Spatial differencing of the transport equation: Positivity vs. accuracy

Authors:
K. D. Lathrop
Affiliations:
Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico, Mexico
Venue:
Journal of Computational Physics
Year:
1969

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Abstract

Positive spatial difference schemes for the Boltzmann equation are derived and compared in x -y geometry. It is found that none of the positive schemes are as accurate as the most commonly used nonpositive scheme. A variable weighted difference scheme in which the weights are chosen depending on the space-angle mesh is shown to give results similar to those obtained with difference schemes based on the method of characteristics. A version of the variable weight scheme in which weights depend not only on the space-angle mesh but also on particle sources and fluxes is suggested as a means of obtaining the highest accuracy consistent with a positive difference scheme, but it is noted that such schemes are computationally more expensive than available corrective recipes used in conjunction with nonpositive schemes.