Thesis Defense • Master of Science
Candidate: Walter Eldridge Pierce IV
Advisor: David Heddle, Ph.D., Associate Professor, PCSE
April 12, 2013 • 11:00 am • Washington Room, DSU
Title: Chimera Grid: The geometry of intersecting 3-dimensional Cartesian and spherical grids
This thesis solves a computational physics and differential geometry problem mapping the intersection of a 3D Cartesian and 2D spherical grid using software written in C#. The grids are created from nonuniform arrays. When a Cartesian cell intersects the sphere, a pre-patch is created, defined by curves connecting the points of intersection. The pre-patch is spliced against the spherical grid, breaking it into smaller patches, each with a unique five-plet of indices. The patches were initially visualized with a Monte Carlo coloring and later compared with the computed patches. Area and perimeter measurements, necessary for potential use in magnetohydrodynamic calculations, are calculated using an analytic approach described here. The analytic patch covering is tested by how well it matches the Monte Carlo visualization and by assessing whether the sum of the patch areas matches the area of a sphere.
Patches generated and overlayed onto a Monte Carlo visualization after 400,000 data points were plotted. The projection is a simple θ, latitude: [0, π) and φ, longitude: [0, 2π) plot.