Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Engineering Physics

First Advisor

Kirk A. Mathews, PhD


In solving the Boltzmann transport equation, most discrete ordinates codes calculate the source term by first approximating the scattering cross section using a Legendre polynomial expansion. Such expansions are insufficient when scattering is anisotropic and the Legendre expansion is truncated prematurely. This can lead to nonphysical negative cross sections, negative source terms and negative angular fluxes. While negative sources are problematic for standard discrete ordinates methods leading to poor convergence or convergence to incorrect results, they are of particular concern to exponential methods, causing such calculations to fail. We've developed and tested a new technique to solve this problem called the Monte Carlo Facet Method. This method is an extension of standard Monte Carlo techniques. It guarantees non-negative cross sections at all directional ordinates. It also ensures within group and next group scatter. This dissertation outlines previous attempts to handle anisotropic scattering to achieve non-negative sources. It develops the theory of the Monte Carlo facet method and its first angular moment conservation. Results are presented examining the scattering matrices for various materials, and finally demonstrating that these scattering matrices perform exceptionally well in a multi-group, anisotropic, unstructured mesh discrete ordinates transport code.

AFIT Designator


DTIC Accession Number