Diffusion Synthetic Acceleration Methods for the Diamond-Differenced Discrete-Ordinates Equations

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Abstract
We investigate a class of acceleration schemes that resemble the conventional synthetic method in that they utilize the diffusion operator in the transport iteration schemes. These schemes are not dependent on diffusion theory as being a good approximation to transport theory; they only make use of the diffusion equation form. The accelerated iteration involves alternate diffusion and transport solutions where coupling between the equations is achieved using a correction term applied to either (a) the diffusion coefficient, (b) the removal cross section, or (c) the source of the diffusion equation. The methods involving the modification of the diffusion coefficient and of the removal term yield nonlinear acceleration schemes and are used in keff calculations, while the source term modification approach is linear at least before discretization and is used for inhomogeneous source problems. A careful analysis shows that there is a preferred differencing method that eliminates the previously observed instabi...

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