Unifying via conformal mapping coarse-mesh neutron diffusion calculations in Cartesian and hexagonal geometries

Modern design methodology for nuclear reactor core designs performs routinely three-dimensional core modeling. The modeling is done with a class of highly accurate nodal method of solving the neutron diffusion equation, which is orders of magnitude faster than the finite difference method. However, these modern nodal methods are powerful only for Cartesian geometry problem applications. For hexagonal geometry problems, there is a fundamental difficulty associated with singularities caused by the geometry. Using the invariance property of the diffusion operator under conformal transformations, the singularities can be removed via conformally mapping a hexagonal node to a rectangular node, making it very easy to extend a nodal code from Cartesian geometry applications to hexagonal geometry applications. Thus applications to the two different geometries can be unified in a single nodal code. The method has been implemented in the Westinghouse neutron diffusion code, ANC-H, and demonstrated to work very well.