| dc.description.abstract | In this dissertation we discuss the development, implementation, analysis and testing of
the Piecewise Linear Discontinuous Finite Element Method (PWLD) applied to the
particle transport equation in two-dimensional cylindrical (RZ) and three-dimensional
Cartesian (XYZ) geometries. We have designed this method to be applicable to
radiative-transfer problems in radiation-hydrodynamics systems for arbitrary polygonal
and polyhedral meshes. For RZ geometry, we have implemented this method in the
Capsaicin radiative-transfer code being developed at Los Alamos National Laboratory.
In XYZ geometry, we have implemented the method in the Parallel Deterministic
Transport code being developed at Texas A&M University.
We discuss the importance of the thick diffusion limit for radiative-transfer problems,
and perform a thick diffusion-limit analysis on our discretized system for both
geometries. This analysis predicts that the PWLD method will perform well in this limit
for many problems of physical interest with arbitrary polygonal and polyhedral cells.
Finally, we run a series of test problems to determine some useful properties of the
method and verify the results of our thick diffusion limit analysis.
Finally, we test our method on a variety of test problems and show that it compares
favorably to existing methods. With these test problems, we also show that our method
performs well in the thick diffusion limit as predicted by our analysis. Based on
PWLD's solid finite-element foundation, the desirable properties it shows under analysis, and the excellent performance it demonstrates on test problems even with
highly distorted spatial grids, we conclude that it is an excellent candidate for radiativetransfer
problems that need a robust method that performs well in thick diffusive
problems or on distorted grids. | en |
