Non-incremental transient solution of the Rayleigh–Bénard convection model by using the PGD

Aghighi, Mohammad Saeid; Ammar, Amine; Métivier, Christel; Normandin, Magdeleine; Chinesta, Francisco

doi:10.1016/j.jnnfm.2012.11.007

Cited by 40 publications

(31 citation statements)

References 28 publications

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“…One of them concerns the so-called LBB condition that restricts the free choice of pressure and velocity approximations. As in Aghighi et al (2013) in what follows we consider a penalty formulation of the incompressibility constraint. Thus, the mass balance we are considering writes:…”

Section: Is Enforced At the Bottom Boundarymentioning

confidence: 99%

“…Functions X u i , X v i and X y i were calculated by solving a series of two-dimensional (2D) boundary value problems and functions Y u i , Y v i and Y y i by solving a series of initial value problems (see Aghighi et al, 2013, for additional details on the solution procedure). Separated representations are involved in the so-called proper generalized decomposition (PGD) methods.…”

Section: Introductionmentioning

confidence: 99%

“…The interested reader can refer to some recent reviews on these techniques (Chinesta et al 2010b(Chinesta et al , 2011a and the references therein. This non-incremental strategy allowed significant CPU time savings (Aghighi et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

“…In our former work (Aghighi et al, 2013) we computed a transient solution in a non-incremental manner without considering any parameter as extra-coordinate.…”

Section: Introductionmentioning

confidence: 99%

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Parametric solution of the Rayleigh-Benard convection model by using the PGD

Aghighi

Ammar

Metivier

et al. 2015

Int Jnl of Num Meth for HFF

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Purpose-The purpose of this paper is to focus on the advanced solution of the parametric non-linear model related to the Rayleigh-Benard laminar flow involved in the modeling of natural thermal convection. This flow is fully determined by the dimensionless Prandtl and Rayleigh numbers. Thus, if one could precompute (off-line) the model solution for any possible choice of these two parameters the analysis of many possible scenarios could be performed on-line and in real time. Design/methodology/approach-In this paper both parameters are introduced as model extracoordinates, and then the resulting multidimensional problem solved thanks to the space-parameters separated representation involved in the proper generalized decomposition (PGD) that allows circumventing the curse of dimensionality. Thus the parametric solution will be available fast and easily. Findings-Such parametric solution could be viewed as a sort of abacus, but despite its inherent interest such calculation is at present unaffordable for nowadays computing availabilities because one must solve too many problems and of course store all the solutions related to each choice of both parameters. Originality/value-Parametric solution of coupled models by using the PGD. Model reduction of complex coupled flow models. Analysis of Rayleigh-Bernard flows involving nanofluids.

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Section: Is Enforced At the Bottom Boundarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In our former work (Aghighi et al, 2013) we computed a transient solution in a non-incremental manner without considering any parameter as extra-coordinate.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parametric solution of the Rayleigh-Benard convection model by using the PGD

Aghighi

Ammar

Metivier

et al. 2015

Int Jnl of Num Meth for HFF

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“…NACA-4 example. Velocity (quiver fields) and pressure (color maps) solutions of the parametrized NACA-4 airfoils for four representative sets of parameter values{c,t,m,p}:[1]={0.53, 0.13, 0.10, 0.51};[2]={0.55, 0.17, 0.00, 0.50};[3]={0.71, 0.17, 0.07, 0.51};[4]={0.77, 0.23, 0.14, 0.38}.…”

mentioning

confidence: 99%

Generalized parametric solutions in Stokes flow

Dı́ez

Zlotnik

Huerta

2017

Computer Methods in Applied Mechanics and Engineering

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Design optimization and uncertainty quantification, among other applications of industrial interest, require fast or multiple queries of some parametric model. The Proper Generalized Decomposition (PGD) provides a separable solution, a computational vademecum explicitly dependent on the parameters, efficiently computed with a greedy algorithm combined with an alternated directions scheme and compactly stored. This strategy has been successfully employed in many problems in computational mechanics. The application to problems with saddle point structure raises some difficulties requiring further attention. This article proposes a PGD formulation of the Stokes problem. Various possibilities of the separated forms of the PGD solutions are discussed and analyzed, selecting the more viable option. The efficacy of the proposed methodology is demonstrated in numerical examples for both Stokes and Brinkman models.

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Model Reduction Methods

Chinesta

Huerta

Rozza

et al. 2017

Encyclopedia of Computational Mechanics Second Edition

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This chapter presents an overview of model order reduction – a new paradigm in the field of simulation‐based engineering sciences, and one that can tackle the challenges and leverage the opportunities of modern ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, a number of challenging problems remain intractable. These problems are of different nature, but are common to many branches of science and engineering. Among them are those related to high‐dimensional problems, problems involving very different time scales, models defined in degenerate domains with at least one of the characteristic dimensions much smaller than the others, model requiring real‐time simulation, and parametric models. All these problems represent a challenge for standard mesh‐based discretization techniques; yet the ability to solve these problems efficiently would open unexplored routes for real‐time simulation, inverse analysis, uncertainty quantification and propagation, real‐time optimization, and simulation‐based control – critical needs in many branches of science and engineering. Model order reduction offers new simulation alternatives by circumventing, or at least alleviating, otherwise intractable computational challenges. In the present chapter, we revisit three of these model reduction techniques: proper orthogonal decomposition, proper generalized decomposition, and reduced basis methodologies.

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Non-incremental transient solution of the Rayleigh–Bénard convection model by using the PGD

Cited by 40 publications

References 28 publications

Parametric solution of the Rayleigh-Benard convection model by using the PGD

Parametric solution of the Rayleigh-Benard convection model by using the PGD

Generalized parametric solutions in Stokes flow

Model Reduction Methods

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