The Boltzmann transport equation (BTE) is a linear PDE which governs the transport of neutral particles (i.e., neutrons, photons) in radiation transport problems. This PDE has 3 spatial dimensions, 2 angular dimensions, 1 energy dimension and a time dimension (7 total). In addition, given different physical materials in a domain, the Boltzmann transport equation can behave in both an elliptic or hyperbolic fashion, challenging deterministic solver technology.

This talk will focus on the approaches developed to solve the BTE within the Applied Modelling and Computation Group (AMCG) at Imperial College. These are centred around our novel adaptive discretisation technology in space and angle, along with a general purpose matrix-free multigrid solver that scales well in parallel. We have also coupled our radiation transport solver with fluids, heat transfer, and multi-phase codes developed in the group.  We use this technology in a number of key areas, including simulating nuclear reactor and shielding, coupled thermal radiation and spectral wave problems, which will be briefly outlined.