Spherical harmonic solutions of the Boltzmann transport equation via discrete ordinates

Discrete ordinates algorithms for deterministically simulating neutron tran sport via the Boltzmann transport equation are discussed. One difficulty th ese methods often have is the problem of ray effects. These undesirable num erical phenomena typically arise in problems with small scattering ratios a nd localized sources. A competing method that does not exhibit ray effects is the spherical harmonic, or PN, method in which particle fluxes are smoot hly represented in a spherical harmonic basis. Although PN methods cannot h ave ray effects, the resulting system of equations is difficult to solve du e to a denser coupling of terms than in discrete ordinates methods. A proce dure, called harmonic projection, is presented that allows a PN solution to be obtained by solving only discrete ordinates equations. Thus, the qualit y of a PN solution can be obtained while exploiting the efficiency (and bet ter 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. (C) 2001 Published by Els evier Science Ltd.