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Approximations to Neutron Transport Problems in Complex Geometries: Part I

Bernard I. Spinrad, James S. Sterbentz

Nuclear Science and Engineering

Volume 90 / Number 4 / August 1985 / Pages 431-441


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The Wigner-Seitz cell problem is treated by integral transport theory as a superposition of black boundary problems using the volume source and sources equivalent to the two lowest order angular components of the reentrant flux. This treatment sheds light on the convergence properties of iterative integral transport solution methods. The outgoing flux is required to have the lowest order components equal and opposite to those of the reentrant flux. Sample problems with this P11 boundary condition give good results. A new approximation to neutron transport theory is also reported. This approximation does not rely on expansion or approximation of the angular flux distribution, but rather on approximating the integral transport kernel by a sum of diffusionlike kernels that preserve spatial moments of the kernel. This might permit transport problems to be treated as a set of coupled diffusion problems in any geometry.

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