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Smith, Michael G. (1961) The approximate solution of the transport equation. Doctoral thesis, Sir John Cass College.
This thesis is concerned with finding approximate solutions to the transport equation for the scattering and absorption of radiation when the average particle size of the scattering medium is large enough compared to the wavelength to ignore quantum effects. In most of the cases treated the scattering is assumed to be isotropic, though this restriction is made for simplicity and is not a necessary part of the approximation.
In the first part the equation is expressed in general orthogonal coordinates, and approximate methods which have been used, which are applicable to such general coordinates, are briefly examined.
The second part is devoted to the equation when the system can be described by one Cartesian coordinate only, which is the form most frequently treated in the literature. Some general relations are deduced and the approximate solution of Chandrasekhar is examined, as well as the method used by the present author.
The main body of the thesis is contained in the third part where the latter method is developed and applied to two problems with spherical symmetry. The one problem where radiation uniform over the forward hemisphere is incident on the inside of a spherical shell of scattering material, and where there is no absorption, is considered numerically for a number of different boundary conditions.
It is shown in the last part that the same method can be extended to the problem with two Cartesian coordinates, though no numerical results are attempted.
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