### Anisotropic Neutron Diffusion for Modeling Nuclear Reactors

##### Travis Trahan, University of Michigan

Due to its relatively low computational cost, neutron diffusion theory remains one of the most commonly used tools for reactor analysis. Although diffusion requires more approximations than higher-order methods such as SN and Monte Carlo, the computational cost of these other methods prohibits their widespread general use. It has long been known that diffusion is anisotropic in heterogeneous reactors. While in many reactors the anisotropic diffusion effects may be negligible, in lattices containing voided or optically thin channels, such as very high temperature reactors (VHTR’s), the effects are significant. In such reactors, neutron leakage is larger parallel to the optically-thin channels than in the transverse directions. It is therefore desirable that the homogenized diffusion coefficient be a tensor in order to capture the anisotropic behavior. First, we derive a fine mesh diffusion tensor for general geometries. Second, we derive a homogenized, coarse mesh diffusion tensor for lattice geometries. In both cases, the diffusion tensor reduces to the standard scalar diffusion coefficient in the case of a homogeneous medium. Both diffusion approximations yield significantly more accurate results than standard neutron diffusion theory.

Abstract Author(s): Travis J. Trahan and Edward W. Larsen