Numerical benchmark solutions for time-dependent neutral particle transport in one-dimensional homogeneous media using integral transport

Abstract

The time-dependent, neutral particle, single-collision kernels have been used to produce benchmark type solutions in one-dimensional planar and spherical geometries. The solution procedure begins with the formulation of an inhomogeneous integral equation for time-dependent transport. This equation is evaluated using standard integral equation methods and numerical integration techniques. Excellent agreement with benchmark values in the available literature have been achieved for singular sources in planar and spherical infinite medium geometries. The solution technique has been further used to produce finite medium benchmark solutions in the same one-dimensional geometries. This work once again demonstrates, what past experience with steady-state problems has shown, that highly accurate solutions for neutral particle transport can be obtained using the integral equation formulation of the transport equation.