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Discrétisation spectrale des équations de Navier-Stokes couplées avec l'équation de la chaleur

Abstract : In this thesis we consider the discretization by spectral method and the numerical simulation of a viscous incompressible fluid in the domain ?, the model being the Navier-Stokes equations. We have chosen to couple them with the heat equation where the viscosity of the fluid depends on the temperature, with boundary conditions which involve the velocity and the temperature. The method is proved to be optimal in the sense that the order of convergence is only limited by the regularity of the solution. The numerical analysis of the discrete problem is performed and numerical experiments are presented, they turn out to be in good coherence with the theoretical results. Finally, we consider the unsteady Navier-Stokes/heat equations which models the time-dependent flow. We propose a discretization of this problem that relies on a backward Euler's scheme in time and spectral methods in space and present some numerical experiments which confirm the interest of the discretization.
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Submitted on : Saturday, March 21, 2015 - 1:01:07 AM
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Rahma Agroum. Discrétisation spectrale des équations de Navier-Stokes couplées avec l'équation de la chaleur. Mathématiques générales [math.GM]. Université Pierre et Marie Curie - Paris VI, 2014. Français. ⟨NNT : 2014PA066195⟩. ⟨tel-01134007⟩



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