2019/11/05 by Steven Dargaville, Dargaville, S., R.P. Smedley‐Stevenson +5
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1911.01747
openalex publication_date 2019/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.