In this thesis, we develop and test a fundamentally new linear-discontinuous
least-squares (LDLS) method for spatial discretization of the one-dimensional (1-D)
discrete-ordinates (SN) equations. This new scheme is based upon a least-squares method
with a discontinuous trial space. We implement our new method, as well as the lineardiscontinuous
Galerkin (LDG) method and the lumped linear-discontinuous Galerkin
(LLDG) method. The implementation is in FORTRAN.
We run a series of numerical tests to study the robustness, L2 accuracy, and the
thick diffusion limit performance of the new LDLS method. By robustness we mean the
resistance to negativities and rapid damping of oscillations. Computational results
indicate that the LDLS method yields a uniform second-order error. It is more robust
than the LDG method and more accurate than the LLDG method. However, it fails to
preserve the thick diffusion limit. Consequently, it is viable for neutronics but not for
radiative transfer since radiative transfer problems can be highly diffusive.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-3026 |
| Date | 15 May 2009 |
| Creators | Zhu, Lei |
| Contributors | Morel, Jim E. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | electronic, application/pdf, born digital |
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