非结构网格中子输运方程的离散纵标节块数值解法

Discrete Nodal Method for Neutron Transport Calculations Based on Unstructured-Meshes

基于离散节块方法(DNTM)的思想,研究了一种新的适用于二维三角形节块的离散坐标数值解法.使用坐标变换将任意三角形变换为正三角形,源项和通量的空间分布使用二次正交多项式展开,横向泄漏项的空间二次分布通过使用二元二次多项式近似正三角形节块的通量分布来获得.针对小尺寸易出现不收敛的情况,提出了一种改进的节块平衡有限差分方法.数值计算结果表明,该方法能满足非结构几何区域问题的求解需求,与细网SN方法相比,该方法在较粗的网格下具有高的精度,同时还适用于较细网格下的中子输运计算.

An efficient numerical solution of discrete nodal transport method in the triangular node was developed for two-dimensional transport equation based on the discrete nodal transport method, where arbitrary triangles were transformed into regular triangles via a coordinate transformation, and the spatial distributions of intra-node flux and source were approximated by an orthogonal quadratic polynomial. A second-order expansion of transverse-leakage was achieved when the spatial distribution of neutron flux was simulated by a binary quadratic polynomial in a regular triangle. An improved nodal-equivalent finite difference algorithm was adopted to eliminate the divergency due to the small mesh width. The numerical results demonstrate the higher efficiency and accuracy of this method for unstructured neutron transport problem.