Entropy Production-Based Closure of the Moment Equations for Radiative Transfer

Abstract

Heat radiation in gases or plasmas is usually out of local thermodynamic equilibrium (LTE) even if the underlying matter is in LTE. Radiative transfer can then be described with the radiative transfer equation (RTE) for the radiation intensity. A common approach to solve the RTE consists in a moment expansion of the radiation intensity, which leads to an infinite set of coupled hyperbolic partial differential equations for the moments. A truncation of the moment equations requires the definition of a closure. We recommend to use a closure based on a constrained minimum entropy production rate principle. It yields transport coefficients (e.g., effective mean absorption coefficients and Eddington factor) in accordance with the analytically known limit cases. In particular, it corrects errors and drawbacks from other closures often used, like the maximum entropy principle (e.g., the M1 approximation) and the isotropic diffusive P1 approximation. This chapter provides a theoretical overview on the entropy production closure, with results for an illustrative artificial example and for a realistic air plasma.