Spectral Numerical Study of a Problem Governed by Navier-Stokes Equations, Influence of Rayleigh and Prandtl Numbers

E. El Guarmah; A. Cheddadi

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 23-28
  • ISSN: 0973-5348

Abstract

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We present in this work a numerical study of a problem governed by Navier-Stokes equations and heat equation. The mathematical problem under consideration is obtained by modelling the natural convection of an incompressible fluid, in laminar flow between two horizontal concentric coaxial cylinders, the temperature of the inner cylinder is supposed to be greater than the outer one. The numerical simulation of the flow is carried out by collocation-Legendre method. The influence of Prandtl and Rayleigh numbers is investigated

How to cite

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El Guarmah, E., and Cheddadi, A.. Taik, A., ed. "Spectral Numerical Study of a Problem Governed by Navier-Stokes Equations, Influence of Rayleigh and Prandtl Numbers." Mathematical Modelling of Natural Phenomena 5.7 (2010): 23-28. <http://eudml.org/doc/197648>.

@article{ElGuarmah2010,
abstract = {We present in this work a numerical study of a problem governed by Navier-Stokes equations and heat equation. The mathematical problem under consideration is obtained by modelling the natural convection of an incompressible fluid, in laminar flow between two horizontal concentric coaxial cylinders, the temperature of the inner cylinder is supposed to be greater than the outer one. The numerical simulation of the flow is carried out by collocation-Legendre method. The influence of Prandtl and Rayleigh numbers is investigated},
author = {El Guarmah, E., Cheddadi, A.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {Navier-Stokes equations; heat equation; collocation-Legendre method; Crank-Nicholson method},
language = {eng},
month = {8},
number = {7},
pages = {23-28},
publisher = {EDP Sciences},
title = {Spectral Numerical Study of a Problem Governed by Navier-Stokes Equations, Influence of Rayleigh and Prandtl Numbers},
url = {http://eudml.org/doc/197648},
volume = {5},
year = {2010},
}

TY - JOUR
AU - El Guarmah, E.
AU - Cheddadi, A.
AU - Taik, A.
TI - Spectral Numerical Study of a Problem Governed by Navier-Stokes Equations, Influence of Rayleigh and Prandtl Numbers
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 23
EP - 28
AB - We present in this work a numerical study of a problem governed by Navier-Stokes equations and heat equation. The mathematical problem under consideration is obtained by modelling the natural convection of an incompressible fluid, in laminar flow between two horizontal concentric coaxial cylinders, the temperature of the inner cylinder is supposed to be greater than the outer one. The numerical simulation of the flow is carried out by collocation-Legendre method. The influence of Prandtl and Rayleigh numbers is investigated
LA - eng
KW - Navier-Stokes equations; heat equation; collocation-Legendre method; Crank-Nicholson method
UR - http://eudml.org/doc/197648
ER -

References

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  1. C. Bernardi, Y. Maday. Approximations spectrales de problèmes aux limites elliptiques. Springer-Verlag France, Paris, 1992.  
  2. C. Canuto, M. Y. Hussaini, A. Quarteroni, T. Zang. Spectral methods in fluid dynamics. Springer, New York, 1988.  Zbl0658.76001
  3. A. Cheddadi, E. El Guarmah. Discrétisation spectrale d’un écoulement fluide à Prandtl infini dans une géométrie annulaire cylindrique. PCN Journal, Physical and Chemical News, 30 (2006), 42–48. 
  4. A. Cheddadi, E. El Guarmah. Influence of the collocation grid on a collocation-Chebyshev procedure for the numerical simulation of Navier-Stokes equations. AMSE Journal, Modelling and Simulation, Best of Book (2005), 127–136.  
  5. A. Cheddadi, M. C. Charrier-Mojtabi, A. Mojtabi. Étude comparative de la convection naturelle dans des espaces annulaires cylindriques fluide et poreux: 1-écoulements bidimensionnels multicellulaires. 6ème Colloque Maghrébin sur les modèles numériques de l’ingénieur (C2MNI6), Tunis, 24-26 Novembre 1998.  
  6. L. Crawford, R. Lemlich. Natural convection in horizontal concentric cylindrical annuli. IEC Fundamentals, 1 (1962), 260–264. 
  7. B. Fornberg. A practical guide to pseudo spectral methods. Cambridge University Press, 1996.  Zbl0844.65084
  8. D. Gray, A. Giorgini. The Validity of the Boussinesq approximation for liquids and gases. Int. J. Heat Mass Transfer, 19 (1976), 545–551. Zbl0328.76066
  9. T. H. Kuehn, R. H. Goldstein. An experimental and theoretical study of natural convection in the annulus between horizonatl concentric cylinders. J. Fluid, 74 (1976), 695–719. Zbl0323.76071
  10. R. Peyret. Introduction to spectral methods. Computational Fluid Dynamics, Lecture Series Von Karman, 1986-04.  
  11. A. Quarteroni. Blending Fourier and Chebyshev interpolation. J. Approx. Theory, 51 (1987), 115–126. Zbl0645.41002
  12. M. Uhlmann. The need for de-aliasing in a Chebyshev pseudo-spectral method. Num. Meth. for Fluid Dynamics, (1986), 463–475.  

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