The Multi-PN angular discretization method of the neutral-particle transport equation for radiation shielding calculations

Abstract

The well-known Discrete Ordinates (SN) approximation is little effective in multidimensional radiation shielding calculations. In the presence of geometrically large and low-scattering media, discrete-ordinates solutions are generally affected by the ray effect and an adequate refinement of the angular discretization is sometimes prohibitive in terms of calculation cost. The Multi-PN method (MPN) is an angular discretization technique leading to SN-like transport equations but less affected by ray effect. It relies on a solid angle expansion of the interface fluxes, allowing for a local coupling between different angular degrees of freedom within the same solid angle. This coupling enables to solve the equation by means of a standard sweeping algorithm. Furthermore, flux angular moments are directly integrated without any use of quadrature rules. The MPN measured error convergence rate with respect to the number of angular degrees of freedom is significantly larger than the one measured with SN.