非结构几何下二阶自共轭中子输运方程中的简化球谐函数方法研究

Simplified Spherical Harmonics Method for Self-Adjoint Angular Flux Transport Equation in Unstructured Geometry

针对球谐函数方法求解中子输运方程时计算量大的缺点,将简化球谐函数(SPN)方法用于离散二阶自共轭(SAAF)中子输运方程的角度变量,同时应用有限元方法在非结构几何下进行空间离散,研究了简化球谐函数方法在SAAF方程中的应用。数值计算结果表明,SPN方法在保证计算精度的条件下,具有比PN方法快的计算速度,而且对于维数越高、网格数越多、展开阶数越高的问题,节省时间的效果越好。

The simplified spherical harmonics （SPN） method is utilized to discrete the angular variables of Self-Adjoint Angular Flux （SAAF） neutron transport equation as spherical harmonics method has the disadvantage of large amount of calculation. To solve the unstructured geometry problem, the spatial variables of SAAF are discretized by using of finite element method. Numerical results of several test problems show that SPN method can obtain high accuracy with a significantly higher computational speed than spherical harmonics （PN） method, and can save more time when dealing with problems with higher dimension, larger amount of meshes, and larger expanding order N.