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arXiv · 2412.01660

Cycle-Free Polytopal Mesh Sweeping for Boltzmann Transport

Ansar Calloo·Matthew Evans·Henry Lockyer·François Madiot·Tristan Pryer·Luca Zanetti
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Abstract

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.

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Ansar Calloo, Matthew Evans, Henry Lockyer, François Madiot, Tristan Pryer, Luca Zanetti. 2024-12-02. Cycle-Free Polytopal Mesh Sweeping for Boltzmann Transport. https://arxiv.org/abs/2412.01660

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