of the stochastic solution and its statistics. The major difficulty of this work is to deal with deterministic transonic flows for which aerodynamics nonlinearities are reported in the uncertain probabilistic space. The efficiency of the present methodology are evaluated for the propagation of random disturbances associated with the angle of attack and the freestream Mach number. An error analysis is carried out in order to determine appropriate physical and stochastic discretization levels. Different stochastic flow regimes are analyzed in details by means of various postprocessing procedures, including error bars, probabilistic density function of the aerodynamic field, and Sobol's coefficients.

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Uncertainty quantification of limit-cycle oscillations

Cited by 105 publications

References 35 publications

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

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

Unsteady Adaptive Stochastic Finite Elements for Aeroelastic Systems with Randomness

Stochastic Investigation of Flows About Airfoils at Transonic Speeds

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