Piecewise Diffusion Synthetic Acceleration scheme for neutron transport simulations in optically thick systems

The method of discrete ordinates (SN) is a popular choice for the solution of the neutron transport equation. It is however well known that it suffers from slow convergence of the scattering source in optically thick and diffusive media, such as pressurized water nuclear reactors (PWR). In reactor physics applications, the SN method is thus often accompanied by an acceleration algorithm, such as Diffusion Synthetic Acceleration (DSA). With the recent increase in computational power, whole core transport calculations have become a reasonable objective. It however requires using large computers and parallelizing the transport solver. Due to the elliptic nature of the DSA operator, its parallelization is not straightforward. In this paper, we present an acceleration operator derived from DSA, but defined in a piecewise way such that its parallel implementation is straightforward. We mathematically show that, for optically thick enough media, this Piecewise Diffusion Synthetic Acceleration (PDSA) scheme preserves the good properties of DSA. This conclusion is supported by numerical experiments.