Natural convection flow in a tall enclosure using a multigrid method

Nader Ben Cheikh; Brahim Ben Beya; Taieb Lili

doi:10.1016/j.crme.2007.01.004

Natural convection flow in a tall enclosure using a multigrid method
[Écoulement de convection naturelle dans une longue cavité à l'aide d'une méthode multigrille]

Présenté par : Sébastien Candel

Nader Ben Cheikh ¹ ; Brahim Ben Beya ¹ ; Taieb Lili ¹

¹ Faculté des Sciences de Tunis, Département de Physique, Campus Universitaire 2092 El-Manar II, Tunisia

Comptes Rendus. Mécanique, Volume 335 (2007) no. 2, pp. 113-118.

Résumé
Abstract

Nous présentons dans ce papier une étude numérique de convection naturelle bidimensionnelle dans une cavité de rapport de forme $A = 9$ , remplie d'air. La méthode numérique est basée sur un schéma de type volumes finis du second ordre et une méthode de projection. Une approche multigrille est utilisée pour accélérer la convergence de l'équation de Poisson. La méthode est brièvement décrite et le nombre de Rayleigh critique au-delà duquel l'écoulement devient instationnaire est déterminé.

A two-dimensional numerical study of natural convection flow in an air filled enclosure of aspect ratio $A = 9$ is investigated in this Note. The numerical method is based on a second order finite volume scheme and a projection method. A full multigrid technique is used to accelerate the convergence of the Poisson pressure equation. The multigrid procedure is briefly described and the critical Rayleigh number above which the flow becomes unsteady is determined.

Reçu le : 2006-04-30
Accepté le : 2007-01-23
Publié le : 2007-02-01

DOI : 10.1016/j.crme.2007.01.004

Keywords: Computational fluid mechanics, Natural convection flow, Multigrid technique
Mots-clés : Mécanique des fluides numérique, Écoulement de convection naturelle, Approche multigrille

Affiliations des auteurs :

Nader Ben Cheikh ¹ ; Brahim Ben Beya ¹ ; Taieb Lili ¹

¹ Faculté des Sciences de Tunis, Département de Physique, Campus Universitaire 2092 El-Manar II, Tunisia

@article{CRMECA_2007__335_2_113_0,
     author = {Nader Ben Cheikh and Brahim Ben Beya and Taieb Lili},
     title = {Natural convection flow in a tall enclosure using a multigrid method},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {113--118},
     publisher = {Elsevier},
     volume = {335},
     number = {2},
     year = {2007},
     doi = {10.1016/j.crme.2007.01.004},
     language = {en},
}

TY  - JOUR
AU  - Nader Ben Cheikh
AU  - Brahim Ben Beya
AU  - Taieb Lili
TI  - Natural convection flow in a tall enclosure using a multigrid method
JO  - Comptes Rendus. Mécanique
PY  - 2007
SP  - 113
EP  - 118
VL  - 335
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crme.2007.01.004
LA  - en
ID  - CRMECA_2007__335_2_113_0
ER  -

%0 Journal Article
%A Nader Ben Cheikh
%A Brahim Ben Beya
%A Taieb Lili
%T Natural convection flow in a tall enclosure using a multigrid method
%J Comptes Rendus. Mécanique
%D 2007
%P 113-118
%V 335
%N 2
%I Elsevier
%R 10.1016/j.crme.2007.01.004
%G en
%F CRMECA_2007__335_2_113_0

Nader Ben Cheikh; Brahim Ben Beya; Taieb Lili. Natural convection flow in a tall enclosure using a multigrid method. Comptes Rendus. Mécanique, Volume 335 (2007) no. 2, pp. 113-118. doi : 10.1016/j.crme.2007.01.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.01.004/

Bibliographie
Cité par

[1] W. Hackbusch Multigrid Methods and Applications, Springer-Verlag, Berlin/New York, 1985

[2] M. Hortmann; M. Peric; G. Scheuerer Finite volume multigrid prediction of laminar natural convection: bench-mark solutions, Int. J. Numer. Methods Fluids, Volume 11 (1990), pp. 189-207

[3] E. Nobile Simulation of time-dependent flow in cavities with the additive-correction multigrid method, Part I: Mathematical formulation, Numer. Heat Transfer B, Volume 30 (1996), pp. 341-350

[4] A. Brandt Multi-level adaptive solutions to boundary-value problems, Math. Comput., Volume 31 (1977), pp. 333-390

[5] R. Barrett et al. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, 1994

[6] D. Braess Towards algebraic multigrid for elliptic problems of second order, Computing, Volume 55 (1995), pp. 379-393

[7] M.A. Christon; P.M. Gresho; S.B. Sutton Computational predictability of time-dependent natural convection flows in enclosures (including a benchmark solution), Int. J. Numer. Methods Fluids, Volume 40 (2002), pp. 953-980

[8] S. Xin; P. Le Quéré An extended Chebyshev pseudo-spectral benchmark for the 8:1 differentially heated cavity, Int. J. Numer. Methods Fluids, Volume 40 (2002), pp. 981-998

[9] R. Peyret; T.D. Taylor Methods for Fluid Flow, Springer-Verlag, Berlin/New York, 1983

[10] Y. Achdou; J.L. Guermond Convergence analysis of a finite element projection/Lagrange–Galerkin method for the incompressible Navier–Stokes equations, SIAM J. Numer. Anal., Volume 37 (2000), pp. 799-826

[11] S.V. Patankar Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980

[12] H. Wang; S. Xin; P. Le Quéré Étude numérique du couplage de la convection naturelle avec le rayonnement de surfaces en cavité carrée remplie d'air, C. R. Mécanique, Volume 334 (2006), pp. 48-57

Salwa Fezai; Nader Ben-Cheikh; Brahim Ben-Beya; Taieb Lili Numerical study of obstacle geometry effect on the vortex shedding suppression and aerodynamic characteristics, International Journal of Numerical Methods for Heat Fluid Flow, Volume 30 (2020) no. 2, p. 469 | DOI:10.1108/hff-01-2016-0019
Basma Souayeh; Huda Alfannakh; Manal Al Mutairi Natural Convection in a Square Enclosure with a Conducting Rectangular Shape Positioned at Different Horizontal Locations, High Temperature, Volume 57 (2019) no. 4, p. 539 | DOI:10.1134/s0018151x19040205
U Prasopchingchana Numerical study of natural convection in a rectangular cavity with variation of cavity aspect ratios and cavity inclination angles, IOP Conference Series: Materials Science and Engineering, Volume 576 (2019) no. 1, p. 012044 | DOI:10.1088/1757-899x/576/1/012044
Hossein Kaydani; Ali Mohebbi; Amir Ahmad Forghani Lattice Boltzmann Simulation of Natural Convection in a Fractured Petroleum Reservoir Domain: Single-Phase and Multi-Phases Investigations, The Open Petroleum Engineering Journal, Volume 11 (2018) no. 1, p. 48 | DOI:10.2174/1874834101811010048
Salwa Fezai; Nader Ben-Cheikh; Brahim Ben-Beya; Taieb Lili Numerical study of vortex shedding suppression and aerodynamic characteristics of three obstacle configurations having two shapes, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Volume 39 (2017) no. 7, p. 2519 | DOI:10.1007/s40430-017-0725-9
B. Souayeh; N. Ben-Cheikh; B. Ben-Beya Effect of thermal conductivity ratio on flow features and convective heat transfer, Particulate Science and Technology, Volume 35 (2017) no. 5, p. 565 | DOI:10.1080/02726351.2016.1180337
M. Y. Abdollahzadeh Jamalabadi; M. Ghassemi; M. H. Hamedi Numerical investigation of thermal radiation effects on open cavity with discrete heat sources, International Journal of Numerical Methods for Heat Fluid Flow, Volume 23 (2013) no. 4, pp. 649-661 | DOI:10.1108/09615531311323791 | Zbl:1356.80014
M Y A Jamalabadi; M Ghassemi; M H Hamedi Two-dimensional simulation of thermal loading with horizontal heat sources, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Volume 226 (2012) no. 5, p. 1302 | DOI:10.1177/0954406211419613
Patrick Oosthuizen; Jane Paul, 10th AIAA/ASME Joint Thermophysics and Heat Transfer Conference (2010) | DOI:10.2514/6.2010-5066
Nasreddine Ouertatani; Nader Ben Cheikh; Brahim Ben Beya; Taieb Lili; Antonio Campo Mixed convection in a double lid-driven cubic cavity, International Journal of Thermal Sciences, Volume 48 (2009) no. 7, p. 1265 | DOI:10.1016/j.ijthermalsci.2008.11.020
Jimmy C. K. Tong; Ephraim M. Sparrow; John P. Abraham Unified Treatment of Natural Convection in Tall Narrow and Flat Wide Rectangular Enclosures, Numerical Heat Transfer, Part A: Applications, Volume 54 (2008) no. 8, p. 763 | DOI:10.1080/10407780802424296

Cité par 11 documents. Sources : Crossref, zbMATH

Commentaires - Politique