A Mesh-Free Method for Approximate Solution of Neutron Transport Equation

Abstract

This paper presents a new method for approximate solution of the multigroup neutron transport equation. The R-function theory is applied to describe the geometric shape of material regions analytically. Resulting formulae form a basis for a mesh-free approximation of the spatial neutron flux distribution. The method of moments is applied to transform the integral transport equation into a system of linear algebraic equations. Calculations of characteristic twodimensional CANDU lattice problems show that the method is capable of accurate modeling of the neutron transport with a significant reduction of the number of unknowns compared to standard mesh-based approximations.