屏蔽计算中空间差分格式适应性研究

Research on Adaptation of Spatial Difference Scheme in Shielding Calculation Problem

在离散纵标方法中,空间变量的处理是求解输运方程的重要部分,对于屏蔽计算问题更加敏感。传统的菱形差分格式易产生非物理解——负通量,大多数理论采用置零修正方法解决,该方法虽能消除负通量,但会降低菱形差分的计算精度,并引发通量密度的空间震荡。本文通过研究带权重差分格式和θ权重差分格式,引入权重系数以保证外推通量密度的非负性。在θ权重差分格式基础上,研究定向θ权重差分格式,通过引入方向权重因子,使得在外推通量非负的前提下,最大程度减缓通量密度的非物理震荡。在NATELSON基准题中,与DORT计算结果对比,通量密度最大相对偏差为2.7%。通过在不同屏蔽计算问题上的应用与分析,结果表明,定向θ权重差分格式更适于屏蔽计算问题(深穿透问题)。

The processing of spatial variable is an important part of solving particle transport equation in discrete ordinates method,and it is more sensitive to the shielding calculation.It is so easy to bring negative flux for the traditional diamond difference scheme that many codes use a zero negative fixup algorithm.Although the algorithm eliminates the negative flux,however,the accuracy of diamond difference scheme is lost.Meanwhile,it causes flux distortions in space.The non-negativity of the extrapolated flux can be assured in weighted diamond difference scheme and theta weighted difference scheme.Based on the theta weighted difference scheme,the directional theta weighted difference scheme adopted directional theta weight to mitigate the distortions in some way.In the NATELSON benchmark,compared with DORT the maximum relative deviation of flux is 2.7%.The results of several shielding benchmarks demonstratethat the directional theta weighted difference scheme is more adaptable in the deep penetration problems.