# Optimal prediction for moment models: Crescendo diffusion and reordered equations - Mathematical Physics

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Abstract: A direct numerical solution of the radiative transfer equation or any kineticequation is typically expensive, since the radiative intensity depends on time,space and direction. An expansion in the direction variables yields anequivalent system of infinitely many moments. A fundamental problem is how totruncate the system. Various closures have been presented in the literature. Wewant to study moment closure generally within the framework of optimalprediction, a strategy to approximate the mean solution of a large system by asmaller system, for radiation moment systems. We apply this strategy toradiative transfer and show that several closures can be re-derived within thisframework, e.g. $P N$, diffusion, and diffusion correction closures. Inaddition, the formalism gives rise to new parabolic systems, the reordered$P N$ equations, that are similar to the simplified $P N$ equations.Furthermore, we propose a modification to existing closures. Although simpleand with no extra cost, this newly derived crescendo diffusion yields betterapproximations in numerical tests.

Author: ** Benjamin Seibold, Martin Frank**

Source: https://arxiv.org/