Characteristic Methods for Solving the Particle Transport Equation in 1-D Spherical Geometry

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Title: Characteristic Methods for Solving the Particle Transport Equation in 1-D Spherical Geometry
Author: Fleming, John Thomas III
Advisors: Dr. Paul J. Turinsky, Committee Member
Dr. Yousry Y. Azmy , Committee Member
Dr. Zhilin Li, Committee Member
Dr. Dmitriy Y. Anistratov, Committee Chair
Abstract: A family of numerical methods for solving the particle transport equation in 1-D spherical geometry are developed using the method of characteristics. The development of these methods is driven by a desire to: (i) provide solutions to transport problems which cannot otherwise be determined using analytic techniques and (ii) provide comparative solutions to test methods developed for other curvilinear geometries. Problems that are of increasing importance to the transport community are those that contain subdomains which are considered optically thick and diffusive. These problems result in high computational costs due to the grid refinement necessary to generate acceptable solutions. As a result, we look to develop vertex-based characteristic methods that can reproduce these diffusive solutions without resorting to significant spatial grid refinement. This research will allow for continued development of advanced conservative characteristic methods with better properties for R-Z geometries. The transport methods derived here are based on a change of coordinates that removes the angular derivative term in the differential operator resulting in a first order differential equation which can be discretized using methods similar to those found in 1-D slab geometry. In this study, we present a family of characteristic methods; Vladimirov's method of characteristics, a conservative long characteristic method, two locally conservative short characteristic methods, a linear long characteristic method, and an explicit slope long characteristic method. The numerical results presented in this thesis demonstrate the performance of each method. We found that the linear and explicit slope long characteristic methods generated numerical solutions which are well behaved in some diffusive problems. Also, we analyzed several of these methods using asymptotic diffusion limit analysis and found that the linear long characteristic method limits to a discretized version of the diffusion equation.
Date: 2009-04-15
Degree: MS
Discipline: Nuclear Engineering

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