Cycle-Free Polytopal Mesh Sweeping for Boltzmann Transport
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915044663492608 |
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| author | Calloo, Ansar Evans, Matthew Lockyer, Henry Madiot, François Pryer, Tristan Zanetti, Luca |
| author_facet | Calloo, Ansar Evans, Matthew Lockyer, Henry Madiot, François Pryer, Tristan Zanetti, Luca |
| contents | We introduce a novel property of bounded Voronoi tessellations that
enables cycle-free mesh sweeping algorithms. We prove that a
topological sort of the dual graph of any Voronoi tessellation is
feasible in any flow direction and dimension, allowing
straightforward application to discontinuous Galerkin (DG)
discretisations of first-order hyperbolic partial differential
equations and the Boltzmann Transport Equation (BTE) without
requiring flux-cycle corrections.
We also present an efficient algorithm to perform the topological
sort on the dual mesh nodes, ensuring a valid sweep ordering. This
result expands the applicability of DG methods for transport
problems on polytopal meshes by providing a robust framework for
scalable, parallelised solutions. To illustrate its effectiveness,
we conduct a series of computational experiments showcasing a DG
scheme for BTE, demonstrating both computational efficiency and
adaptability to complex geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cycle-Free Polytopal Mesh Sweeping for Boltzmann Transport Calloo, Ansar Evans, Matthew Lockyer, Henry Madiot, François Pryer, Tristan Zanetti, Luca Numerical Analysis 65F08 (Primary), 65N50 (Secondary) We introduce a novel property of bounded Voronoi tessellations that enables cycle-free mesh sweeping algorithms. We prove that a topological sort of the dual graph of any Voronoi tessellation is feasible in any flow direction and dimension, allowing straightforward application to discontinuous Galerkin (DG) discretisations of first-order hyperbolic partial differential equations and the Boltzmann Transport Equation (BTE) without requiring flux-cycle corrections. We also present an efficient algorithm to perform the topological sort on the dual mesh nodes, ensuring a valid sweep ordering. This result expands the applicability of DG methods for transport problems on polytopal meshes by providing a robust framework for scalable, parallelised solutions. To illustrate its effectiveness, we conduct a series of computational experiments showcasing a DG scheme for BTE, demonstrating both computational efficiency and adaptability to complex geometries. |
| title | Cycle-Free Polytopal Mesh Sweeping for Boltzmann Transport |
| topic | Numerical Analysis 65F08 (Primary), 65N50 (Secondary) |
| url | https://arxiv.org/abs/2412.01660 |