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Erschienen in:
Introduction and Chronological Perspective Kapitel lesen Erstes Kapitel lesen

2013 | OriginalPaper | Buchkapitel

9. Elementary Solutions and Analytical Discrete-Ordinates for Radiative Transfer

verfasst von : Laurent Gosse

Erschienen in: Computing Qualitatively Correct Approximations of Balance Laws

Verlag: Springer Milan

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Abstract

This chapter is entirely devoted to the exposition of the method of elementary solutions, which has been introduced and developed during the 50’s–60’s mainly by Chandrasekhar, Case, Cercignani, Siewert and Zweifel. In particular, Chandrasekhar’s discrete ordinates approximation has been refined by Siewert and his collaborators into a so-called analytical discrete ordinates (ADO) method through a systematic use of elementary solutions. It appeared that it was exactly what is needed in order to set up a time-dependent well-balanced numerical scheme for linear kinetic equations by furnishing an explicit scattering matrix at each interface of the computational grid. The main goal is first to derive a WB scheme which solves the Cauchy problem for a simple model of “grey” radiative transfer:
$$ \begin{array}{cc} {\partial}_tf+v{\partial}_xf=\frac{c}{2}{\displaystyle {\int}_{-1}^1f\left(t,x,{v}^{\prime}\right)d{v}^{\prime }-f,} & v\in \left[-1,1\right],x\in \mathbb{R},t>0. \end{array} $$

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Vorheriges Kapitel The Special Case of 2-Velocity Kinetic Models
Nächstes Kapitel Aggregation Phenomena with Kinetic Models of Chemotaxis Dynamics
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Metadaten
Titel
Elementary Solutions and Analytical Discrete-Ordinates for Radiative Transfer
verfasst von
Laurent Gosse
Copyright-Jahr
2013
Verlag
Springer Milan
Buch
Computing Qualitatively Correct Approximations of Balance Laws

Print ISBN: 978-88-470-2891-3

Electronic ISBN: 978-88-470-2892-0

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-88-470-2892-0_9