An efficient space-angle subgrid scale discretisation of the neutron transport equation

Whilst the spatial discretisation has been previously documented, it is the angular treatment that is critical for efficient solutions. This is particularly the case for large angular expansion sizes involving angular discretisations that couple moments through the streaming term (i.e. not discrete ordinate schemes), where it is shown here that the computing costs are reduced to O(M) from O(M3), where M denotes the angular expansion size. It is shown how the method increases efficiency of the solving process through the improved efficiency of matrix vector multiplication which forms the most expensive component of a Krylov based solver. This matrix vector product is also computed without the matrix being stored in memory which would be a requirement for large scale radiation transport calculations. The method's capabilities are demonstrated by solving fixed source problems involving a range of material types - from optically thin to opaque. In all cases the new method yields accurate and stable solutions.