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This paper describes an angular adaptivity algorithm for Boltzmann transportapplications which uses Pn and filtered Pn expansions, allowing for differentexpansion orders across space/energy. Our spatial discretisation isspecifically designed to use less memory than competing DG schemes and alsogives us direct access to the amount of stabilisation applied at each node. Forfiltered Pn expansions, we then use our adaptive process in combination withthis net amount of stabilisation to compute a spatially dependent filterstrength that does not depend on a priori spatial information. This appliesheavy filtering only where discontinuities are present, allowing the filteredPn expansion to retain high-order convergence where possible. Regular andgoal-based error metrics are shown and both the adapted Pn and adapted filteredPn methods show significant reductions in DOFs and runtime. The adaptedfiltered Pn with our spatially dependent filter shows close to fixed iterationcounts and up to high-order is even competitive with P0 discretisations inproblems with heavy advection.

Angular adaptivity with spherical harmonics for Boltzmann transport