Discretization and solving of the transport equation has been an area of great
research where many methods have been developed. Under the deterministic transport
methods, the method of characteristics, MOC, is one such discretization and solution
method that has been applied to large-scale problems. Although these MOC,
specifically long characteristics, LC, have been thoroughly applied to discretize and
solve transport problems in the spatial domain, there is a need for an equally adequate
time-dependent discretization. A method has been developed that uses LC discretization
of the time and space variables in solving the transport equation. This space-time long
characteristic, STLC, method is a discrete ordinates method that applies LC
discretization in space and time and employs a least-squares approximation of sources
such as the scattering source in each cell. This method encounters the same problems
that previous spatial LC methods have dealt with concerning achieving all of the
following: particle conservation, exact solution along a ray, and smooth variation in
reaction rate for specific problems. However, quantities that preserve conservation in
each cell can also be produced with this method and compared to the non-conservative results from this method to determine the extent to which this STLC method addresses
the previous problems.
Results from several test problems show that this STLC method produces
conservative and non-conservative solutions that are very similar for most cases and the
difference between them vanishes as track spacing is refined. These quantities are also
compared to the results produced from a traditional linear discontinuous spatial
discretization with finite difference time discretization. It is found that this STLC
method is more accurate for streaming-dominate and scattering-dominate test problems.
Also, the solution from this STLC method approaches the steady-state diffusion limit
solution from a traditional LD method. Through asymptotic analysis and test problems,
this STLC method produces a time-dependent diffusion solution in the thick diffusive
limit that is accurate to O(E) and is similar to a continuous linear FEM discretization
method in space with time differencing. Application of this method in parallel looks
promising, mostly due to the ray independence along which the solution is computed in
this method.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-12-7484 |
| Date | 2009 December 1900 |
| Creators | Pandya, Tara M. |
| Contributors | Adams, Marvin |
| Source Sets | Texas A and M University |
| Language | English |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | application/pdf |
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