The angular dependence of the differential scattering cross section is typically represented as a truncated Legendre series expansion. If the scattering cross section is highly anisotropic, these expansions may result in negative regions in the -1 ≤ μ0 ≤ +1 interval, thus representing the cross section by negative values. These negative regions may cause negative components in the discrete ordinates scattering source, which are non-physical and which may adversely affect the iterative convergence of the exponential discontinuous spatial discretization scheme. Two methods are presented which produce a positive representation of the scattering cross section, and are designed to calculate a strictly positive scattering source. The first method constructs a scattering matrix from the exponential representation of the cross section derived from maximum entropy. Accuracy of these matrices is further improved by the application of SMART scattering theory. The second method adjusts the Legendre cross section moments with a constrained least squares algorithm. The adjustment is subject to constraints that the zeroth and first moment remain unchanged and that the resulting expansion is positive on all scattering angle cosines derived from a standard S N quadrature set. Extra moments from the maximum entropy representation of the cross section are also used to decrease the relative error of the modified moments. Numerical transport calculations using these two methods demonstrate consistent results with those using the standard truncated Legendre expansion of the cross section. The exponential discontinuous spatial scheme is shown to iteratively converged when these two methods are used. A comparison of these methods with results from multigroup and continuous energy Monte Carlo calculations are also shown to be consistent.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/284105 |
| Date | January 1999 |
| Creators | Dahl, Jon Alan |
| Contributors | Ganapol, Barry D. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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