节块SP_3方法求解中子输运方程

Nodal SP_3 Method for Solving Neutron Transport Equation

采用3阶简化球谐函数(SP3)方法将中子输运方程转化为2个耦合的、数学形式与扩散方程相同的方程,建立一种扩散节块方法求解SP3方程组。该节块方法,通过将节块内的精细中子通量密度分布展开成指数函数和的形式获得节块响应关系,并用于求解边界分流,同时用中子平衡方程构造节块平均中子通量密度。数值结果表明:该方法适用于不同的空间几何网格形状,具有良好的并行特性;节块SP3程序NSPn的计算速度约为节块SN(N=4)程序DNTR的6倍。

This paper establishes a nodal method to solve the two coupled equations transformed from the transport equation by SP3 method.In the nodal method,diffusion equation is discretized into average fluxes in the nodes and partial currents on the nodal boundaries.Nodal response relationship is obtained by expanding the detailed nodal flux into a sum of exponential functions.Numerical results demonstrates that the nodal SP3 method can treat polygonal meshes in different shapes with good parallel property,and that it can provide a similar accuracy while runs about six times faster than the nodal-SN(N=4) method DNTR under the same mesh.