International audienceIn statistical methods of characterisation of porous media radiative properties, inter-facial extinction cumulative distribution functions, scattering or absorption cumulative probabilities and general phase functions are generally determined from shots issued from random volume points instead of random interfacial points. Indeed, the first method is numerically much simpler and accurate than the second one. The validity of this approach is discussed and its limitations enhanced for both Beerian and non Beerian homogenised phases, and in the case of a diffuse reflection law or a general one. The explanation of the identity or difference between the results of the two previous types of extinction cumulative distribution functions comes from the comparison between the spatial scale at which these functions are determined and the own scales of the divided medium. The conditions for which a medium follows the Beer's law are then defined in terms of spatial scales. Moreover, the modeling of interfacial emission for a non Beerian homogenised phase is in principle based on the reciprocity theorem and an integral formulation of the Generalised Radiative Transfer Equation. The validity of a simpler approach based on an effective absorption coefficient is also discussed, from the previous analysis. The validity of results of recent works published in IJHMT are finally discussed

No abstract

High temperature gases, for instance in hypersonic reentry flows, show complex phenomena like excitation of rotational and vibrational energy modes, and even chemical reactions. For flows in the continuous regime, simulation codes use analytic or tabulated constitutive laws for pressure and temperature. In this paper, we propose a BGK model which is consistent with any arbitrary constitutive laws, and which is designed to make high temperature gas flow simulations in the rarefied regime. A Chapman-Enskog analysis gives the corresponding transport coefficients. Our approach is illustrated by a numerical comparison with a compressible Navier-Stokes solver with rotational and vibrational non equilibrium. The BGK approach gives a deterministic solver with a computational cost which is close to that of a simple monoatomic gas.