19 results found
Dargaville S, Smedley-Stevenson RP, Smith PN, et al., 2020, Goal-based angular adaptivity for Boltzmann transport in the presence of ray-effects, Journal of Computational Physics, Vol: 421, Pages: 1-19, ISSN: 0021-9991
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 propagate. These “ray-effects” are problematic for goal-based error metrics with angular adaptivity, 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 are 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 in which traditional error metrics fail. We show our method is robust and produces adapted angular discretisations that match results produced by fixed a priori refinement with either reduced runtime or a constant additional cost even with angular refinement.
Dargaville S, Buchan AG, Smedley-Stevenson RP, et al., 2020, A comparison of element agglomeration algorithms for unstructured geometric multigrid, Publisher: arXiv
This paper compares the performance of seven different element agglomerationalgorithms on unstructured triangular/tetrahedral meshes when used as part of ageometric multigrid. Five of these algorithms come from the literature on AMGemultigrid and mesh partitioning methods. The resulting multigrid schemes aretested matrix-free on two problems in 2D and 3D taken from radiation transportapplications; one of which is in the diffusion limit. In two dimensions allcoarsening algorithms result in multigrid methods which perform similarly, butin three dimensions aggressive element agglomeration performed by METISproduces the shortest runtimes and multigrid setup times.
Dargaville S, Buchan AG, Smedley-Stevenson RP, et al., 2020, Scalable angular adaptivity for Boltzmann transport, Journal of Computational Physics, Vol: 406, Pages: 1-32, ISSN: 0021-9991
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 P0 FEM discretisation of a 2D angular domain, allowing different anisotropic angular resolution to be applied across space/energy. These wavelets can be mapped back to their underlying P0 space scalably, allowing traditional DG-sweep algorithms if desired. Instead we build a spatial discretisation on unstructured grids designed to use less memory than competing alternatives in general applications and construct a compatible matrix-free multigrid method which can handle our adapted angular discretisation. Fixed angular refinement, along with regular and goal-based error metrics are shown in three example problems taken from neutronics/radiative transfer applications.
Buchan AG, Dargaville S, Pain CC, 2019, A combined immersed body and adaptive mesh method for simulating neutron transport within complex structures, ANNALS OF NUCLEAR ENERGY, Vol: 134, Pages: 88-100, ISSN: 0306-4549
Dargaville S, Buchan AG, Smedley-Stevenson RP, et al., 2019, Angular adaptivity with spherical harmonics for Boltzmann transport, Journal of Computational Physics, Vol: 397, Pages: 1-19, ISSN: 0021-9991
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.
Soucasse L, Buchan AG, Dargaville S, et al., 2019, An angular reduced order model for radiative transfer in non grey media, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol: 229, Pages: 23-32, ISSN: 0022-4073
Adigun BJ, Buchan AG, Adam A, et al., 2018, A Haar wavelet method for angularly discretising the Boltzmann transport equation, PROGRESS IN NUCLEAR ENERGY, Vol: 108, Pages: 295-309, ISSN: 0149-1970
Soucasse L, Dargaville S, Buchan AG, et al., 2017, A goal-based angular adaptivity method for thermal radiation modelling in non grey media, JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, Vol: 200, Pages: 215-224, ISSN: 0022-4073
Dargaville S, Buchan A, Smedley-Stevenson R, et al., 2017, Adaptive angle and parallel multigrid for deterministic shielding problems, 13th International Conference on Radiation Shielding (ICRS) / 19th Topical Meeting of the Radiation-Protection-and-Shielding-Division-of-the-American-Nuclear-Society (RPSD), Publisher: E D P SCIENCES, ISSN: 2100-014X
Smith P, Lillington J, Pain C, et al., 2016, Directions in Radiation Transport, INTERNATIONAL JOURNAL OF MULTIPHYSICS, Vol: 10, Pages: 355-377, ISSN: 1750-9548
Dargaville S, Goffin MA, Buchan AG, et al., 2015, Solving the Boltzmann transport equation with multigrid and adaptive space/angle discretisations, ANNALS OF NUCLEAR ENERGY, Vol: 86, Pages: 99-107, ISSN: 0306-4549
Buchan AG, Calloo AA, Goffin MG, et al., 2015, A POD reduced order model for resolving angular direction in neutron/photon transport problems, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 296, Pages: 138-157, ISSN: 0021-9991
Goffin MA, Buchan AG, Dargaville S, et al., 2015, Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 281, Pages: 1032-1062, ISSN: 0021-9991
Dargaville S, Farrell TW, 2015, A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Vol: 273, Pages: 225-244, ISSN: 0377-0427
Dargaville S, Farrell TW, 2013, A comparison of mathematical models for phase-change in high-rate LiFePO4 cathodes, ELECTROCHIMICA ACTA, Vol: 111, Pages: 474-490, ISSN: 0013-4686
Dargaville S, Farrell TW, 2013, The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport: The Cahn-Hilliard-reaction equation and the role of defects (vol 94, pg 143, 2013), ELECTROCHIMICA ACTA, Vol: 108, Pages: 876-876, ISSN: 0013-4686
Dargaville S, Farrell TW, 2013, The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport: The Cahn-Hilliard-reaction equation and the role of defects, ELECTROCHIMICA ACTA, Vol: 94, Pages: 143-158, ISSN: 0013-4686
Dargaville S, Crawford R, Simpson J, et al., 2012, What is the optimum regime for calibration bias adjustments?, ANZIAM JOURNAL, Vol: 54, Pages: M47-M82, ISSN: 1446-1811
Dargaville S, Farrell TW, 2010, Predicting Active Material Utilization in LiFePO4 Electrodes Using a Multiscale Mathematical Model, JOURNAL OF THE ELECTROCHEMICAL SOCIETY, Vol: 157, Pages: A830-A840, ISSN: 0013-4651
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