Single channel synthesis with finite element trial functions for three-dimensional reactor calculations

A single channel continuous synthesis model employing finite element trial functions in radial planes has been developed for three-dimensional reactor computations based on multi-group diffusion theory. The use of finite element method instead of the conventional finite difference method for the planar trial functions allows one to perform the integrals in radial planes analytically within each element. Due to the possibility of choosing relatively large elements the time of computation for the trial function calculations is reduced and the evaluation of the integrals needed for synthesis calculation is also rendered easy. Further in synthesis approach, since the problem is broken into two steps of 2-D and 1-D calculations, the exceedingly large requirement of computer time and memory by a straight 3-D finite element solution is avoided. An IAEA benchmark problem, thoroughly analysed by previous authors, serves as an example to demonstrate the feasibility of the present approach. Considerable saving of computer time is achieved for the sample problem relative to previous methods. Some final remarks are made as to how the finite element synthesis method can be extended to realistic LWR core calculations both for steady state and time-dependent neutron flux solutions. (orig.)