Flux Synthesis Using Green's Function in Two-Dimensional Group Diffusion Equations

The group diffusion equations in two dimensions are solved by assuming the separation of variables sectionally. Using one-dimensional Green's functions, the two-dimensional diffusion equations are transformed into two sets of one-dimensional three-point difference equations at fine-mesh points. Assuming that the separation of variables of x and y coordinates is possible in a coarse mesh in a reactor, the two sets of one-dimensional difference equations are solved by the alternating direction iteration method. Sample calculations for ²³⁵U-H₂O thermal reactors show that this method gives fairly good results with few coarse and fine meshes and the computation time can be considerably reduced compared with the usual finite difference method.