Time integration of the neutron diffusion equation on hexagonal geometries

To study the behavior of nuclear reactors like the Russian VVER reactors it is necessary to solve the time dependent neutron diffusion equation using a hexagonal mesh. Two methods are proposed to solve this equation. In both methods the spatial part of the equations is discretized using a high order spectral element method, based on assuming that the neutron flux can be expanded in terms of the modified Dubiner’s polynomials. For the time discretization of the equations two different strategies have been considered. For the first a finite differences one-step implicit method has been used and the other method is based on a modal expansion of the flux in terms of the dominant Lambda modes of the reactor core. The performance of both methods has been tested for an hypothetical transient in a 2-dimensional VVER 440 reactor.