Numerical Methods in Multidimensional Radiative Transfer

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ISBN 10: 3540853685 / ISBN 13: 9783540853688

Published by Springer, 2008

About this Item

Zustand: Sehr gut | Seiten: 320 | Sprache: Englisch | Produktart: Bücher | Traditionally, radiative transfer has been the domain of astrophysicists and climatologists. In nuclear technology one has been dealing with the ana- gous equations of neutron transport. In recent years, applications of radiative transferincombustionmachinedesignandinmedicinebecamemoreandmore important. In all these disciplines one uses the radiative transfer equation to model the formation of the radiation ?eld and its propagation. For slabs and spheres e?ective algorithms for the solution of the transfer equation have been ava- able for quite some time. In addition, the analysis of the equation is quite well developed. Unfortunately, in many modern applications the approximation of a 1D geometry is no longer adequate and one has to consider the full 3D dependencies. This makes the modeling immensely more intricate. The main reasons for the di?culties result from the fact that not only the dimension of the geometric space has to be increased but one also has to employ two angle variables (instead of one) and very often one has to consider frequency coupling (due to motion or redistribution in spectral lines). In actual cal- lations this leads to extremely large matrices which, in addition, are usually badly conditioned and therefore require special care. Analytical solutions are not available except for very special cases. Although radiative transfer problems are interesting also from a ma- ematical point of view, mathematicians have largely neglected the transfer equation for a long time.

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Bibliographic Details

• Title: Numerical Methods in Multidimensional Radiative Transfer
• Publisher: Springer
• Publication Date: 2008
• Language: English
• ISBN 10: 3540853685
• ISBN 13: 9783540853688
• Binding: Soft cover
• Condition: Sehr gut
• Seller catalogs:
  • Bücher

About this title

Synopsis

Traditionally, radiative transfer has been the domain of astrophysicists and climatologists. In nuclear technology one has been dealing with the ana- gous equations of neutron transport. In recent years, applications of radiative transferincombustionmachinedesignandinmedicinebecamemoreandmore important. In all these disciplines one uses the radiative transfer equation to model the formation of the radiation ?eld and its propagation. For slabs and spheres e?ective algorithms for the solution of the transfer equation have been ava- able for quite some time. In addition, the analysis of the equation is quite well developed. Unfortunately, in many modern applications the approximation of a 1D geometry is no longer adequate and one has to consider the full 3D dependencies. This makes the modeling immensely more intricate. The main reasons for the di?culties result from the fact that not only the dimension of the geometric space has to be increased but one also has to employ two angle variables (instead of one) and very often one has to consider frequency coupling (due to motion or redistribution in spectral lines). In actual cal- lations this leads to extremely large matrices which, in addition, are usually badly conditioned and therefore require special care. Analytical solutions are not available except for very special cases. Although radiative transfer problems are interesting also from a ma- ematical point of view, mathematicians have largely neglected the transfer equation for a long time.

From the Back Cover

The book provides an overview of the numerical modelling of radiation fields in multidimensional geometries. It covers advances and problems in the mathematical treatment of the radiative transfer equation, a partial integro-differential equation of high dimension that describes the propagation of the radiation in various fields. Highly accurate and fast methods with sound analytical foundations are particularly emphasized. The volume should not only serve as a basis for the selection of suitable methods for actual radiative transfer problems in disciplines from astronomy and climatology to radiological diagnostics but also be a starting point for additional mathematical investigations on many still unknown aspects of the transfer equation.