Coarse time-step integration method for burnup calculation of LWR lattice containing gadolinium-poisoned rods.

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Abstract
For the purpose of enhancing the efficiency of the burnup calculation of LWR lattice, two coarse time-step integration methods have been developed, both of which are to be used in combination with the ordinary Runge-Kutta-Gill method. It has been ensured through the numerical results of model problems simulating the depletion of 157Gd in a gadolinium-poisoned rod that the maximum time-step size allowed by the proposed methods is roughly 4 or 5 times larger than that achieved by the Predictor-Corrector method known as an effective coarse time-step method, and consequently that the proposed methods would reduce the computation time to a half or less when applied to an LWR lattice burnup calculation. The factor of reduction of computation time is still more significant if compared with other conventional methods such as the Runge-Kutta-Gill method etc. In addition, it has been demonstrated through their application to the LWR lattice physics code TGBLA that no appreciable error is observed over the range of time-step size up to 1 GWd/t in the burnup calculation for a typical BWR lattice containing gadolinium-poisoned rods. Although the method development and verification presented here place emphasis on the cases of LWR lattice burnup, it is expected that the proposed methods would be applicable equally well to general problems dealing with the nuclide transmutation due to burnup.

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