粒子流体力学与镶嵌技术
Particle hydrodynamics with tessellation techniques
摘要：
拉格朗日光滑粒子流体动力学（SPH）是一种在天体物理问题中建立流体模型的成熟方法，这要归功于其几何灵活性和自动调整空间分辨率以适应物质聚集的能力。然而，最近的一些研究强调了SPH在处理流体不稳定性方面的不准确性。这些数值问题的起源可以追溯到虚假的表面效应跨越接触不连续性，和SPH的固有的防止混合在颗粒水平。在这里，我们研究了一种新的流体粒子模型，其中密度估计是在辅助网格的帮助下进行的，该辅助网格被构造为模拟粒子的Voronoi曲面细分，而不是自适应平滑内核。这种基于Voronoi的方法提高了该方案表示尖锐接触不连续性的能力。我们表明，这消除了SPH中存在的虚假表面张力效应，并在抑制某些流体不稳定性中发挥作用。我们发现，新的'Voronoi粒子流体动力学'这里所描述的产生可比的结果比SPH的冲击，更好的纯流体动力学模拟的湍流制度。我们还讨论了配方的人工粘度需要在这个计划中，以及如何明智地选择校正力可以推导出，以保持高度的粒子秩序，因此定期Voronoi网格。这在使用用于N体模拟的现有重力求解器模拟自重力流体时特别有用。
英文摘要：
Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of matter. However, a number of recent studies have emphasized inaccuracies of SPH in the treatment of fluid instabilities. The origin of these numerical problems can be traced back to spurious surface effects across contact discontinuities, and to SPH's inherent prevention of mixing at the particle level. We here investigate a new fluid particle model where the density estimate is carried out with the help of an auxiliary mesh constructed as the Voronoi tessellation of the simulation particles instead of an adaptive smoothing kernel. This Voronoi-based approach improves the ability of the scheme to represent sharp contact discontinuities. We show that this eliminates spurious surface tension effects present in SPH and that play a role in suppressing certain fluid instabilities. We find that the new `Voronoi Particle Hydrodynamics' described here produces comparable results than SPH in shocks, and better ones in turbulent regimes of pure hydrodynamical simulations. We also discuss formulations of the artificial viscosity needed in this scheme and how judiciously chosen correction forces can be derived in order to maintain a high degree of particle order and hence a regular Voronoi mesh. This is especially helpful in simulating self-gravitating fluids with existing gravity solvers used for N-body simulations.
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