  We apply the method of penalization to the Dirichlet problem for the
Navier-Stokes-Fourier system governing the motion of a general viscous
compressible fluid confined to a bounded Lipschitz domain. The physical domain
is embedded into a large cube on which the periodic boundary conditions are
imposed. The original boundary conditions are enforced through a singular
friction term in the momentum equation and a heat source/sink term in the
internal energy balance. The solutions of the penalized problem are shown to
converge to the solution of the limit problem. Numerical experiments are
performed to illustrate the efficiency of the method.

Analysis of PDEs;Numerical Analysis;Numerical Analysis