Abstract
A polynomial nodal model which uses Legendre expansions was developed for the multi group diffusion equation in 1-D. The development depends upon a least-squares minimization of the approximate functions over the node. Analytical expressions were developed for the polynomial coefficients. Diffusion theory interface and boundary conditions have been applied. Sample problems with analytical solutions and fine-mesh finite-difference solutions have been compared with the method. For most reactor-type problems, fourth-order polynomial expansions appear to be adequate.
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