El Mahdi El Guarmah ; Abdelkhalek Cheddadi ; Mejdi Azaier - Spectral Procedure with Diagonalization of Operators for 2D Navier-Stokes and Heat Equations in Cylindrical Geometry

arima:1860 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, August 7, 2006, Volume 5, Special Issue TAM TAM'05, november 2006 - https://doi.org/10.46298/arima.1860
Spectral Procedure with Diagonalization of Operators for 2D Navier-Stokes and Heat Equations in Cylindrical Geometry

Authors: El Mahdi El Guarmah ; Abdelkhalek Cheddadi ; Mejdi Azaier

We present in this paper a spectral method for solving a problem governed by Navier-Stokes and heat equations. The Fourier-Chebyshev technique in the azimuthal direction leads to a system of Helmholtz equations. The Collocation-Chebyshev method in the radial direction has been used for the simulation of these equations. The Crank-Nicholson scheme is employed to solve the Helmholtz systems obtained for wide ranges of parameters, and its efficiency is considerably improved by diagonalization of the obtained operators. The results are in a very good agreement with the experimental data available in the literature.


Volume: Volume 5, Special Issue TAM TAM'05, november 2006
Published on: August 7, 2006
Submitted on: February 1, 2006
Keywords: Heat equation, Chebyshev Gauss-Lobatto, Crank-Nicholson, Diagonalization, Spectral Space, Physical Space,Navier-Stokes,Heat equation,Chebyshev Gauss-Lobatto,Crank-Nicholson,Diagonalization,Spectral Space,Physical Space,[MATH] Mathematics [math],[INFO] Computer Science [cs]


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