On the artificial compressibility method for the Navier-Stokes-Fourier system

Abstract

This paper deals with the artificial compressibility approximation method adapted to the incompressible Navier Stokes Fourier system. Two different types of approximations will be analyzed: one for the full Navier Stokes Fourier system (or the so-called Rayleigh-Benard equations) where viscous heating effects are considered and the other for when the dissipative function S : ∇ u \mathbb {S}:abla u is omitted. The convergence of the approximating sequences is achieved by exploiting the dispersive properties of the wave equation structure of the pressure of the approximating system.