Calibrated reduced-order POD-Galerkin system for fluid flow modelling

Couplet, Mathieu; Basdevant, C.; Sagaut, Pierre

doi:10.1016/j.jcp.2005.01.008

Cited by 227 publications

(192 citation statements)

References 20 publications

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“…However, in this study, we will consider that this expression remains valid and determine the coefficients of the POD ROM with calibration methods based on optimization problems [63][64][65]. These calibration techniques are similar to those which had been used in [15] to represent accurately the controlled dynamics of reference with a POD ROM based on velocity only.…”

Section: Pod Rom Of the Controlled Cylinder Wakementioning

confidence: 99%

Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

Bergmann

Cordier

2008

Journal of Computational Physics

178

154

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In this paper, optimal control theory is used to minimize the total mean drag for a circular cylinder wake flow in the laminar regime (Re = 200). The control parameters are the amplitude and the frequency of the time-harmonic cylinder rotation. In order to reduce the size of the discretized optimality system, a Proper Orthogonal Decomposition (POD) Reduced-Order Model (ROM) is derived to be used as state equation. We then propose to employ the Trust-Region Proper Orthogonal Decomposition (TRPOD) approach, originally introduced by Fahl (2000), to update the reduced-order models during the optimization process. A lot of computational work is saved because the optimization process is now based only on low-fidelity models. A particular care was taken to derive a POD ROM for the pressure and velocity fields with an appropriate balance between model accuracy and robustness. The key enablers are the extension of the POD basis functions to the pressure data, the use of calibration methods for the POD ROM and the addition in the POD expansion of several non-equilibrium modes to describe various operating conditions. When the TRPOD algorithm is applied to the wake flow configuration, this approach converges to the minimum predicted by an open-loop control approach and leads to a relative mean drag reduction of 30% at reduced cost.

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Section: Pod Rom Of the Controlled Cylinder Wakementioning

confidence: 99%

Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

Bergmann

Cordier

2008

Journal of Computational Physics

178

154

View full text Add to dashboard Cite

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“…The neglect of small scales results in ¦ltering of high frequencies and vanishing of energy transfers between resolved and unresolved scales of a §uid §ow [42] that decrease the quality of the model.…”

Section: Model Calibrationmentioning

confidence: 99%

“…To correct the behavior and improve the accuracy of Reduced Order Galerkin Model, the coe©cients of the Galerkin system of ordinary di¨erential equations (ODE) are adjusted [42].…”

Section: Flow Controlmentioning

confidence: 99%

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Arbitrary Lagrangian-Eulerian approach in reduced order modeling of a flow with a moving boundary

Stankiewicz

Roszak

Morzyński

2013

Progress in Flight Physics

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Flow-induced de §ections of aircraft structures result in oscillations that might turn into such a dangerous phenomena like §utter or bu¨eting. In this paper the design of an aeroelastic system consisting of Reduced Order Model (ROM) of the §ow with a moving boundary is presented. The model is based on Galerkin projection of governing equation onto space spanned by modes obtained from high-¦delity computations. The motion of the boundary and mesh is de¦ned in Arbitrary Lagrangian Eulerian (ALE) approach and results in additional convective term in Galerkin system. The developed system is demonstrated on the example of a §ow around an oscillating wing.

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“…A popular physics-based meta-modeling technique consists of carrying out the approximation on the full vector fields using PCA and Galerkin projection [5] in CFD [6] as well as in structural analysis [7]. This approach has been successfully applied to a number of areas such as flow modeling [8,9] optimal flow control [10], aerodynamics design optimization [11] or structural mechanics [12]. However, this requires manipulation of the input variablesV .…”

Section: Introduction Literature Reviewed and Motivation For Researchmentioning

confidence: 99%

Towards simultaneous reduction of both input and output spaces for interactive simulation-based structural design

Raghavan¹,

Xia²,

Breitkopf³

et al. 2013

Computer Methods in Applied Mechanics and Engineering

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International audienceEngineering design problems generally involve a high-dimensional input space of design variables yielding an output space by means of costly high-fidelity evaluations. In order to decrease the overall cost, reduced-order models for the output space such as Proper Orthogonal Decomposition (POD) and Proper Generalized Decomposition (PGD) are an active area of research. However, little research has been conducted into alleviating the problems associated with a high-dimensional input space. In addition to higher dimensionality being an impediment to efficient design by itself, complex shapes involve a high number of explicit/implicit constraints restricting the design space. Geometric parameterization methods in traditional CAD present difficulties in expressing these constraints leading to a high failure rate and the generation of inadmissible shapes. In this paper, we propose a simultaneous meta-modeling protocol for both input and output spaces. We perform a reparametrization of the input space using constrained shape interpolation by introducing the concept of an alpha-manifold of admissible meshed shapes. The output space is reduced using constrained Proper Orthogonal Decomposition. By simultaneously using metamodeling for both spaces, we facilitate interactive design space exploration for the purpose of design. The proposed approach is applied to the industrial problem of designing a car engine intake port

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Calibrated reduced-order POD-Galerkin system for fluid flow modelling

Cited by 227 publications

References 20 publications

Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

Arbitrary Lagrangian-Eulerian approach in reduced order modeling of a flow with a moving boundary

Towards simultaneous reduction of both input and output spaces for interactive simulation-based structural design

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