Diffusion Synthetic Acceleration for polytopic discretisations of Boltzmann transport

TL;DR

This paper computationally studies diffusion synthetic acceleration (DSA) for Boltzmann transport equations discretized with polytopic discontinuous Galerkin methods, comparing classical and modified interior penalty formulations.

Contribution

It introduces a modified interior penalty (MIP) DSA scheme that remains robust across various parameters, outperforming the classical SIP approach.

Findings

MIP-based DSA is robust across different optical thicknesses and scattering ratios.

SIP-based DSA can lose robustness in intermediate regimes.

Convergence factors for MIP schemes are typically below 0.6 in challenging settings.

Abstract

We present a computational study of diffusion synthetic acceleration (DSA) for the monoenergetic, isotropically scattering $S_N$ transport equations, discretised in space by a polytopic discontinuous Galerkin method. Using a discrete ordinates angular discretisation, we construct the DSA correction with an interior-penalty diffusion operator and compare a classical symmetric interior penalty (SIP) formulation with a modified interior penalty (MIP) variant, together with homogeneous Dirichlet and Marshak (Robin) diffusion boundary conditions imposed weakly in the DG framework. We quantify the observed convergence behaviour of the resulting source iteration across variations in optical thickness, scattering ratio, angular quadrature, mesh refinement, polynomial degree and mesh anisotropy on families of bounded Voronoi meshes. The results show that MIP-based DSA remains robust across the parameter ranges tested, whereas SIP-based DSA can lose robustness in the intermediate regime. In challenging optically thick, highly scattering settings, the observed convergence factors for the MIP-based schemes are typically below $0.6$.