A variational method for the solution of multidimensional multigroup problems in diffusion approximation

A newly developed synthesis method for the solution of multidimensional problems in multigroup diffusion approximation is described. With the aid of this method the original multidimensional problem can be reduced to the solution of a system of ordinary differential equations with certain boundary and transition conditions. The relationship between the method and the conventional Galerkin-type methods is established. On the basis of the method a two-dimensional computer code has been developed which makes it possible, in the case of piecewise constant macroscopic coefficients, to carry out multigroup calculations even on relatively small computers. The method yields another advantage in that the trial functions for establishing the solution in question match the very nature of the problem, thus offering the possibility to estimate more accurately the solution behaviour in certain domains, for example, in regions where a rapid change of the neutron flux takes place. From the rigorous mathematical point of view, the trial functions used also form a complete system of functions which is of importance in investigating the convergence of the method. Practical use of the method is shown in a model criticality calculation and the space-energy distribution of the neutron flux of a 1000 MW(th) sodium-cooled fast reactor. The rate of convergence is determined considering the number of trial functions and other approximations used in numerical calculations. The results are compared with those obtained from standard difference codes. (author)