E pur si muove：基于移动网格的伽利略不变宇宙流体动力学模拟
E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh
摘要：
流体动力学宇宙学模拟目前通常采用拉格朗日SPH技术，或欧拉流体动力学的笛卡尔网格与自适应网格细化。这两种方法都有缺点，在某些情况下会对其准确性产生负面影响。我们在这里提出了一个新的计划，在很大程度上消除了这些弱点。它是基于一个移动的非结构化网格定义的一组离散点的Voronoi镶嵌。网格是用来解决理想流体动力学的双曲守恒律与有限体积法，基于二阶不分裂Goddom格式与精确的黎曼求解器。原则上，网格生成点可以任意移动。如果它们被选择为平稳的，则该格式等价于具有二阶精度的普通欧拉方法。如果它们以局部流的速度移动，则获得流体动力学的拉格朗日公式，该公式不会受到其他基于网格的拉格朗日方案中固有的网格失真限制。在这种模式下，我们的新方法是完全伽利略不变的，不像普通的欧拉代码，一个属性，是宇宙学模拟的重要性。此外，新方案可以自动连续地调整其空间分辨率，从而继承了SPH在模拟宇宙结构增长方面的主要优点。欧拉方法在处理激波方面的高精度得到保留，而接触不连续性的处理得到改进。我们将讨论如何实现这种方法在我们的新的并行代码AREPO，无论是在2D和3D。我们使用一套测试问题来检查新代码的性能，并认为它提供了一个有吸引力的和有竞争力的替代目前的SPH和欧拉技术。（节略）
英文摘要：
Hydrodynamic cosmological simulations at present usually employ either the Lagrangian SPH technique, or Eulerian hydrodynamics on a Cartesian mesh with adaptive mesh refinement. Both of these methods have disadvantages that negatively impact their accuracy in certain situations. We here propose a novel scheme which largely eliminates these weaknesses. It is based on a moving unstructured mesh defined by the Voronoi tessellation of a set of discrete points. The mesh is used to solve the hyperbolic conservation laws of ideal hydrodynamics with a finite volume approach, based on a second-order unsplit Godunov scheme with an exact Riemann solver. The mesh-generating points can in principle be moved arbitrarily. If they are chosen to be stationary, the scheme is equivalent to an ordinary Eulerian method with second order accuracy. If they instead move with the velocity of the local flow, one obtains a Lagrangian formulation of hydrodynamics that does not suffer from the mesh distortion limitations inherent in other mesh-based Lagrangian schemes. In this mode, our new method is fully Galilean-invariant, unlike ordinary Eulerian codes, a property that is of significant importance for cosmological simulations. In addition, the new scheme can adjust its spatial resolution automatically and continuously, and hence inherits the principal advantage of SPH for simulations of cosmological structure growth. The high accuracy of Eulerian methods in the treatment of shocks is retained, while the treatment of contact discontinuities improves. We discuss how this approach is implemented in our new parallel code AREPO, both in 2D and 3D. We use a suite of test problems to examine the performance of the new code and argue that it provides an attractive and competitive alternative to current SPH and Eulerian techniques. (abridged)
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
