SPHERICAL HARMONICS SOLUTIONS TO SECOND ORDER FORMS OF THE BOLTZMANN TRANSPORT EQUATION USING PARTICLE TRANSPORT CODE SCEPTRE

Open Access
Author:
Bielen, Andrew Scott
Graduate Program:
Nuclear Engineering
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
None
Committee Members:
  • Yousry Y Azmy, Thesis Advisor
Keywords:
  • spherical harmonics
  • charged particles
  • particle transport
Abstract:
Numerical simulations of basic physical processes are fundamental to how science is performed in this day in age. One of the processes of great interest to nuclear scientists and engineers is particle transport, in which the distribution of fundamental particles is calculated within a given region based on internal source distributions and external boundary conditions. The distribution can then be used to estimate physical effects of interest. The equation describing this process is known as the Boltzmann transport equation. In this work, second order forms of the transport equation are discretized in angle using the spherical harmonics methodology. The coefficients arising from the discretization were found to be consistent with expected values. The resulting discretization is implemented in Sandia National Laboratories’ coupled photon-electron charged particle code SCEPTRE, and two test problems are presented. The solution to the equation and the convergence rates of the error with increasing spatial refinement are shown. It was found that the convergence rates for the second test problem were about an order lower than what was expected. The discrepancy is due to possible discontinuities in the first derivative of the solution, errors arising from an averaging procedure carried out on the output, or a lack of knowledge of the estimated convergence rate in the finite elements solver utilized by SCEPTRE.