Hydrodynamic fluctuations in a dilute gas subjected to a constant heat flux are studied by both a computer simulation and the Landau-Lifshitz formalism. The latter explicitly incorporates the boundary conditions of the finite system, thus permitting quantitative comparison with the former. Good agreement is demonstrated.
Alejandro Garcia, G. Lie, and E. Clementi. "Fluctuating Hydrodynamics in a Dilute Gas" Physical Review Letters (1987): 874-877. doi:http://dx.doi.org/10.1103/PhysRevLett.58.874