Revisit interior penalty based diffusion synthetic acceleration for the SN transport equation discretized with discontinuous Galerkin method

Abstract

Diffusion Synthetic Acceleration (DSA) techniques based on symmetric and nonsymmetric versions of the Interior Penalty (IP) method have been proposed to accelerate the scattering source iteration of the SN transport equation discretized with discontinuous Galerkin (DG) method in the previous researches. The performances of DSA based on various IP methods need to be compared comprehensively. The Robin boundary condition is usually adopted to treat the vacuum boundaries in solving the diffusion equation of DSA, but in the thick diffusive limit, the Dirichlet boundary condition was derived for the diffusion equation to give the correct leading-order interior solution. The influence of the boundary condition for the vacuum boundaries in DSA needs to be analyzed. In this study, the DSA schemes with three various IP methods (SIP, IIP and NIP) in conjunction with Krylov iterative method are summarized in a complete view, and the approaches to dealing with the instability problem of DSA in the optically thick and nearly voided regimes are discussed. From the numerical experiments, it suggests that the DSA schemes with IIP, NIP and SIP perform closely to each other, and there is no specific IP method which shows advantages over the others under any conditions. With other conditions fixed, the performance of the DSA scheme with the Dirichlet boundary condition becomes better than that with the Robin boundary condition with the increase of optical cell thickness. There is no apparent relationship between the performance of the DSA scheme and the discretization order of DG.