Spherical harmonic solutions of the Boltzmann transport equation via discrete ordinates

Abstract

Discrete ordinates algorithms for deterministically simulating neutron transport via the Boltzmann transport equation are discussed. One difficulty these methods often have is the problem of ray effects. These undesirable numerical phenomena typically arise in problems with small scattering ratios and localized sources. A competing method that does not exhibit ray effects is the spherical harmonic, or P N , method in which particle fluxes are smoothly represented in a spherical harmonic basis. Although P N methods cannot have ray effects, the resulting system of equations in difficult to solve due to a denser coupling of terms than in discrete ordinates methods. A procedure, called harmonic projection, is presented that allows a P N solution to be obtained by solving only discrete ordinates equations. Thus, the quality of a P N solution can be obtained while exploiting the efficiency (and better parallelizability) of discrete ordinates methods. Numerical results on several benchmark problems are presented that demonstrate the effectiveness of the new algorithm in eliminating ray effects.