Speaker: Dean Wang (The Ohio State University).

It has been well known that the analytic neutron transport solution limits to the analytic solution of a diffusion problem for optically thick systems with small absorption and source. The standard technique for proving the asymptotic diffusion limit is constructing an asymptotic power series of the neutron angular flux in small positive parameter, which is the ratio of a typical mean free path of a particle to a typical dimension of the domain under consideration. In this workshop, we will present a new proof to directly show that the analytical neutron transport solution satisfies the diffusion equation at the asymptotic limit based on a recently obtained closed-form analytical solution of the monoenergetic SN neutron transport equation in slab geometry. In numerical solution of the SN neutron transport equation, a spatial discretization is of practical interest if it possesses the optically thick diffusion limit. Such a numerical scheme will yield accurate solutions for diffusive problems if the spatial mesh size is thin with respect to a diffusion length, whereas the mesh cells are thick in terms of a mean free path. We will present a recently obtained theoretical result on the asymptotic diffusion limit of numerical schemes and what mesh sizes should be used to achieve accurate results. In addition, we will present an interesting implication of the asymptotic diffusion limit on Fourier analysis for CMFD schemes. Audience: anyone.

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