A Reduced Order Cyclic Method for Computation of Limit Cycles

Beran, Philip S.; Lucia, David J.

doi:10.1007/s11071-005-1921-1

Cited by 44 publications

(19 citation statements)

References 24 publications

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“…In order to find the amplitudes and periods of the limit cycles excited by the fluid flow over the plate, a cyclic method similar to [70,71] is employed. In this method, the modal amplitudes α n and period of vibration for the system T are sought such that…”

Section: Fluid-structure Interactionmentioning

confidence: 99%

Reduced order modeling of fluid/structure interaction.

Barone¹,

Kalashnikova²,

Segalman³

et al. 2009

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This report describes work performed from October 2007 through September 2009 under the Sandia Laboratory Directed Research and Development project titled "Reduced Order Modeling of Fluid/Structure Interaction." This project addresses fundamental aspects of techniques for construction of predictive Reduced Order Models (ROMs). A ROM is defined as a model, derived from a sequence of high-fidelity simulations, that preserves the essential physics and predictive capability of the original simulations but at a much lower computational cost. Techniques are developed for construction of provably stable linear Galerkin projection ROMs for compressible fluid flow, including a method for enforcing boundary conditions that preserves numerical stability. A convergence proof and error estimates are given for this class of ROM, and the method is demonstrated on a series of model problems. A reduced order method, based on the method of quadratic components, for solving the von Karman nonlinear plate equations is developed and tested. This method is applied to the problem of nonlinear limit cycle oscillations encountered when the plate interacts with an adjacent supersonic flow. A stability-preserving method for coupling the linear fluid ROM with the structural dynamics model for the elastic plate is constructed and tested. Methods for constructing efficient ROMs for nonlinear fluid equations are developed and tested on a one-dimensional convectiondiffusion-reaction equation. These methods are combined with a symmetrization approach to construct a ROM technique for application to the compressible Navier-Stokes equations.

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Section: Fluid-structure Interactionmentioning

confidence: 99%

Reduced order modeling of fluid/structure interaction.

Barone¹,

Kalashnikova²,

Segalman³

et al. 2009

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“…The cyclic method in combination with the finite difference method for the time discretization has been described in previous work. 1 The cyclic method will again be described here for clarity. Two other computational techniques, the Time Spectral method and the Spectral Element method will be used in conjunction with the cyclic method in place of the finite difference discretization.…”

Section: Formulationmentioning

confidence: 99%

Comparative Analysis of Computational Methods for Limit-Cycle Oscillations

Gopinath¹,

Beran²,

Jameson³

2006

47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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14
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Various methods are explored in the computation of time-periodic solutions for autonomous systems. The purpose of the work is to illuminate the capabilities and limitations of methods, including a new method developed as part of the work, not based on time integration for the fast computation of limit-cycle oscillations (LCO). Discussion will focus on methodology, robustness, accuracy, and frequency prediction. Results for a model problem are shown in which temporal discetization errors during LCO are taken to machine zero. Treatment of sharp transients during LCO is also discussed.

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“…Two studies have been identified in the literature. Prediction of a subcritical LCO has been investigated using a reduced-order cyclic method for a pitch-plunge aerofoil in incompressible flow [4,13]. The method combines the techniques of proper orthogonal decomposition and computation of LCO in the modal subspace using an orbital approach and allows for the direct computation of LCO.…”

Section: Introductionmentioning
confidence: 99%

Nonlinear reduced-order modelling for limit-cycle oscillation analysis
Gai
¹
,
Timme
²

2015
Nonlinear Dyn
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4
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A nonlinear model reduction based on eigenmode decomposition and projection for the prediction of sub-and supercritical limit-cycle oscillation is presented herein. The paper focuses on the derivation of the reduced-order model formulation to include expansion terms up to fifth order such that higher-order nonlinear behaviour of a physical system can be captured. The method is applied to a two degree-of-freedom pitch-plunge aerofoil structural model in unsteady incompressible flow. Structural stiffness nonlinearity is introduced as a fifth-order polynomial, while the aerodynamics follow linear theory. It is demonstrated that the reduced-order model is capable of accurately capturing sub-and supercritical limit-cycle oscillations arising both from initial disturbances and gust excitation. Furthermore, an analysis of the computational cost associated with constructing such reduced-order model and its applicability to more complex aeroelastic problems is given.

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A Reduced Order Cyclic Method for Computation of Limit Cycles

Cited by 44 publications

References 24 publications

Reduced order modeling of fluid/structure interaction.

Reduced order modeling of fluid/structure interaction.

Comparative Analysis of Computational Methods for Limit-Cycle Oscillations

Nonlinear reduced-order modelling for limit-cycle oscillation analysis

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