University of Arizona
A New Solution for the 1D Radiative Transfer Equation
A new solution to the angularly discretized radiative transfer equation in a 1D slab medium with anisotropic scattering has been proposed. While similar to other solutions involving linear algebra, the proposed solution avoids instability caused by stiffness by expressing the complimentary part in terms of the hyperbolic sinh rather than simple exponentials. The effectiveness of this solution to produce extreme benchmark quality reflectances and transmittances with Wynn-epsilon convergence acceleration is demonstrated.
The Fourier Transform Solution for the Green’s Function of Monoenergetic Neutron Transport Theory
Nearly 65 years ago, Ken Case published his seminal paper on the singular eigenfunction solution for the Green’s function of the monoenergetic neutron transport equation with isotropic scattering. Previously, the solution had been obtained by Fourier transform. While it is apparent the two had to be equivalent, a convincing equivalence proof for general anisotropic scattering remained a challenge until now.