PID adaptive control of incremental and arclength continuation in nonlinear applications

Valli, Andrea M. P.; Elias, Renato N.; Carey, G. F.; Coutinho, Álvaro L. G. A.

doi:10.1002/fld.1998

Cited by 7 publications

(7 citation statements)

References 38 publications

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“…However, practical computations are very often performed with adaptive time step control. In [50,51] adaptive time step control is regarded as a feedback control problem, where the CFL condition (CFL = min e u h t h e ) is kept within an input range, typically for transient problems, 0.5 ≤ CFL ≤ 5. Thus, if we express the time step as a function of CFL and substitute it into Eq.…”

Section: Residual Based Variational Multiscale Methodsmentioning

confidence: 99%

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Residual-based variational multiscale simulation of free surface flows

et al. 2010

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In this work we apply the residual-based variational multiscale method (RB-VMS) to the volume-of-fluid (VOF) formulation of free-surface flows. Using this technique we are able to solve such problems in a Large Eddy Simulation framework. This is a natural extension of our Navier-Stokes solver, which uses the RB-VMS finite element formulation, edge-based data structures, adaptive time step control, inexact Newton solvers and supports several parallel programming paradigms. The VOF interface capturing variable is advected using the computed coarse and fine scales velocity field. Thus, the RB-VMS technique can be readily applied to the free-surface solver with minor modifications on the implementation. We apply this technique to the solution of two problems where available data indicate complex free-surface behavior. Results are compared with numerical and experimental data and show that the present formulation can achieve good accuracy with minor impacts on computational efficiency.Keywords Variational multiscale method · Edge-based computations · Volume of fluid · Free surface flows

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Section: Residual Based Variational Multiscale Methodsmentioning

confidence: 99%

“…We consider here two different simulations with RB-VMS-VOF. The first simulation with a fixed time step of 10 −3 s, and in the other simulation we consider the time step adapted by the PID feedback control algorithm given in [50] and [51]. The PID controller is set to adapt the time step to the CFL range of 0.5-1.5.…”

Section: Wave Impact On a Containermentioning

confidence: 99%

Residual-based variational multiscale simulation of free surface flows

et al. 2010

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“…To assess the influence of the system parameters (γ,λ S ,ψ,κ 0 ) on the average steady-state penetration rate, the shooting procedure has been embedded in an arclength-parameterized continuation one [37][38][39]. This predictor/corrector-based procedure allows the computation of solution branches upon variation of one parameter of the governing equations.…”

Section: Limit-cycling Behaviormentioning

confidence: 99%

A drifting impact oscillator with periodic impulsive loading: Application to percussive drilling

Depouhon

Denoël

Detournay

2013

Physica D: Nonlinear Phenomena

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Percussive drilling is extensively used to drill hard rocks in the earth resource industry, where it performs best compared to other drilling technologies. In this paper, we propose a novel model of the process that consists of a drifting oscillator under impulsive loading coupled with a bilinear force/penetration interface law, together with a kinetic energy threshold for continuous bit penetration. Following the formulation of the model, we analyze its steady-state response and show that there exists a parallel between theoretical and experimental predictions, as both exhibit a maximum of the average penetration rate with respect to the vertical load on bit. In addition, existence of complex long-term dynamics with the coexistence of periodic solutions in certain parameter ranges is demonstrated.

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“…However, the use of adaptive timestep control presents some advantages. In [73,74], adaptive time-step control is regarded as a feedback control problem, where the CFL condition is kept within an input range (see Sect. 3.4).…”

Section: Weak Formulation For Incompressible Flowmentioning

confidence: 99%

A staggered procedure for fluid–object interaction with free surfaces, large rotations and driven by adaptive time stepping

Miras

Camata

Elias

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

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The coupling between a rigid body under large rotations and incompressible fluids is investigated within the arbitrary Lagrangian-Eulerian framework. We use here a staggered type of coupling with a predictor/corrector approach for the forces applied to the rigid body. Adaptive time stepping based on feedback control theory imposing a CFL condition on the mesh is investigated. The coupling scheme is first tested on a case illustrating vortex-induced vibrations around a rotating plate. We show the advantages of using the residual-based variational multiscale method for the fluid in the present context. Also, the time-step control and the role of the parameters introduced for the predictor/corrector approach are illustrated using the same test case. A reduced model FPSO ship is then studied, comparing its pitch decay with experimental results. A complex wave-rigid body interaction calculation is finally presented. Results demonstrated the robustness of the predictor/corrector staggered approach with adaptive time-step control for simulating complex interactions of a rigid body under large rotations and free-surface flows.

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PID adaptive control of incremental and arclength continuation in nonlinear applications

Cited by 7 publications

References 38 publications

Residual-based variational multiscale simulation of free surface flows

Residual-based variational multiscale simulation of free surface flows

A drifting impact oscillator with periodic impulsive loading: Application to percussive drilling

A staggered procedure for fluid–object interaction with free surfaces, large rotations and driven by adaptive time stepping

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