Ordinary numerical methods can attain a high degree of accuracy, but especially for two- or three-dimensional cases, the time of computation required can be very high.

This problem becomes very important in cases where the diffusion calculations have to be repeated many times in the course of a time-dependent analysis (burn-up or kinetics codes).

Various time-saving methods have been developed especially for use in the diffusion theory routines of kinetics and burn-up codes. A technique sometimes used in these cases is the so-called “nodal method” in which the reactor is divided in a certain number of sub-regions or “nodes” for which average power or flux is calculated. This method can be compared with a finite difference method with very coarse meshes. The essential problem consists in obtaining coupling constants between the nodes, maintain­ing neutron balance within each node and between nodes. Analytical solutions of the diffusion equations with an appropriate choice of boundary conditions are sometimes employed in order to get the coupling between nodes/22’30’ A method using finite difference in coarse meshes with corrections taking into account the form of the within-mesh flux distribution is used in the UKAEA CRISP and APEX codes/31’32’ Sometimes the so-called “flux synthesis” methods are used in which approximate three-dimensional flux shapes are obtained combining the results of one — and two­dimensional calculations. The simplest way is to assume separability of the axial flux dependence. This assumption is sometimes made for obtaining rough approximations. A flux synthesis method based on a variational principle is described in ref. 33. A single-channel flux synthesis method is used by the General Atomic SC ANAL code135’ in which two to four two-dimensional GAUGE calculations, corresponding to horizontal slices through several axial elevations in the core, are coupled by means of a one-dimensional axial calculation. Each slice is homogenized and used as an axial zone in the one-dimensional FEVER code. In this code it is not actually the flux but the power distribution which is synthetized. This approach has been found to be more accurate than calculating the power distribution from synthetized fluxes.