Study on Direct Integration Method for Solving Neutron Transport Equation in Three-Dimensional Geometry

摘要

A numerical method is presented for calculating neutron transport problems in three-dimensional (x, y, z) geometry based on a method of direct integration of the transport equation. Several new techniques are introduced to the method to make it well adopted to practical neutron transport calculations in three-dimensional geometry. Use of a functional approximation for spatial distribution of source term with a combination of linear and exponential functions enables one to perform calculations with coarse spatial mesh intervals keeping the results accurate. An auxiliary code is made for accurate reaction rate calculation using third order natural spline function. Further, a multi-group neutron cross section library is generated for neutron transport codes based on a direct integration method, including nuclear data for 27 nuclides and 4 mixtures which are important in shielding calculations. In order to verify the validity of the present method, several PALLAS-XYZ calculations are presented and compared with shielding benchmark experiments, with Monte Carlo, and with two- and three-dimensional S sub(n) calculations. The PALLAS-XYZ calculation without any three-dimensional leakage correction agrees well (with a maximum error of 30%) with the PCA benchmark experiment. (Atomindex citation 14:797981)