Minimum entropy production closure of the photo-hydrodynamic equations for radiative heat transfer

In the framework of a two-moment photo-hydrodynamic modelling of radiation transport, we introduce a concept for the determination of effective radiation transport coefficients based on the minimization of the local entropy production rate of radiation and matter. The method provides the nonequilibrium photon distribution from which the effective absorption coefficients and the variable Eddington factor (VEF) can be calculated. The photon distribution depends on the frequency dependence of the absorption coefficient, in contrast to the distribution obtained by methods based on entropy maximization. The calculated mean absorption coefficients are not only correct in the limit of optically thick and thin media, but even provide a reasonable interpolation in the cross-over regime between these limits, notably without introducing any fit parameter. The method is illustrated and discussed for grey matter and for a simple example of non-grey matter with a two-band absorption spectrum. The method is also briefly compared with the maximum entropy concept.

💡 Research Summary

The paper addresses the longstanding closure problem in two‑moment photo‑hydrodynamic models of radiative heat transfer. In such models the first two angular moments of the radiation intensity—energy density (E) and flux (F)—are evolved, but a relation for the second‑order moment (the radiation pressure tensor P) is required to close the system. Traditional closures rely on the Maximum Entropy (MaxEnt) principle, which assumes that the nonequilibrium photon distribution maximizes the radiation entropy under the constraints of given E and F. While mathematically convenient, MaxEnt ignores the frequency dependence of the material absorption coefficient κν, leading to inaccurate predictions especially for non‑grey media and in the transition regime between optically thin and thick limits.

The authors propose a fundamentally different closure based on the minimum entropy production principle. They define the local entropy production rate σ(r,t) associated with absorption and emission processes:

σ = ∫ dν ∫ dΩ κν