Optimal prediction for radiative transfer: A new perspective on moment closure

Martin Frank; Benjamin Seibold

doi:10.3934/krm.2011.4.717

Article Contents

2011, Volume 4, Issue 3: 717-733. Doi: 10.3934/krm.2011.4.717

This issue Previous Article Fast diffusion equations: Matching large time asymptotics by relative entropy methods Next Article Non--local macroscopic models based on Gaussian closures for the Spizer-Härm regime

Optimal prediction for radiative transfer: A new perspective on moment closure

Martin Frank^1, and
Benjamin Seibold^2,

1.
RWTH Aachen University, Department of Mathematics, Schinkelstrasse 2 52062 Aachen
2.
Temple University, Department of Mathematics, 1805 North Broad Street Philadelphia, PA 19122

Received: May 31, 2011

Published: August 2011

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Abstract

Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of infinitely many moments. The truncation of this infinite system is the moment closure problem. Many types of closures have been presented in the literature. In this note, we demonstrate that optimal prediction, an approach originally developed to approximate the mean solution of systems of nonlinear ordinary differential equations, can be used to derive moment closures. To that end, the formalism is generalized to systems of partial differential equations. Using Gaussian measures, existing linear closures can be re-derived, such as $P_N$, diffusion, and diffusion correction closures. This provides a new perspective on several approximations done in the process and gives rise to ideas for modifications to existing closures.

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Mathematics Subject Classification: 85A25, 78M05, 82Cxx.

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