Angular adaptivity with spherical harmonics for Boltzmann transport

Highlights: • Shows evidence of adaptive P_n outperforming uniform in both runtime and memory use. • Uses filtered Pn with spatially dependent filter values combined with adaptivity. • Competitive with adapted P⁰ discretisations up to high order on problems with heavy streaming. -- Abstract: This paper describes an angular adaptivity algorithm for Boltzmann transport applications which uses P_n and filtered P_n expansions, allowing for different expansion orders across space/energy. Our spatial discretisation is specifically designed to use less memory than competing DG schemes and also gives us direct access to the amount of stabilisation applied at each node. For filtered P_n expansions, we then use our adaptive process in combination with this net amount of stabilisation to compute a spatially dependent filter strength that does not depend on a priori spatial information. This applies heavy filtering only where discontinuities are present, allowing the filtered P_n expansion to retain high-order convergence where possible. Regular and goal-based error metrics are shown and both the adapted P_n and adapted filtered P_n methods show significant reductions in DOFs and runtime. The adapted filtered P_n with our spatially dependent filter shows close to fixed iteration counts and up to high-order is even competitive with P⁰ discretisations in problems with heavy advection.