Proper general decomposition (PGD) for the resolution of Navier–Stokes equations

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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“…For more details about the different methods the reader may see [9,10,[25][26][27][28]. In this work the POD approach is used.…”

Section: Generation Of the Pod Spacesmentioning

confidence: 99%

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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“…We conclude this section by mentioning also some additional techniques quite close to POD for generating efficiently reduced spaces, the Centroidal Voronoi Tessellation (CVT) [25,26,46] and the Proper Generalized Decomposition (PGD) method [92], which has been recently applied to the solution of Navier-Stokes equations [47,117]. Recent contributions are also contained in MS&A Vol.…”

Section: Reduced Basis Construction By Greedy Algorithmsmentioning

confidence: 99%

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Lassila

Manzoni

Quarteroni

et al. 2014

Reduced Order Methods for Modeling and Computational Reduction

161

179

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This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities -which are mainly related either to nonlinear convection terms and/or some geometric variability -that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and -in the unsteady case -long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.

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“…Two additional techniques -indeed quite close to POD -for generating reduced spaces are the Centroidal Voronoi Tessellation [7][8][9] and the Proper Generalized Decomposition [10,11,16,36].…”

Section: Alternative Approachesmentioning

confidence: 99%

Computational Reduction for Parametrized PDEs: Strategies and Applications

2012

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Abstract. In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of the reduced basis method, focusing on greedy algorithms for the construction of the reduced spaces. An alternative family of reduction techniques based on surrogate response surface models is briefly recalled too. Then, a simple example dealing with inviscid flows is presented, showing the reliability of the reduced basis method and a comparison between this technique and some surrogate models.Mathematics Subject Classification (2010). Primary 78M34; Secondary 49J20, 65N30, 76D55.

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Proper general decomposition (PGD) for the resolution of Navier–Stokes equations

Cited by 110 publications

References 36 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

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Computational Reduction for Parametrized PDEs: Strategies and Applications

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