Solving the Boltzmann transport equation with multigrid and adaptive space/angle discretisations

• Summary of the latest work on the radiation transport component of FETCH.
• We use a multigrid preconditioner to achieve good scaling as the spatial and angular mesh is refined.
• Goal-based adaptivity can focus the spatial and angular resolution on quantities of interest.
• A wavelet basis in angle allows the use of anisotropic angular adaptivity.

This paper presents the current capabilities of the radiation transport solver within FETCH, a coupled multi-physics code. The radiation transport component has been designed to solve the Boltzmann transport equation with a stable sub-grid scale finite element approach and various angular discretisations. These capabilities are demonstrated through the solution of two challenging example problems: the 2D C5G7 MOX benchmark and a 3D problem from the Kobayashi benchmarks. A multigrid-based matrix-free solver is used on the C5G7 problem in parallel with a PnPn discretisation in angle. The results show that the number of iterations stays mostly constant as both the spatial mesh is refined and the angular resolution is increased. The second problem considered is from the Kobayashi benchmarks and is used to illustrate the spatial and angular goal-based adaptivity. In particular, we show the capabilities of a wavelet discretisation in angle, which when used with angular adaptivity applies anisotropic resolution in angle and enables significant reduction in the degrees of freedom used in heavy streaming problems.