Nuclear Engineering ETDs

Publication Date

Fall 2020


A natural coordinate system for calculating neutral particle propagation in the atmosphere due to point sources is two-dimensional spherical-polar coordinates. Deterministic methods for solving the transport equation in this coordinate system require some interesting implementation details stemming from the two angular derivatives present in this form of the equation. In this dissertation, we present a bilinear discontinuous spatial discretization of the transport equation in this coordinate system. The weighted diamond difference discretization is applied to the angular derivative term in two angular dimensions, using zero-weighted starting directions to start the differencing. To our knowledge, the only previous deterministic code that solved the transport equation in the spherical-polar coordinate system was written more than 50 years ago; the development of the deterministic methods we present here and the application to atmospheric transport is new. Numerical experiments are shown to verify that method has better than second-order accuracy and correctly solves the spherical-polar form of the transport equation.


multi-dimensional orthogonal curvilinear discontinuous method, discret ordinates, neutron transport, atmospheric transport

Document Type




Degree Name

Nuclear Engineering

Level of Degree


Department Name

Nuclear Engineering

First Committee Member (Chair)

Anil Prinja

Second Committee Member

James Warsa

Third Committee Member

Cassiano Oliveira

Fourth Committee Member

Dmitriy Anistratov