Reduced modelling through identification on 2D incompressible laminar flows

Balima, O.; Rouizi, Yassine; Favennec, Yann; Petit, Daniel; Charette, André B.

doi:10.1080/17415970802166410

Cited by 7 publications

(14 citation statements)

References 10 publications

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“…We give here only pieces of information on the adjoint problem solution. The reader may refer to [5] or [8] for more details. The adjoint equation reads…”

Section: The Inverse Problem Solution For Model Reductionmentioning

confidence: 99%

“…where ( · , · ) is the inner product in Y (see [4] for more explanation). The solution of the optimization problem is performed through an iterative quasi-Newton algorithm.…”

Section: The Inverse Problem Solution For Model Reductionmentioning

confidence: 99%

“…The identification method has recently been adapted for some fluid mechanics problems in stationary cases [4]. In [4], the stream function-vorticity (Ψ − ω) formulation was used for simplicity.…”

Section: Introductionmentioning

confidence: 99%

“…In [4], the stream function-vorticity (Ψ − ω) formulation was used for simplicity. However, the choice for the application of the boundary conditions is uneasy and impractical.…”

Section: Introductionmentioning

confidence: 99%

“…Among the large variety of reduction methods, the modal identification method has shown to be efficient in our considered cases in transient heat transfer. The modal identification method was developed earlier on to identify reduced models for both linear [1] and nonlinear systems [2,3] in heat conduction problems.The identification method has recently been adapted for some fluid mechanics problems in stationary cases [4]. In [4], the stream function-vorticity (Ψ − ω) formulation was used for simplicity.…”

mentioning

confidence: 99%

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Model reduction on 2-D incompressible laminar flows: Application on the flow over a backward-facing step

Rouizi

Favennec

Girault

et al. 2008

J. Phys.: Conf. Ser.

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Abstract. The computation of fluid mechanics problems usually leans on a discretization of the Navier-Stokes equations which has to be so fine that the dimensions of the linear systems to be solved are very high. As a direct consequence, the Central Processing Unit time needed to solve complex systems my become extremely large when accuracy is demanded. When coupling numerical modeling schemes to inversion or control problems, the size of linear systems to be solved has to be drastically reduced. Within this context, the identification method consists in identifying the components of a low-order matrix system. The identification process works as an inverse problem of parameter estimation. The test case shows the ability of the proposed method to reduced with accuracy a particular fluid mechanics problem. IntroductionThe numerical solution of fluid mechanics problems usually needs a fine spatial discretization of the considered domain. Consequently, the matrix systems may be large and the computational times may be elevated. This common approach gives the so-called detailed model. Though these models may be highly reliable and accurate, the computational cost can be cumbersome to treat applications such as in-time control or inverse problems for instance. The alternative is to build a model of much lower number of degrees of freedom that reproduces well enough the dynamics of the detailed model. Among the large variety of reduction methods, the modal identification method has shown to be efficient in our considered cases in transient heat transfer. The modal identification method was developed earlier on to identify reduced models for both linear [1] and nonlinear systems [2,3] in heat conduction problems.The identification method has recently been adapted for some fluid mechanics problems in stationary cases [4]. In [4], the stream function-vorticity (Ψ − ω) formulation was used for simplicity. However, the choice for the application of the boundary conditions is uneasy and impractical. This is the reason why the reduced model formulation has been revisited based on the primal variables that are the velocities and the pressure. The direct Navier-Stokes equations are discretized. The modal form is then derived leading to the structure for the reduced model. The components of the matrix system form the vector of parameters that is to be identified. The identification is based on the solution of an optimization problem that consists in minimizing a cost function. A gradient quasi-Newton method is used. The cost function gradient is computed through the solution of the adjoint state problem [5].

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“…We give here only pieces of information on the adjoint problem solution. The reader may refer to [5] or [8] for more details. The adjoint equation reads…”

Section: The Inverse Problem Solution For Model Reductionmentioning

confidence: 99%

“…where ( · , · ) is the inner product in Y (see [4] for more explanation). The solution of the optimization problem is performed through an iterative quasi-Newton algorithm.…”

Section: The Inverse Problem Solution For Model Reductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In [4], the stream function-vorticity (Ψ − ω) formulation was used for simplicity. However, the choice for the application of the boundary conditions is uneasy and impractical.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Model reduction on 2-D incompressible laminar flows: Application on the flow over a backward-facing step

Rouizi

Favennec

Girault

et al. 2008

J. Phys.: Conf. Ser.

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Model reduction through identification – Application to some diffusion–convection problems in heat transfer, with an extension towards control strategies

Rouizi¹,

Favennec²,

Jarny³

et al. 2013

Comptes Rendus. Mécanique

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The simulation of heat convection problems usually leads to very large matrix systems because both Navier-Stokes equations and the energy equations are to be taken into account and discretized. Of course, such large matrix systems cannot be used for online control algorithms due to memory limitations and computation time. On-line control algorithms should rather consider much smaller matrix systems. Bearing this in mind, model reduction techniques present a large interest to obtain a suitable low-order model that can further be used in control processes. In this paper, reduced models are obtained through the modal identification method. This method relies on the solution of an optimization problem of parameter estimation following the steps: (i) the structure of the state model is first defined, (ii) the related vectors and matrices are estimated through the minimization of a corresponding functional, (iii) the reduced order model then must be validated with input data different from those used within the identification process. These steps being completed, other control algorithms can "plug" such reduced models. Among linear control algorithms, the feedback control laws considered in this paper are based either on the reduced state or on the output. A Kalman filter evaluates the state through a limited number of measurements. The developed numerical application deals with a temperature field within a 2D stationary flow over a backward-facing step. The goal is to keep the outlet temperature as close as possible to a given temperature profile downstream from the step, whatever the pipe inlet temperature fluctuations. One thus searches some "optimal" heat fluxes upstream from the step that counteract the inlet temperature variations.

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Model reduction by the Modal Identification Method in forced convection: Application to a heated flow over a backward-facing step

Rouizi

Girault

Favennec

et al. 2010

International Journal of Thermal Sciences

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Reduced modelling through identification on 2D incompressible laminar flows

Abstract: International audienc

Cited by 7 publications

References 10 publications

Model reduction on 2-D incompressible laminar flows: Application on the flow over a backward-facing step

Model reduction on 2-D incompressible laminar flows: Application on the flow over a backward-facing step

Model reduction through identification – Application to some diffusion–convection problems in heat transfer, with an extension towards control strategies

Model reduction by the Modal Identification Method in forced convection: Application to a heated flow over a backward-facing step

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