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

摘要

A class of acceleration schemes is investigated which resembles the conventional synthetic method in that they utilize the diffusion operator in the transport iteration schemes. The accelerated iteration involves alternate diffusion and transport solutions where coupling between the equations is achieved by using a correction term applied to either the diffusion coefficient, the removal cross section, or 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 k/sub eff/ 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 which eliminates the previously observed instability of the conventional synthetic method. Use of this preferred difference scheme results in an acceleration method which is at the same time stable and efficient. This preferred difference approach renders the source correction scheme, which is linear in its continuous form, nonlinear in its differenced form. An additional feature of these approaches is that they may be used as schemes for obtaining improved diffusion solutions for approximately twice the cost of a diffusion calculation. Numerical experimentation on a wide range of problems in one and two dimensions indicates that improvement from a factor of two to ten over rebalance or Chebyshev acceleration is obtained. The improvement is most pronounced in problems with large regions of scattering material where the unaccelerated transport solutions converge very slowly. (ERA citation 02:031441)