Discrete ordinates (SN) method for the first solution of the transport equation using Chebyshev polynomials

Hakan Öztürk

doi:10.1051/epjconf/201612803002

Abstract

First estimates for the numerical solution of the one-dimensional neutron transport equation for one-speed neutrons in a finite homogeneous slab is studied. The neutrons are assumed to be scattered isotropically through the medium. Then the discrete ordinates form of the transport equation is solved for the eigenvalue spectrum using the Chebyshev polynomials of second kind in the neutron angular flux. Therefore, the calculated eigenvalues for various values of the c 0 , the mean number of secondary neutrons per collision, are given in the tables using the Gauss-Chebyshev quadrature set.

Highlights

First estimates for the numerical solution of the one-dimensional neutron transport equation for one-speed neutrons in a finite homogeneous slab is studied
Since the neutrons starts the fission in the system, it is important not to lose them to continue the fission chain reaction
Monte Carlo (MCNP) and the source iteration (SI) techniques are extensively used in the solution algorithm of the transport equation

Summary

Introduction

First estimates for the numerical solution of the one-dimensional neutron transport equation for one-speed neutrons in a finite homogeneous slab is studied. In the studies about neutron transport through any medium, the scattering of the neutrons should be taken into considerations carefully. This constant power situation can be sensed as isotropic scattering of the neutrons in the system. It is still worth to study the isotropic scattering of the neutrons in transport theory.

Results

Conclusion