三维非稳态Boltzmann输运方程的谱有限元分析

Coupling Method of Spectral and Finite Element Method for Neutron Transport Equation

系统分析了三维非稳态Ｂｏｌｔｚｍａｎｎ输运方程的谱有限元求解。根据球谐函数展开提出了关于处理方向变量的近似方法，导出了“扩散型”近似方程及其Ｇａｌｅｒｋｉｎ变分形式，证明了变分问题解的存在唯一性。研制了对二维、三维都适用的有限元程序，实现了对稳态与非稳态问题的处理。计算实例表明此方法是可行的。

Abstract In this paper, we study the three dimensional Boltzmann transport equation with scattering and absorption. Spherical functions expansion is used to reduce the direction variables of the equation. A finite element program is developed to solve the simplified equation numerically. The scheme is applied to the neutron well logging and its results are satified.