Abstract
We consider the steady multigroup neutron transport equation in a spatially periodic medium, with a spatially periodic source, and vacuum boundary conditions. We require (1) the ratio of a cell diameter to the diameter of the entire medium to be small, and (2) the transport operator to have N ≥ 1 eigenvalues which are small in magnitude, and simple. Then we show that the transport equation solution is approximated by the solution of an explicit system of N homogenized diffusion equations. We briefly discuss these equations and their properties.
Work performed under the auspices of the U. S. Energy Research and Development Administration.
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References
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Larsen, E.W. (1979). A homogenized multigroup diffusion theory for the neutron transport equation. In: Glowinski, R., Lions, J.L., Laboria, I. (eds) Computing Methods in Applied Sciences and Engineering, 1977, I. Lecture Notes in Mathematics, vol 704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063631
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DOI: https://doi.org/10.1007/BFb0063631
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