Goal-based angular adaptivity for Boltzmann transport in the presence of ray-effects

TL;DR

This paper introduces a goal-based angular adaptivity method for Boltzmann transport problems that overcomes ray-effects by using rotationally invariant spherical harmonics to bootstrap error metrics, enabling efficient anisotropic refinement.

Contribution

It proposes a novel bootstrap approach using low-order filtered spherical harmonics to enable goal-based angular adaptivity unaffected by ray-effects.

Findings

Method produces refined angular discretisations matching fixed refinement results.

Approach is robust across tested streaming problems.

Achieves similar accuracy with reduced or comparable computational cost.

Abstract

Boltzmann transport problems often involve heavy streaming, where particles propagate long distance due to the dominance of advection over particle interaction. If an insufficiently refined non-rotationally invariant angular discretisation is used, there are areas of the problem where no particles will propogate. These "ray-effects" are problematic for goal-based error metrics with angular adaptivty, as the metrics in the pre-asymptotic region will be zero/incorrect and angular adaptivity will not occur. In this work we use low-order filtered spherical harmonics, which is rotationally invariant and hence not subject to ray-effects, to "bootstrap" our error metric and enable highly refined anisotropic angular adaptivity with a Haar wavelet angular discretisation. We test this on three simple problems with pure streaming where we know a priori where refinement should occur. We show our method is robust and produces adapted angular discretisations that match the results produced by fixed refinement with either reduced runtime or a constant additional cost with angular refinement.