A 1-D multigroup diffusion equation nodal model using the orthogonal collocation method

A I-D nodal model is developed for solving the multigroup diffusion equation. The neutron flux is calculated at certain collocation points within a given node using an iterative process. The partial currents are used at the nodal interfaces. The location of the collocation points within a node is determined from the roots of the transformed Legendre polynomials. Two sample problems, using two and four internal collocation points, were used to test the accuracy of the model. In both sample problems, the results of the nodal model matched the results of the fine-mesh finite-difference calculations. The model presented here has been developed in a general format and the necessary equations for any number of collocation points can be obtained with great ease