Hydrodynamic limits, Knudsen layers and numerical fluxes

Considering kinetic equations (Boltzmann, BGK, say...) in the small mean free path regime lead to conservation laws (the Euler system, typically) When the problem is set in a domain, boundary layers might occur due to the fact that incoming fluxes could be far from equilibrium states. We consider the problem from a numerical perspective and we propose a definition of numerical fluxes for the Euler system which is intended to account for the formation of these boundary layers.