Stabilization of two-dimensional Rayleigh–Bénard convection by means of optimal feedback control

Park, Hyung‐Min; Sung, M. C.

doi:10.1016/j.physd.2003.07.001

Cited by 6 publications

(4 citation statements)

References 9 publications

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“…[12][13][14][15]). Park and Sung proposed a stabilization for Rayleigh-Bénard convection by using feedback control [16]; for consistently stabilized finite element methods, Barth et al classified the stabilization techniques and studied influence of the stabilization parameter in convergence [17]; Bochev et al stated the requirements on choice of stabilization parameter if time step and mesh are allowed to vary independently [18]. As far as we know, it may not be enough to investigate what stabilization techniques are efficient for nonsteady and nonlinear flow problems approximated by Lagrange-Galerkin methods in a domain decomposition system, where the interface problem can be solved by preconditioned conjugate gradient (PCG) method.…”

Section: Introductionmentioning

confidence: 99%

A Pressure-Stabilized Lagrange-Galerkin Method in a Parallel Domain Decomposition System

Yao¹,

Zhu²

2013

Abstract and Applied Analysis

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A pressure-stabilized Lagrange-Galerkin method is implemented in a parallel domain decomposition system in this work, and the new stabilization strategy is proved to be effective for large Reynolds number and Rayleigh number simulations. The symmetry of the stiffness matrix enables the interface problems of the linear system to be solved by the preconditioned conjugate method, and an incomplete balanced domain preconditioner is applied to the flow-thermal coupled problems. The methodology shows good parallel efficiency and high numerical scalability, and the new solver is validated by comparing with exact solutions and available benchmark results. It occupies less memory than classical product-type solvers; furthermore, it is capable of solving problems of over 30 million degrees of freedom within one day on a PC cluster of 80 cores.

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Section: Introductionmentioning

confidence: 99%

A Pressure-Stabilized Lagrange-Galerkin Method in a Parallel Domain Decomposition System

Yao¹,

Zhu²

2013

Abstract and Applied Analysis

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“…POD-G reduced order models were used for solving optimization problems for natural convection flows. Let us cite for instance the estimation of the strength of a heat source [5], the control of a thermally driven flow of an electrically conducting fluid in a 2D cavity using a magnetic field as actuator [6], and the suppression of Rayleigh-Bénard convection in a 2D cavity by adapting the heat flux profile at the bottom wall [7]. As a preliminary step of deriving a model-based controller for mixed convection flows, this work focuses on the derivation of low order models.…”

Section: Introductionmentioning

confidence: 99%

Reduced Order Modeling by Modal Identification Method and POD-Galerkin approach of the heated circular cylinder wake in mixed convection

Cordier

Girault

Petit

2012

J. Phys.: Conf. Ser.

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Abstract. When dealing with control of thermal systems, the first step in the design of a model-based controller is the development of a model which accurately captures heat transfer dynamics. Classical high-fidelity models directly derived from the application of conservation laws on the discretized space domain, lead to sets of Ordinary Differential Equations in time whose size is usually too huge for practical implementation of real-time control. A variety of techniques have been developed for building low order models, involving a small number of degrees of freedom compared to high-fidelity models. Here, we focus on two approaches: Modal Identification Method, mainly used in heat transfer, and a POD-Galerkin method, based on Proper Orthogonal Decomposition and traditionally employed in fluid mechanics. The objective of this work is to compare on a simple 2D mixed convection problem, the accuracy of the reduced order models derived by both methods for describing the flow dynamics. Results are presented for the heated circular cylinder wake at a Reynolds number equal to 200 and a Richardson number equal to 2. Velocity and temperature fields at different time instants, computed with a reference Finite Element model, are used as data for both approaches.

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“…Additional motivation for the control of broad-area lasers stems from the general thrust for control techniques for Though some approaches exist in different chemical and physical systems, these investigations are just at their starting point (e.g. [23]). In nonlinear optics a Fourier space based feedback technique was suggested for nonlinear resonators [24] motivating many successful implementations in single-mirror feedback schemes [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Control of the spatial emission structure of broad-area vertical-cavity surface-emitting lasers by feedback

Schulz-Ruhtenberg¹,

Tanguy²,

Huang³

et al. 2009

J. Phys. D: Appl. Phys.

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The wave number of transverse spatial structures in broad-area vertical-cavity surface-emitting lasers (VCSELs) is controlled via frequency-selective feedback from an external self-imaging cavity in a broad range of wave numbers and emission frequencies. The selected states follow the dispersion curves of the free-running laser. A control range of about 2.5 µm −1 in spatial frequency space and 2.5 nm in emission wavelength was obtained for square VCSELs and of about 3 µm −1 and 8 nm for circular VCSELs having a different dispersion curve. By spatial filtering in Fourier space, the shape of the structures can also be controlled to some extent. It is argued that the feedback techniques are useful to 'probe' emission states of the free-running laser.

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Stabilization of two-dimensional Rayleigh–Bénard convection by means of optimal feedback control

Cited by 6 publications

References 9 publications

A Pressure-Stabilized Lagrange-Galerkin Method in a Parallel Domain Decomposition System

A Pressure-Stabilized Lagrange-Galerkin Method in a Parallel Domain Decomposition System

Reduced Order Modeling by Modal Identification Method and POD-Galerkin approach of the heated circular cylinder wake in mixed convection

Control of the spatial emission structure of broad-area vertical-cavity surface-emitting lasers by feedback

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