T. Pandya, M. L. Adams,
"Method of Long Characteristics Applied in Space and Time,"
International Conference on Advances in Mathematics, Computational Methods, and Reactor Physics, an international conference sponsored by the ANS, Saratoga, NY, May 3-7, 2009.
have developed a long-characteristic (LC) discretization of the
time and space variables in the transport equation and tested it in
slab geometry. The method's sole approximation is in the spatial
shape of the scattering-plus- fission source. Many LC spatial
discretizations assume constant sources in each cell, but because
we are interested in thick diffusive problems we must construct
sources with at least linear variation in each cell. We have
developed a least-squares procedure for constructing such sources.
We recognize that it is not possible to simultaneously obtain all
three of the following desirable properties: 1) exact solution
along each ray in the purely-absorbing limit; 2) cellwise particle
conservation; 3) smoothly varying cellwise reaction rates in smooth
problems. To illustrate this we construct and display a
cellwise-linear scalar flux that produces conservative reaction
rates and one that produces smooth reaction rates. These quantities
are similar for most cases and the difference between them vanishes
in the limit of fine ray spacing. We compare our LC results against
results from a traditional linear discontinuous spatial
discretization with standard finite-difference time
discretizations. We find that our method is more accurate for both
streaming-dominated and scattering-dominated test problems.
Finally, we remark that application of this method in parallel
looks promising, partly due to the independence of the separate
rays along which the solution is computed.
Associated Project(s):SHIELD (Smuggled HEU Interdiction through Enhanced anaLysis and Detection): A Framework for Developing Novel Detection Systems Focused on Interdicting Shielded HEU