Angular adaptive discrete ordinates method for transport equation

Accurate shielding calculation method is an important foundation of shielding design of nuclear system. Discrete ordinates method (S_N) is one of the main shielding calculation methods. An angular adaptive algorithm together with a goal oriented error estimate was proposed to eliminate the angular discretization errors. The importance of the objective function was obtained by solving the adjoint transport equation. Local angular discretization errors were weighted by the importance of a given angular region toward the computational goal, providing an appropriate goal oriented angular adaptivity. The mapping schemes were applied to the transition of angular flux solution between adjacent spatial regions with different quadrature sets during the source iteration process. The numerical results demonstrate that at the same accuracy, the number of angular discretization is reduced by 1-2 orders for shielding problems with straight or zigzag channels and the amount of computation is greatly reduced. The adaptive method generates the most effective discrete angle distribution and eliminates the influence of angular discretization errors on the shielding calculation. (authors)