Spectral discretization of the time-dependent Navier-Stokes problem coupled with the heat equation

29 pages avec calculsThe aim of this work is to present the unsteady Navier{Stokes equations coupled with the heat equation where the viscosity depends on the temperature. We propose a discretization of theses equations that combines Euler's implicit scheme in time and spectral methods in space. We prove optimal error estimates between the continuous and discrete solutions. Some numerical experiments con rm the interest of this approach