Analytic solution of two-group static neutron diffusion equation using different transverse leakage approximations in 2D cartesian geometry

Hosseini, Mohammad; Khalafi, Hossein; Zangian, Mehdi

Analytic solution of two-group static neutron diffusion equation using different transverse leakage approximations in 2D cartesian geometry

Document Type : Research Paper

Authors

Mohammad Hosseini

Hossein Khalafi

Mehdi Zangian

Abstract

Nodal is a method for solving the neutron diffusion equation. It is categorized to analytic, semi-analytic and expansion nodal methods. In this research work, a software is developed in order to solve two group neutron diffusion equations in two dimensional Cartesian geometries. There are some approaches to the analytical solution of the neutron diffusion. An interesting approach, that is our recent concern, is the transverse leakage approximation. Based on this approximation, the two-dimensional diffusion equation is split into two one-dimensional equations and is solved analytically for each energy group. In this paper, we used flat and quadratic polynomials in order to approximate the transverse leakage terms. Finally, two reference problems are solved for verifying the proposed method. The results showed that the analytic nodal method with quadratic transverse leakage approximation gives very accurate results for the reactor core calculations.

Keywords

Neutron diffusion equation

Analytic nodal

Transverse leakage

Flat approximation

Quadratic approximation

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