标题： 流体动力学和N体方案在非结构化自适应网格上的应用及其在宇宙学模拟中的应用 显示英文标题

标题： Hydrodynamic and N-body Schemes On An Unstructured, Adaptive Mesh with Applications to Cosmological Simulations

摘要： 数值方法在非结构化网格上的理论和应用近年来得到了显著改进。 由于网格可以在空间中任意放置，非结构化网格可以提供比常规网格更高的空间分辨率。 非结构化网格的网格自适应特性为模拟涉及无碰撞暗物质和有碰撞气体动力学的高动态、分层问题提供了一种方法。 在本文中，我们描述了通过Delaunay三角剖分从一组具有周期性边界条件的点构造非结构化网格的算法，以及在非结构化网格上求解流体动力学和N体问题的算法。 一种局部变换算法与传统的Bowyer-Watson算法相结合，提供了一种高效执行Delaunay三角剖分的方法。 描述了一种在非结构化网格上求解N体运动方程的新算法。 使用共轭梯度法求解泊松方程。 基于BGK模型的气体动力学方案用于求解欧拉方程。 我们将这些算法应用于求解涉及暗物质和重子物质的宇宙学问题。 代码中包含了原始重子物质的各种冷却和加热过程。 数值结果表明，基于非结构化网格并具有网格细化的N体和流体动力学算法非常适合分层结构形成问题。 显示英文摘要

摘要： The theory and application of numerical methods for unstructured meshes have been improved significantly in recent years. Because the grids can be place arbitrarily in space, unstructured meshes can provide much higher spatial resolution than regular meshes. The built-in nature of mesh adaptivity for unstructured meshes gives one way to simulate highly dynamic, hierarchical problems involving both collisionless dark matter and collisional gas dynamics. In this paper, we describe algorithms to construct unstructured meshes from a set of points with periodic boundary conditions through Delaunay triangulation, and algorithms to solve hydrodynamic and N-body problems on an unstructured mesh . A combination of a local transformation algorithm and the traditional Bowyer-Watson algorithm gives an efficient approach to perform Delaunay triangulation. A novel algorithm to solve N-body equations of motion on an unstructured mesh is described. Poisson's equation is solved using the conjugate gradient method. A gas-kinetic scheme based on the BGK model to solve Euler equations is used to evolve the hydrodynamic equations. We apply these algorithms to solve cosmological settings, which involve both dark and baryonic matter. Various cooling and heating processes for primordial baryonic matter are included in the code. The numerical results show that the N-body and hydrodynamic algorithms based on unstructured meshes with mesh refinement are well-suited for hierarchical structure formation problems.