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Solutions of the Diffusion Equation by the Spectral-Synthesis Method

Paul G. Lorenzini, Alan H. Robinson

Nuclear Science and Engineering

Volume 44 / Number 1 / April 1971 / Pages 27-36


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The spectral-synthesis method is investigated to assess its applicability for solving the diffusion equation in fast reactor design. The equations are derived so they may be solved by a standard diffusion theory code that allows upscattering. A reference 1000-MW(e) fast reactor is studied and two-dimensional solutions are obtained. The problem of selecting trial functions is examined and four different sets are used in the calculations. The results are compared with few-group calculations to test both accuracy and running times. The few-group and synthesis approximations are, in turn, compared with a 26-group solution which is treated as an exact solution. Some numerical instabilities are experienced and examined. It is concluded that the instabilities are caused by a complete coupling between equations in the scattering matrix. The accuracy of the synthesis approximation is comparable with the few-group approximation for calculating eigenvalues and is slightly superior for determining the flux in the core.

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