Encapsulated formulation of the selective frequency damping method

Jordi, Bastien; Cotter, Colin J.; Sherwin, Spencer J.

doi:10.1063/1.4867482

Cited by 45 publications

(42 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Fig. 4(a), the drag of the unstable (steady) equilibrium is also plotted (this value was computed by using selective frequency damping 34,35 ). Clearly, the controlled flow-field has been stabilized to a drag state that is close to that of this unstable equilibrium.…”

Section: A Suppression Of Vortex Sheddingmentioning

confidence: 99%

Optimal control of circular cylinder wakes using long control horizons

Flinois

Colonius

2015

Physics of Fluids

View full text Add to dashboard Cite

The classical problem of suppressing vortex shedding in the wake of a circular cylinder by using body rotation is revisited in an adjoint-based optimal control framework. The cylinder's unsteady and fully unconstrained rotation rate is optimized at Reynolds numbers between 75 and 200 and over horizons that are longer than in previous studies, where they are typically of the order of a vortex shedding period or shorter. In the best configuration, the drag is reduced by 19%, the vortex shedding is effectively suppressed, and this low drag state is maintained with minimal cylinder rotation after transients. Unlike open-loop control, the optimal control is shown to maintain a specific phase relationship between the actuation and the shedding in order to stabilize the wake. A comparison is also given between the performance of optimizations for different Reynolds numbers, cost functions, and horizon lengths. It is shown that the long horizons used are necessary in order to stabilize the vortex shedding efficiently.

show abstract

Section: A Suppression Of Vortex Sheddingmentioning

confidence: 99%

Optimal control of circular cylinder wakes using long control horizons

Flinois

Colonius

2015

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…It has since become one of the standard approaches for fixed point computation in fluid dynamics due to its ease of implementation. Note that various implementations of the original selective frequency damping method have been proposed over the years [39,40,19]. Moreover, it has since been extented to compute steady states of the Reynolds-Averaged-Navier-Stokes (RANS) equations [67] as well as for the computation of unstable periodic orbits [70].…”

Section: Selective Frequency Dampingmentioning

confidence: 99%

Time-Stepping and Krylov Methods for Large-Scale Instability Problems

Loiseau

Bucci

Cherubini

et al. 2018

Computational Methods in Applied Sciences

View full text Add to dashboard Cite

With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted however that the memory capabilities of computers increase at a slower rate than their computational capabilities. Consequently, the traditional matrix-forming approaches wherein the Jacobian matrix of the system considered is explicitly assembled become rapidly intractable. Over the past two decades, so-called matrixfree approaches have emerged as an efficient alternative. The aim of this chapter is thus to provide an overview of well-grounded matrix-free methods for fixed points computations and linear stability analyses of very large-scale nonlinear dynamical systems.

show abstract

“…The base flow, shown in Fig. 12, was computed using Selective Frequency Damping (SFD) [2,26]. The SFD parameters values chosen here were χ = 0.4391 and ∆ = 3.1974, as suggested by [26] for the cylinder flow at Re = 100.…”

Section: Application To a Two-dimensional Unstable Flow-fieldmentioning

confidence: 99%

Projection-free approximate balanced truncation of large unstable systems

2015

View full text Add to dashboard Cite

In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition algorithm theoretically yields a converged transformation that balances the Gramians (including the unstable subspace). We then apply the method to a spatially developing unstable system and show that it results in reduced-order models of similar quality to the ones obtained with existing methods. Due to the unbounded growth of unstable modes, a practical restriction on the final impulse response simulation time appears, which can be adjusted depending on the desired order of the reduced-order model. Recommendations are given to further reduce the cost of the method if the system is large and to improve the performance of the method if it does not yield acceptable results in its unmodified form. Finally, the method is applied to the linearized flow around a cylinder at Re = 100 to show that it actually is able to accurately reproduce impulse responses for more realistic unstable large-scale systems in practice. The well-established approximate balanced truncation numerical framework therefore can be safely applied to unstable systems without any modifications. Additionally, balanced reduced-order models can readily be obtained even for large systems, where the computational cost of existing methods is prohibitive.

show abstract

Encapsulated formulation of the selective frequency damping method

Cited by 45 publications

References 15 publications

Optimal control of circular cylinder wakes using long control horizons

Optimal control of circular cylinder wakes using long control horizons

Time-Stepping and Krylov Methods for Large-Scale Instability Problems

Projection-free approximate balanced truncation of large unstable systems

Contact Info

Product

Resources

About