Analytical nodal method for solution of neutron diffusion equation in polar coordinates

Abstract

The well-known analytic nodal method approach as proposed in earlier work for Cartesian coordinates with constant transverse leakage approximation is adapted to solve the neutron diffusion equation in 2-d polar coordinates. The approach in present work incorporates the recently developed methodology to overcome the problem involved with the transverse integration in θ–direction. Unlike the earlier methods which solve for surface averaged fluxes, the node averaged fluxes are obtained in the present work. The advantage of using node average flux is that it allows the straightforward coupling with mesh centered schemes for thermal hydraulics or other physics. Furthermore, the conventional time marching schemes can be developed in a simplified manner using this approach. The solutions obtained from the current approach are compared with the available analytical and benchmark solutions. The eigenvalues obtained with current methodology is in good agreement with those obtained for analytical and internationally available benchmark solutions.