Efficient Higher Order Analytical Nodal Methods for the Numerical Resolution of the Multigroup Neutron Diffusion Equations

This work describes a solution techniques for the two-dimensional multigroup neutron diffusion equation in Cartesian geometry based on the use of Three efficient higher order analytical nodal methods. The successive polynomial-weighted transverse integrations technique is used to convert one- group diffusion equation to a system of coupled one-dimensional ordinary differential equations. These equations are then solved analytically over each homogenized cell. Coupling between the approximate transverse flux-moments is achieved by imposing uniqueness constraint on their moments values. Adjacent elements are coupled by enforcing continuity conditions on the flux and current moments at interfaces cells. The weighted cell-balance equations and current-continuity conditions are then used to derive the discrete equations. These methods are on the two group 2D-PWR benchmark problem. Numerical results demonstrates the efficiency of theses nodal methods. (author)