中子输运方程的三角形节块S_N方法研究

Nodal S_N Method for Neutron Transport Equation in Triangular Geometry

利用面积坐标思想，将任意三角形变换为正三角形，使用横向积分方法对正三角形节块进行处理。节块内横向积分通量、中子源的空间分布使用新的正交二次多项式近似；横向泄漏项的空间分布使用二阶多项式近似；中子通量和横向泄漏的角度通过离散纵坐标（SN）求积组离散。采用节块平衡有限差分方法建立稳定有效的迭代方案；编制了二维三角形节块SN输运计算程序（DNTR），对一系列基准题进行了验证。结果表明，本方法在同等计算精度下比细网差分程序（DOT4．2）快5～7倍，在同等计算精度和相同节块尺寸下比矩形离散节块输运方法（DNTM）快1～3倍，但DNTR程序可应用于非结构几何区域问题，具有DNTM等其它结构化节块SN程序无可比拟的优势。

Using the theory of area coordinate, arbitrary triangles were transformed into regular triangles. The transverse integration was done on the regular triangle. The spatial distribution of intra-node flux and source were approximated by a new orthogonal quadratic polynomial expansion, and a second-order polynomial provided the spatial expansion of transverse-leakage. The neutron angular distribution of flux and transverse-leakage were represented by the SN quadrature set. Additionally, the nodal-equivalent finite difference algorithm was applied in order to establish a stable and efficient iterative scheme. A two-dimension triangular nodal SN transport calculation program （DNTR） was coded according to the model. A series of numerical results for the test problems demonstrate that this triangular nodal SN method is faster 5 to 7 times than the fine mesh difference code （DOT4.2） with the same precision and faster 1 to 3 times than the rectangular discrete nodal transport method （DNTM） with the same precision and equal mesh width. However, this method can be applied to solve the unstructured neutron transport problems, and has an unexampled advantage of the nodal SN methods used on the structured meshes, such as DNTM.