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

Mathematical Modelling of Natural Phenomena (2010)

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

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topEl 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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- 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.
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- 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
- R. Peyret. Introduction to spectral methods. Computational Fluid Dynamics, Lecture Series Von Karman, 1986-04.
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- 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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