Radiative transfer can be modeled by a kinetic equation that describes the evolution of the particle density function in a phase space of time, position, and the angle of flight (possibly more). While the direct simulation of this high dimensional mesoscopic equation is possible (albeit costly), in many applications it is desirable to have a description in terms of macroscopic equations. An expansion in the angular variable yields an equivalent system of infinitely many macroscopic moment equations. The fundamental question how to best truncate this system is the moment closure problem. Many types of closure strategies exist. These are typically based on an asymptotic arguments or assume higher moments be quasi-stationary. In this talk, we present a very different approach to derive moment closures, based on the Mori-Zwanzig formalism of irreversible statistical mechanics. Here, the influence of the truncated moments on the resolved moments is modeled by a memory term. Moment closures are then defined by a choice of a probability measure on the phase space and suitable approximations to the memory term. We demonstrate that existing closures, such as PN, SPN, and diffusion correction closures, can be re-derived with this formalism. In addition, new closures arise, such as the crescendo-diffusion closure.
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