相空间有限元方法在解二维中子输运方程中的应用

Finite Element Method Applied to the Two-Dimensional Neutron Transport Equation

本文采用相空间有限元方法求解了柱形临界多群中子输运问题。其中对于方程中的坐标变量用分片连续线性多项式作为试探函数，对于方程中的角度变量用分片连续双线性多项式作为试探函数。整个求解空间区域和角度区域分别采用三角形和矩形单元划分，然后利用迦辽金方法得到一个以网格点处角通量为未知数的线性联立代数方程组，方程组中的系数矩阵的存储采用了压缩存储技术。最后用高斯消元法解此有限元方程组，表明相空间有限元方法计算收敛性较好、计算精度高。

The phase-space finite element method is applied to the multigroup neutron transport equation in cylindrical critical systems. The continuous piecewise polynomial trial functions are trilinear in the space variables and bilinear in the angle variables. Elements are triangular in the spatial domain and rectangular in the angle domain- Galerkin method is used to derive a set of simultaneous algebraic equations. The coefficient matrices of the algebraic equations are compressed and stored. The resulting finite element equations are solved by gaussion elimination method. Numerical results are compared to those obtained by SN calculations. FEM was observed to yield a higher order of convergence and accuracy.