Higher order analytical nodal methods in response-matrix formulation for the multigroup neutron diffusion equations

A higher analytical nodal method for the multigroup neutron diffusion equations, based on the transverse integration procedure, is presented. The discrete 1D equations are cast with the interface partial current techniques in response matrix formalism. The remaining Legendre coefficients of the transverse leakage moment are determined exactly in terms of the different neutron flux moments order in the reference node. In the weighted balance equations, the transverse leakage moments are linearly written in terms of the partial currents, facial and centered fluxes moments. The self-consistent is guaranteed. Furthermore, as the order k increase the neutronic balance in each node and the copulate between the adjacent cell are reinforced. The convergence order in L2-norm is of O(hk+3−δk0) under smooth assumptions. The efficacy of the method is showed for 2D-PWR, 2D-IAEA LWR and 2D-LMFBR benchmark problems.