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

Donatelli, Donatella

doi:10.1090/S0033-569X-2010-01163-6

Author: Donatella Donatelli
Journal: Quart. Appl. Math. 68 (2010), 469-485
MSC (2000): Primary 35Q30; Secondary 35B35, 35Q35, 76D03, 76D05
DOI: https://doi.org/10.1090/S0033-569X-2010-01163-6
Published electronically: May 21, 2010
MathSciNet review: 2676972
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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 $\mathbb {S}:\nabla u$ 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.

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