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

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.

15 pages; version 4: sections removed, major reformulations

References in corpus (2)

• Optimal prediction for moment models: Crescendo diffusion and reordered equations
• Optimal prediction in molecular dynamics

Cited by in corpus (5)

• Implicit Asymptotic Preserving Method for Linear Transport Equations
• Asymptotic Derivation and Numerical Investigation of Time-Dependent Simplified Pn Equations
• Accurate front capturing asymptotic preserving scheme for nonlinear gray radiative transfer equation
• Diffusive Corrections to Pn Approximations
• Representation of Conditional Expectations in Gaussian Analysis on Sequence Spaces