A numerical investigation of velocity–pressure reduced order models for incompressible flows

Caiazzo, Alfonso; Iliescu, Traian; John, Volker; Schyschlowa, Swetlana

doi:10.1016/j.jcp.2013.12.004

Cited by 123 publications

(131 citation statements)

References 42 publications

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“…Such approach, that is proposed in literature by several authors [12,24] for FEM approximations, is here adapted to a FVM framework.…”

Section: The Reduced Order Modelmentioning

confidence: 99%

“…In the reduced framework, the continuity equation cannot be directly exploited because the velocity modes, which are generated with divergence free snapshots, are in turn divergence free up to numerical precision. The additional unknowns inside (20) are multiplied by the gradient of pressure that in many cases is neglected [24,35]; in fact, in many contributions available in literature no attempt to recover the pressure term is performed. The projection of the pressure gradient onto the POD spaces is in fact zero for the case of enclosed flows as presented in [11,36,37] or in the case of inletoutlet problems with outlet far from the obstacle [12].…”

Section: Rom For Pressure -Poisson Equation For Pressurementioning

confidence: 99%

“…According to [24] in literature one can find basically two different approaches for pressure ROMs depending if they use pressure POD modes or not. In methods using only a POD basis for velocity the momentum equation without the gradient of pressure term is solved.…”

Section: Rom For Pressure -Poisson Equation For Pressurementioning

confidence: 99%

“…Respect to what done in [12,24] as shown in equation 19, the gradient of pressure term is not neglected in the momentum equation and this gives rise to a coupled system also at reduced order level.…”

Section: Rom For Pressure -Poisson Equation For Pressurementioning

confidence: 99%

See 3 more Smart Citations

POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

Stabile

Hijazi

Mola

et al. 2017

Communications in Applied and Industrial Mathematics

142

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Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible flow around a circular cylinder is presented in this work. The ROM is built performing a Galerkin projection of the governing equations onto a lower dimensional space. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) the projection of the Governing equations (momentum equation and Poisson equation for pressure) performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework. The accuracy of the reduced order model is assessed against full order results.

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“…Such approach, that is proposed in literature by several authors [12,24] for FEM approximations, is here adapted to a FVM framework.…”

Section: The Reduced Order Modelmentioning

confidence: 99%

Section: Rom For Pressure -Poisson Equation For Pressurementioning

confidence: 99%

Section: Rom For Pressure -Poisson Equation For Pressurementioning

confidence: 99%

Section: Rom For Pressure -Poisson Equation For Pressurementioning

confidence: 99%

See 2 more Smart Citations

POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

Stabile

Hijazi

Mola

et al. 2017

Communications in Applied and Industrial Mathematics

142

View full text Add to dashboard Cite

show abstract

“…where ϕ j and λ j denote the vector of the FE coefficients of the POD basis functions and the POD eigenvalues, respectively, Y denotes the snapshot matrix, whose columns correspond to the FE coefficients of the snapshots, M h denotes the FE mass matrix, and N is the dimension of the FE space X h [41]. The eigenvalues are real and nonnegative, so they can be ordered as follows:…”

Section: Proper Orthogonal Decomposition (Pod)mentioning

confidence: 99%

Approximate deconvolution reduced order modeling

Xie

Wells

Wang

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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Highlights• A new large eddy simulation reduced order model (LES-ROM) framework.• A new approximate deconvolution ROM (AD-ROM) not of eddy viscosity type.• Successful application of AD-ROM to 3D flow past cylinder at Re = 1000. AbstractThis paper proposes a large eddy simulation reduced order model (LES-ROM) framework for the numerical simulation of convection-dominated flows. In this LES-ROM framework, the proper orthogonal decomposition (POD) is used to define the ROM basis and a ROM differential filter is used to define the large ROM structures. An approximate deconvolution (AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the three-dimensional flow past a circular cylinder at a Reynolds number Re = 1000.

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An evolve‐then‐filter regularized reduced order model for convection‐dominated flows

Wells

Wang

Xie

et al. 2017

Numerical Methods in Fluids

118

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Summary In this paper, we propose a new evolve‐then‐filter reduced order model (EF‐ROM). This is a regularized ROM (Reg‐ROM), which aims to add numerical stabilization to proper orthogonal decomposition (POD) ROMs for convection‐dominated flows. We also consider the Leray ROM (L‐ROM). These two Reg‐ROMs use explicit ROM spatial filtering to smooth (regularize) various terms in the ROMs. Two spatial filters are used: a POD projection onto a POD subspace (Proj) and a POD differential filter (DF). The four Reg‐ROM/filter combinations are tested in the numerical simulation of the three‐dimensional flow past a circular cylinder at a Reynolds number Re=1000. Overall, the most accurate Reg‐ROM/filter combination is EF‐ROM‐DF. Furthermore, the spatial filter has a higher impact on the Reg‐ROM than the regularization used. Indeed, the DF generally yields better results than Proj for both the EF‐ROM and L‐ROM. Finally, the CPU times of the four Reg‐ROM/filter combinations are orders of magnitude lower than the CPU time of the DNS. Copyright © 2017 John Wiley & Sons, Ltd.

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A numerical investigation of velocity–pressure reduced order models for incompressible flows

Cited by 123 publications

References 42 publications

POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

Approximate deconvolution reduced order modeling

An evolve‐then‐filter regularized reduced order model for convection‐dominated flows

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