Nodal collocation method for the multidimensional PL equations applied to neutron transport source problems

Abstract

A PL spherical harmonics-nodal collocation method is applied to the solution of the multidimensional neutron source transport equation. Vacuum boundary conditions are approximated by setting Marshak's conditions. The method is applied to several 1D, 2D and 3D problems with isotropic fixed source and with isotropic and anisotropic scattering. These problems are chosen to test this method in limit conditions, showing that in some cases a high order $P_L$ approximation is required to obtain accurate results and convergence. Results are also compared with the ones provided by several reference codes showing good agreement. It is also shown that Marshak's approximation to vacuum boundary conditions gives the same results that simulating vacuum with a purely absorbing medium and setting zero flux boundary conditions.