High-order analytical nodal method for the multigroup diffusion equations

We develop a high-order analytical nodal method for the multigroup diffusion equations. Based on the transverse integration procedure, the discrete 1D equations are analytically approximated using the combined direct algebraic evaluation of trigonometric functions of multigroup matrices, and the truncated Legendre series. The remaining Legendre coefficients of the transverse leakage moments are determined exactly in terms of the different neutron flux moments order. The self-consistent is guaranteed. In the weighted balance equations, the transverse leakage moments are linearly written in terms of the partial currents, facial and centered fluxes moments. Furthermore, as the order increases, the neutron balance in each node and the coupling between the adjacent cell are reinforced. The efficacy of the method is shown for 2D-PWR and 2D-LMFBR benchmark problems.