Research And Application On Difference Schemes In Discrete Ordinates Method

The discrete ordinates method is one of the most useful methods for nuclear devices' shielding design and analysis in nuclear engineering field.The spatial variable is an important part of solving particle transport equation in discrete ordinates method,and it is more sensitive to the shielding problem.It is so easy to produce negative flux for the traditional Diamond Difference scheme that many solutions use a zero negative fixup algorithm.Although the negative fixup algorithm eliminates the negative flux,meanwhile,the accuracy of Diamond Difference scheme is lost and it may cause the flux distortions in space.DONTRAN2D is developed based on the first-order form of the steady-state Boltzmann transport equation.The equation's energy dependence is modeled using multiple energy groups.The angular dependence is modeled using discrete ordinates method.The spatial variable is modeled using finite differencing scheme.The overall solution technique is source iteration.Meanwhile,several adaptive difference schemes are developed to solve the deep penetration problem.The non-negativity of the extrapolated flux can be assured in Weighted Diamond Difference scheme and Theta Weighted Diamond Difference scheme.The Directional Theta Weighted difference scheme mitigates the flux distortions in some way.Meanwhile,the Exponentional Directional Weighted scheme is more accurate than Directional Theta Weighted scheme.DONTRAN2D is capable of calculating k eigenvalue and fixed source problem with arbitrary order anisotropic scattering in two dimensional geometry.DONTRAN2D is verified through a large number of scientific benchmarks.The results show that DONTRAN2D is capable of calculating k eigenvalue and deep penetration problems in high precision.The result of NATELSON benchmark demonstrates that Directional Theta Weighted difference scheme mitigates the distortions to the greatest extent.The results of the spent fuel benchmark and reactor shielding benchmark demonstrate that Directional Theta Weighted difference scheme is more adaptable in the deep penetration problems.