TITLE

Optimal prediction for moment models: crescendo diffusion and reordered equations

AUTHOR(S)
Seibold, Benjamin; Frank, Martin
PUB. DATE
December 2009
SOURCE
Continuum Mechanics & Thermodynamics;Dec2009, Vol. 21 Issue 6, p511
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We want to generally study the moment closure within the framework of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. We apply this strategy to radiative transfer and show that several closures can be re-derived within this framework, such as P N, diffusion, and diffusion correction closures. In addition, 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 simple and with no extra cost, this newly derived crescendo diffusion yields better approximations in numerical tests.
ACCESSION #
47129196

 

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