论文标题
关于疯狂移动Voronoi网格的高阶任意拉格朗日 - 欧拉群岛计划
High-order Arbitrary-Lagrangian-Eulerian schemes on crazy moving Voronoi meshes
论文作者
论文摘要
双曲线偏微分方程（PDE）涵盖了从人和炉膛科学到天体物理学的广泛有趣现象：这不可避免地需要对许多时空尺度进行处理，以便同时描述观察者大小的宏观结构，多尺度尺度尺度，多尺度的特征以及零速度震荡。此外，解决双曲线PDE的数值方法必须可靠地处理不同的波浪系列：光滑的稀有因素以及冲击和接触类型的不连续性。为了实现这些目标，一种有效的方法在于基于时空的高级方案的组合，即使在粗网格上也非常准确地具有Lagrangian方法，该方法通过与流体流动的网格移动网格，从而产生了高度分辨的，并且在冲击和触点上产生了高度分辨的和微小的消散结果。但是，确保高质量的移动网格是一个巨大的挑战，需要开发创新和非常规技术。这里提出的计划属于任意拉格朗日 - 欧拉（ALE）方法的家庭，并具有通过连通性变化来发展网格元素形状的独特额外自由。我们的目的是通过简单而非常显着的例子，基于高阶时空处理拓扑变化的高级ALE方案的功能以及我们的新技术的功能。
Hyperbolic partial differential equations (PDEs) cover a wide range of interesting phenomena, from human and hearth-sciences up to astrophysics: this unavoidably requires the treatment of many space and time scales in order to describe at the same time observer-size macrostructures, multi-scale turbulent features, and also zero-scale shocks. Moreover, numerical methods for solving hyperbolic PDEs must reliably handle different families of waves: smooth rarefactions, and discontinuities of shock and contact type. In order to achieve these goals, an effective approach consists in the combination of space-time-based high-order schemes, very accurate on smooth features even on coarse grids, with Lagrangian methods, which, by moving the mesh with the fluid flow, yield highly resolved and minimally dissipative results on both shocks and contacts. However, ensuring the high quality of moving meshes is a huge challenge that needs the development of innovative and unconventional techniques. The scheme proposed here falls into the family of Arbitrary-Lagrangian-Eulerian (ALE) methods, with the unique additional freedom of evolving the shape of the mesh elements through connectivity changes. We aim here at showing, by simple and very salient examples, the capabilities of high-order ALE schemes, and of our novel technique, based on the high-order space-time treatment of topology changes.
