We present a new iterative approach to solving neutral-particle transport
problems. The scheme divides the transport solution into its particular and
homogeneous or “source-free” components. The particular problem is solved directly,
while the homogeneous problem is found iteratively. To organize the iterative inversion
of the homogeneous components, we exploit the structures of the so called Case-modes
that compose it. The asymptotic Case-modes, those that vary slowly in space and angle,
are assigned to a diffusion solver. The remaining transient Case-modes, those with large
spatial gradients, are assigned to a transport solver. The scheme iterates on the
contribution from each solver until the particular plus homogeneous solution converges.
The iterative method is implemented successfully in slab geometry with isotropic
scattering and one energy group. The convergence rate of the method is only weakly
dependent on the scattering ratio of the problem. Instead, the rate of convergence
depends strongly on the material thickness of the slab, with thick slabs converging in
few iterations. The transient solution is obtained by applying a One Cell Inversion
scheme instead of a Source Iteration based scheme. Thus, the transient unknowns are
calculated with little coordination between them. This independence among unknowns
makes our scheme ideally suited for transport calculations on parallel architectures.
The slab geometry iterative scheme is adapted to XY geometry. Unfortunately,
this attempt to extend the slab geometry iterative scheme to multiple dimensions has not
been successful. The exact filtering scheme needed to discriminate asymptotic and
transient modes has not been obtained and attempts to approximate this filtering process resulted in a divergent iterative scheme. However, the development of this iterative
scheme yield valuable analysis tools to understand the Case-mode structure of any
spatial discretization under arbitrary material properties.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-3207 |
| Date | 15 May 2009 |
| Creators | Maslowski Olivares, Alexander Enrique |
| Contributors | Adams, Marvin L |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
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