Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Engineering Physics

First Advisor

Kirk A. Mathews, PhD


Characteristic spatial quadratures for discrete ordinates calculations on meshes of arbitrary tetrahedra are derived and tested, including the step (SC), linear (LC), and exponential (EC) characteristic quadratures and variants that assume constant distributions on cell faces. Tetrahedral meshes accurately model curved surfaces with few cells. A split cell approach subdivides tetrahedra along the streaming direction, reducing the transport to one dimension. Assumed forms of the cell source and entering flux distributions have sufficient parameters to match the zeroth and first spatial moments. These parameters are determined by analytically inverting a linear system (LC), or by numerical inversion using Newton's method (EC). Efficient algorithms for the two and three dimensional rootsolves are derived. The constant face methods proved unacceptable in empirical testing. Both LC and EC exhibited third order convergence. LC provided accurate results on cells with optical thickness on the order of one mean free path while EC was accurate with fewer, thicker cells. LC can produce negative fluxes; EC is strictly positive. Although more costly per cell, EC is robust and can be more efficient than LC or SC by using coarse meshes.

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