标题： 无环多面体网格扫掠法用于玻尔兹曼输运 显示英文标题

标题： Cycle-Free Polytopal Mesh Sweeping for Boltzmann Transport

摘要： 我们引入了有界Voronoi镶嵌的一种新特性，该特性使无环网格扫掠算法成为可能。我们证明了任何Voronoi镶嵌的对偶图的拓扑排序在任何流动方向和维度下都是可行的，使得可以直接应用于一阶双曲偏微分方程和玻尔兹曼输运方程（BTE）的不连续伽辽金（DG）离散化，而无需进行通量循环修正。我们还提出了一种高效的算法，在对偶网格节点上执行拓扑排序，确保有效的扫掠顺序。这一结果通过提供可扩展和并行化的解决方案的稳健框架，扩大了DG方法在多面体网格上的传输问题的应用范围。为了说明其有效性，我们进行了一系列计算实验，展示了BTE的DG方案，同时展示了计算效率和对复杂几何结构的适应性。 显示英文摘要

摘要： 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.