Angular adaptivity with spherical harmonics for Boltzmann transport

This paper describes an angular adaptivity algorithm for Boltzmann transport applications which uses Pn and filtered Pn 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 Pn 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 Pn expansion to retain high-order convergence where possible. Regular and goal-based error metrics are shown and both the adapted Pn and adapted filtered Pn methods show significant reductions in DOFs and runtime. The adapted filtered Pn 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.Comment: arXiv admin note: text overlap with arXiv:1901.0492

Scalable angular adaptivity for Boltzmann transport

This paper describes an angular adaptivity algorithm for Boltzmann transport applications which for the first time shows evidence of $\mathcal{O}(n)$ scaling in both runtime and memory usage, where $n$ is the number of adapted angles. This adaptivity uses Haar wavelets, which perform structured $h$-adaptivity built on top of a hierarchical P$_0$ FEM discretisation of a 2D angular domain, allowing different anisotropic angular resolution to be applied across space/energy. Fixed angular refinement, along with regular and goal-based error metrics are shown in three example problems taken from neutronics/radiative transfer applications. We use a spatial discretisation designed to use less memory than competing alternatives in general applications and gives us the flexibility to use a matrix-free multgrid method as our iterative method. This relies on scalable matrix-vector products using Fast Wavelet Transforms and allows the use of traditional sweep algorithms if desired

AIR multigrid with GMRES polynomials (AIRG) and additive preconditioners for Boltzmann transport

We develop a reduction multigrid based on approximate ideal restriction (AIR) for use with asymmetric linear systems. We use fixed-order GMRES polynomials to approximate $A_\textrm{ff}^{-1}$ and we use these polynomials to build grid transfer operators and perform F-point smoothing. We can also apply a fixed sparsity to these polynomials to prevent fill-in. When applied in the streaming limit of the Boltzmann Transport Equation (BTE), with a P$^0$ angular discretisation and a low-memory spatial discretisation on unstructured grids, this "AIRG" multigrid used as a preconditioner to an outer GMRES iteration outperforms the lAIR implementation in hypre, with two to three times less work. AIRG is very close to scalable; we find either fixed work in the solve with slight growth in the setup, or slight growth in the solve with fixed work in the setup when using fixed sparsity. Using fixed sparsity we see less than 20% growth in the work of the solve with either 6 levels of spatial refinement or 3 levels of angular refinement. In problems with scattering AIRG performs as well as lAIR, but using the full matrix with scattering is not scalable. We then present an iterative method designed for use with scattering which uses the additive combination of two fixed-sparsity preconditioners applied to the angular flux; a single AIRG V-cycle on the streaming/removal operator and a DSA method with a CG FEM. We find with space or angle refinement our iterative method is very close to scalable with fixed memory use

Evolution of Antarctic ozone in September-December predicted by CCMVal-2 model simulations for the 21st century

Chemistry-Climate Model Validation phase 2 (CCMVal-2) model simulations are used to analyze Antarctic ozone increases in 2000–2100 during local spring and early summer, both vertically integrated and at several pressure levels in the lower stratosphere. Multi-model median trends of monthly zonal mean total ozone column (TOC), ozone volume mixing ratio (VMR), wind speed and temperature poleward of 60° S are investigated. Median values are used to account for large variability in models, and the associated uncertainty is calculated using a bootstrapping technique. According to the trend derived from the twelve CCMVal-2 models selected, Antarctic TOC will not return to a 1965 baseline, an average of 1960–1969 values, by the end of the 21st century in September–November, but will return in ~2080 in December. The speed of December ozone depletion before 2000 was slower compared to spring months, and thus the decadal rate of December TOC increase after 2000 is also slower. Projected trends in December ozone VMR at 20–100 hPa show a much slower rate of ozone recovery, particularly at 50–70 hPa, than for spring months. Trends in temperature and winds at 20–150 hPa are also analyzed in order to attribute the projected slow increase of December ozone and to investigate future changes in the Antarctic atmosphere in general, including some aspects of the polar vortex breakup.J. M. Siddaway, S. V. Petelina, D. J. Karoly, A. R. Klekociuk, and R. J. Dargavill