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

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    Genre
    Journal Article
    Date
    2011-09-01
    Author
    Frank, M
    Seibold, B
    Subject
    Radiative transfer
    method of moments
    optimal prediction
    measure
    diffusion approximation
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/6028
    
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    DOI
    10.3934/krm.2011.4.717
    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 PN, 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. © American Institute of Mathematical Sciences.
    Citation to related work
    American Institute of Mathematical Sciences (AIMS)
    Has part
    Kinetic and Related Models
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/6010
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