The analytical solution of neutron transport equation has fascinated mathematicians and physicists alike since the Milne half-space problem was introduce in 1921 . Numerous numerical solutions exist, but understandably, there are only a few analytical solutions, with the prominent one being the singular eigenfunction expansion (SEE) introduced by Case  in 1960. For the half-space, the method, though yielding, an elegant analytical form resulting from half-range completeness, requires numerical evaluation of complicated integrals. In addition, one finds closed form analytical expressions only for the infinite medium and half-space cases. One can find the flux in a slab only iteratively. That is to say, in general one must expend a considerable numerical effort to get highly precise benchmarks from SEE. As a result, investigators have devised alternative methods, such as the CN , FN  and Greens Function Method (GFM)  based on the SEE have been devised. These methods take the SEE at their core and construct a numerical method around the analytical form. The FN method in particular has been most successful in generating highly precise benchmarks. No method yielding a precise numerical solution has yet been based solely on a fundamental discretization until now. Here, we show for the albedo problem with a source on the vacuum boundary of a homogeneous medium, a precise numerical solution is possible via Lagrange interpolation over a discrete set of directions. Since this is an initial progress report of a new solution, we will consider only the simplest case in the half-space. In particular, the source will be isotropic and the medium isotropically scattering.
|Original language||English (US)|
|State||Published - Jul 5 2020|
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