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Books > Computing & IT > Applications of computing > Artificial intelligence
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Numerical Methods in Multidimensional Radiative Transfer (Paperback, 2009 ed.)
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Numerical Methods in Multidimensional Radiative Transfer (Paperback, 2009 ed.)
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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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