E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh
E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh
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DOI：
10.1111/j.1365-2966.2009.15715.x
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发表时间：
2009-01
影响因子：
4.8
通讯作者：
V. Springel
中科院分区：
文献类型：
--
作者：
V. Springel
流体动力学宇宙学模拟目前通常采用拉格朗日光滑粒子流体动力学（SPH）技术或欧拉流体动力学的笛卡尔网格（可选）自适应网格细化（AMR）。这两种方法都有缺点，在某些情况下会对它们的准确性产生负面影响，例如在SPH的情况下会抑制流体不稳定性，在AMR的情况下会缺乏伽利略不变性和存在过度混合。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定律与有限体积法，基于二阶不可分裂Goddom计划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，该计划是等效的一个普通的欧拉方法与二阶精度。如果他们，而不是移动的速度，当地的流动，得到一个拉格朗日公式的连续流体动力学，不遭受网格变形的限制，固有的其他网格为基础的拉格朗日计划。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，一个属性是非常重要的宇宙学模拟，其中高度超音速的大流量是常见的。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也得到了保留，而接触不连续性的处理得到了改进。我们将讨论如何在我们的新代码arepo中实现这种方法，无论是在2D还是在3D中，并为分布式内存计算机并行化。我们还讨论了非结构化网格的自适应细化或去细化技术。我们引入了一个单独的时间步长方法有限体积流体力学，并提出了一个高精度的处理气体的自引力，使新的方法无缝结合的高分辨率处理无碰撞的暗物质。我们使用一套测试问题来检查新代码的性能，并认为这里提出的流体动力学移动网格方案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。
Hydrodynamic cosmological simulations at present usually employ either the Lagrangian smoothed particle hydrodynamics (SPH) technique or Eulerian hydrodynamics on a Cartesian mesh with (optional) adaptive mesh refinement (AMR). Both of these methods have disadvantages that negatively impact their accuracy in certain situations, for example the suppression of fluid instabilities in the case of SPH, and the lack of Galilean invariance and the presence of overmixing in the case of AMR. 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 continuum 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 where highly supersonic bulk flows are common. 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 also retained, while the treatment of contact discontinuities improves. We discuss how this approach is implemented in our new code arepo, both in 2D and in 3D, and is parallelized for distributed memory computers. We also discuss techniques for adaptive refinement or de-refinement of the unstructured mesh. We introduce an individual time-step approach for finite-volume hydrodynamics, and present a high-accuracy treatment of self-gravity for the gas that allows the new method to be seamlessly combined with a high-resolution treatment of collisionless dark matter. We use a suite of test problems to examine the performance of the new code and argue that the hydrodynamic moving-mesh scheme proposed here provides an attractive and competitive alternative to current SPH and Eulerian techniques.