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The method of discrete ordinates ($S_N$) is a popular choice for the solutionof the neutron transport equation. It is however well known that it suffersfrom slow convergence of the scattering source in optically thick and diffusivemedia, such as pressurized water nuclear reactors (PWR). In reactor physicsapplications, the $S_N$ method is thus often accompanied by an accelerationalgorithm, such as the Diffusion Synthetic Acceleration (DSA). With the recentincrease in computational power, whole core transport calculations have becomea reasonable objective. It however requires using large computers andparallelizing the transport solver. Due to the elliptic nature of the DSAoperator, its parallelization is not straightforward. In this paper, we presentan acceleration operator derived from the DSA, but defined in a piecewise waysuch that its parallel implementation is straightforward. We show that, foroptically thick enough media, this Piecewise Diffusion Synthetic Acceleration(PDSA) preserves the good properties of the DSA. This conclusion is supportedby numerical experiments.

Piecewise Diffusion Synthetic Acceleration Scheme for Neutron Transport Simulations in Diffusive Media