Proper orthogonal decomposition with high number of linear constraints for aerodynamical shape optimization

Xiao, Manyu; Breitkopf, Piotr; Coelho, Rajan Filomeno; Villon, Pierre; Zhang, Weihong

doi:10.1016/j.amc.2014.09.068

Cited by 11 publications

(9 citation statements)

References 20 publications

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“…However, upon truncating the decomposition to arrive at a reduced dimension, this property is generally lost. We therefore propose to enforce property (50) by using an approach that enforces linear constraints in constructing the POD basis, as detailed in [56,57]. In short, the idea is to change the minimization problem that underlies the SVD (equation ( 34)) by a constrained minimization problem, which can be efficiently solved by using a QR-decomposition of the constraint matrix and a projected snapshot set.…”

Section: Momentum Conservation Of the Rommentioning

confidence: 99%

Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods

Sanderse

2020

Journal of Computational Physics

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A novel reduced-order model (ROM) formulation for incompressible flows is presented with the key property that it exhibits non-linearly stability, independent of the mesh (of the full order model), the time step, the viscosity, and the number of modes. The two essential elements to non-linear stability are: (1) first discretise the full order model, and then project the discretised equations, and (2) use spatial and temporal discretisation schemes for the full order model that are globally energy-conserving (in the limit of vanishing viscosity). For this purpose, as full order model a staggered-grid finite volume method in conjunction with an implicit Runge-Kutta method is employed. In addition, a constrained singular value decomposition is employed which enforces global momentum conservation. The resulting 'velocity-only' ROM is thus globally conserving mass, momentum and kinetic energy. For non-homogeneous boundary conditions, a (onetime) Poisson equation is solved that accounts for the boundary contribution. The stability of the proposed ROM is demonstrated in several test cases. Furthermore, it is shown that explicit Runge-Kutta methods can be used as a practical alternative to implicit time integration at a slight loss in energy conservation.

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Section: Momentum Conservation Of the Rommentioning

confidence: 99%

Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods

Sanderse

2020

Journal of Computational Physics

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“…Another interesting and promising approach is the application of the proper orthogonal decomposition (POD) as a model reduction technique, which has now found applications in different fields of engineering and physics (e.g., Refs. [10][11][12][13][14][15][16][17][18]) following the pioneeristic studies of Refs. [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Proper Orthogonal Decomposition Framework for the Explicit Solution of Discrete Systems With Softening Response

Ceccato

Zhou

Pelessone

et al. 2018

Journal of Applied Mechanics

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The application of explicit dynamics to simulate quasi-static events often becomes impractical in terms of computational cost. Different solutions have been investigated in the literature to decrease the simulation time and a family of interesting, increasingly adopted approaches are the ones based on the proper orthogonal decomposition (POD) as a model reduction technique. In this study, the algorithmic framework for the integration of the equation of motions through POD is proposed for discrete linear and nonlinear systems: a low dimensional approximation of the full order system is generated by the so-called proper orthogonal modes (POMs), computed with snapshots from the full order simulation. Aiming to a predictive tool, the POMs are updated in itinere alternating the integration in the complete system, for the snapshots collection, with the integration in the reduced system. The paper discusses details of the transition between the two systems and issues related to the application of essential and natural boundary conditions (BCs). Results show that, for one-dimensional (1D) cases, just few modes are capable of excellent approximation of the solution, even in the case of stress–strain softening behavior, allowing to conveniently increase the critical time-step of the simulation without significant loss in accuracy. For more general three-dimensional (3D) situations, the paper discusses the application of the developed algorithm to a discrete model called lattice discrete particle model (LDPM) formulated to simulate quasi-brittle materials characterized by a softening response. Efficiency and accuracy of the reduced order LDPM response are discussed with reference to both tensile and compressive loading conditions.

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“…The Gappy POD method is a deformable usage of the Snapshot POD method proposed by Sirvorch and Kirby [3], which addresses some defects in the original POD method, such as improving the efficiency and stability of eigenvalue solution and having better applicability in data prediction. Therefore, it has been widely employed in the optimization design of airfoil and turbomachinery [4][5][6][7], flow field efficiency and stability of eigenvalue solution and having better applicability in data prediction. Therefore, it has been widely employed in the optimization design of airfoil and turbomachinery [4][5][6][7], flow field analysis [8][9][10][11], and data mining [12].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, it has been widely employed in the optimization design of airfoil and turbomachinery [4][5][6][7], flow field efficiency and stability of eigenvalue solution and having better applicability in data prediction. Therefore, it has been widely employed in the optimization design of airfoil and turbomachinery [4][5][6][7], flow field analysis [8][9][10][11], and data mining [12]. The third author [13][14][15] of this paper applied the POD method to the inverse problem of a centrifugal pump impeller, with a modal analysis of the flow field and a reconstruction of the gas-liquid two-phase flow field of a liquid ring pump, which extends the ideas and methods of flow characteristic analysis and optimization design of a centrifugal pump.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction and Prediction of Flow Field Fluctuation Intensity and Flow-Induced Noise in Impeller Domain of Jet Centrifugal Pump Using Gappy POD Method

Ren

Zhang

2018

Energies

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To analyze the interrelations among impeller blade geometry, flow field fluctuation intensity and impeller-induced hydrodynamic noise of jet centrifugal pump (JCP), a Gappy proper orthogonal decomposition (POD) method combined with computational fluid dynamics/computational fluid acoustics (CFD/CFA) technique was proposed to reconstruct and predict the unsteady flow field fluctuation intensity and flow-induced noise in impeller region. The snapshot sets were composed of blade profile parameters, flow field fluctuation intensity data and the data of sound pressure level of hydrodynamic noise in the frequency domain. Similar mesh reconstruction and flow field interpolation were carried out to have the same number of flow field data. The snapshot sets were decomposed into a linear combination of orthogonal bases using the singular value decomposition (SVD) method. The orthogonal basis coefficients corresponding to the objective variables were fitted by the least square method. The results show that the proposed method has a good accuracy in predicting the flow field fluctuation intensity and flow-induced noise of the JCP impeller domain. The relative error of pressure fluctuation intensity field is less than 4.0%, relative velocity fluctuation intensity field is less than 3.0%, turbulent kinetic energy fluctuation intensity field is less than 4.5%, and impeller-induced hydrodynamic noise is less than 10%. Taking the method as a surrogate model to predict the flow field fluctuation intensity and the radiation level of hydrodynamic noise in the optimization process of centrifugal pump impeller, it could not only reduce the calculation amount and time significantly and improve optimization speed and efficiency greatly but could also provide a reference for vibration characteristics of the models.

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Proper orthogonal decomposition with high number of linear constraints for aerodynamical shape optimization

Cited by 11 publications

References 20 publications

Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods

Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods

Proper Orthogonal Decomposition Framework for the Explicit Solution of Discrete Systems With Softening Response

Reconstruction and Prediction of Flow Field Fluctuation Intensity and Flow-Induced Noise in Impeller Domain of Jet Centrifugal Pump Using Gappy POD Method

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