The absence of ray-effects in the discrete ordinate solution to the transport equation in spherical coordinates in multi-dimensions

The streaming operator of the transport equation is derived for spherical coordinates by starting from Newton’s second law for a free particle expressed in spherical coordinates. We shall show that the partial derivatives with respect to the velocity variables of the particle, which are absent in the Cartesian coordinate formulation of the transport equation, arise in the spherical coordinate formulation of the transport equation in response to the centrifugal force which prevents a free particle from ‘falling into the origin’ of the coordinate system.. Authors: Becker, Linda [Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)]; Chang, Britton [Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)]. DOE Contract: AC52-07NA27344. Subjects: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; characteristics; classical mechanics; differential geometry; multi-dimensions; ray-effects; spherical coordinates; transport equation