Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Engineering Physics

First Advisor

Kirk A. Mathews, PhD


A new discrete ordinates spatial quadrature for arbitrary triangular cells is derived and compared to its rectangular cell linear characteristic counterpart. The triangular mesh is more flexible, allowing curved surfaces and off-axis angles to be approximated with many fewer spatial cells. The triangle method is consistently more accurate on example problems tested here. Arbitrary orientation and size of the triangles allow non-patterned meshes to be developed which appears to ameliorate numerical diffusion. The triangle linear characteristic quadrature converges at nearly the same rate as rectangular Linear characteristic on Lathrop's problem. Mesh sensitivity measurements show large variations in triangle vertex locations produce less than 1.0 percent variation in results. Test cases included a rectangular region with diagonal vacuum duct, and cylindrical source region with rotated rings of annular segmented reflectors. The triangle linear characteristic quadrature is more cost effective on these problems achieving a relative error of less than 1.0 percent with a factor of three to over a hundred fewer spatial cells, with less than three times the computational cost per cell. This spatial cell savings should increase the practical problem domain for which discrete ordinates is usable.

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The author's Vita page is omitted.