In this paper, dedicated polar angle quadrature sets for the method of characteristics (MOC) are developed, based on the equivalence between MOC and the collision probability method. The discretization error of polar angle in MOC can be considered as an approximation error of the Bickley function used in the collision probability method; the Bickley function is numerically integrated in MOC using a quadrature set for polar direction (i.e., a set of polar angles and weights). Therefore, by choosing an appropriate quadrature set, the approximation error of the Bickley function which appears in MOC can be reduced, thus the calculation accuracy of MOC increases. Quadrature sets from one to three polar angle divisions are derived by minimizing the maximum approximation error of the Bickley function. The newly derived polar angle quadrature set (Tabuchi-Yamamoto or the TY quadrature set) is tested in the C5G7 and 4-loop PWR whole core problems and its accuracy is compared with other quadrature sets, e.g., Gauss-Legendre. The calculation results indicate that the TY quadrature set that is newly developed in the present paper provides better accuracy than the other methods. Since the number of polar angle divisions is proportional to computation time of MOC, utilization of the TY quadrature set will be computationally efficient.

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When the transport correction is applied to the total cross-section, the self-scattering cross-section could have a negative value in order to preserve the balance of partial cross-sections. The negative self-scattering cross-section may lead to a negative impact on the convergence behavior for the method of characteristics (MOC), especially in a problem with large moderator regions containing hydrogen. In order to address this issue, the spectral radius of the inner iteration of MOC is theoretically estimated for various self-scattering cross-sections. It is found that the spectral radius of the inner iteration of MOC could exceed unity for a large negative self-scattering cross-section, which results in numerical divergence. A countermeasure for the divergence using the successive over relaxation method is also discussed in this paper.

In this paper, dedicated polar angle quadrature sets for the method of characteristics (MOC) are developed, based on the equivalence between MOC and the collision probability method. The discretization error of polar angle in MOC can be considered as an approximation error of the Bickley function used in the collision probability method; the Bickley function is numerically integrated in MOC using a quadrature set for polar direction (i.e., a set of polar angles and weights). Therefore, by choosing an appropriate quadrature set, the approximation error of the Bickley function which appears in MOC can be reduced, thus the calculation accuracy of MOC increases. Quadrature sets from one to three polar angle divisions are derived by minimizing the maximum approximation error of the Bickley function. The newly derived polar angle quadrature set (Tabuchi-Yamamoto or the TY quadrature set) is tested in the C5G7 and 4-loop PWR whole core problems and its accuracy is compared with other quadrature sets, e.g., Gauss-Legendre. The calculation results indicate that the TY quadrature set that is newly developed in the present paper provides better accuracy than the other methods. Since the number of polar angle divisions is proportional to computation time of MOC, utilization of the TY quadrature set will be computationally efficient.