A Three-dimensional Analytical Nodal Method for the Multigroup Diffusion Calculation in Hexagonal Geometry

A new nodal method based on both symmetries of the problem and an analytic representation of the nodal flux distribution is presented.The proposed method eliminates the singular problem that arises in the application of conventional nodal method in the hexagonal geometry and the solution derived in the method satisfies the neutron diffusion equation at any point of the node.The only approximations employed in deriving the method are the treatment of unknown functions.Furthermore,by introducing a new type of boundary condition that simultaneously requires the continuity of both zero and first order partial current moment in the radial nodal coupling,the radial nodal solution has been noticeably improved.The results of 3D WWER benchmark problems demonstrate that it is an advanced method for the solution of multigroup diffusion equation in hexagonal geometry.