English

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

Numerical Analysis 2019-11-06 v1 Numerical Analysis

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.

Keywords

Cite

@article{arxiv.1911.01747,
  title  = {Goal-based angular adaptivity for Boltzmann transport in the presence of ray-effects},
  author = {S. Dargaville and R. P. Smedley-Stevenson and P. N. Smith and C. C. Pain},
  journal= {arXiv preprint arXiv:1911.01747},
  year   = {2019}
}