Reformulation and evaluation of robust characteristic-based discretization for the discrete ordinates equation on structured hexahedron grids

Abstract

Strong flux attenuation and intense material heterogeneity are extremely challenging conundrums of discrete ordinates transport calculations for neutron or gamma deep-penetration shielding problems. The spatial discretization methods of high accuracy and strong robustness are indispensable for varying materials, including absorbers and cavities, and for meshes of large or small size. A family of the characteristic-based spatial schemes is chosen to construct a suit of the stable and efficient transport architecture for the nuclear installation shielding problems. The reformulations of a series of the characteristic-based schemes are presented based on Cartesian hexahedron grids. The related optimizations are proposed about parameter calculation, solving procedure and stability improvement for higher accuracy and efficiency. Numerical results and evaluations are given for several monoenergetic benchmarks and self-designed problems. The behaviors of the short characteristic and the zero-order finite difference schemes are compared for meshes of different optical thicknesses. The linear and exponential short characteristic schemes exhibit excellent accuracy advantages over the tested cell-average-based discretization methods. The slice-balance-approach-based DD-like scheme is more accurate and stable than the constant short characteristic method. Exponential short characteristic method possesses the best coarse mesh accuracy with RMS error norms slightly higher than 10% using 10-times-optical-thickness grids for the self-designed streaming-dominated deep-penetration problem.