HYDRODYNAMIC AND N-BODY SCHEMES ON AN UNSTRUCTURED, ADAPTIVE MESH WITH APPLICATIONS TO COSMOLOGICAL SIMULATIONS

The theory and application of numerical methods for unstructured meshe s have been improved significantly in recent years. Because the grids can be placed arbitrarily in space, unstructured meshes can provide mu ch higher spatial resolution than regular meshes. The built-in nature of mesh adaptivity for unstructured meshes gives one way to simulate h ighly dynamic, hierarchical problems involving both collisionless dark matter and collisional gas dynamics. In this paper, we describe algor ithms to construct unstructured meshes from a set of points with perio dic 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 Bo wyer-Watson algorithm gives an efficient approach to perform Delaunay triangulation. A novel algorithm to solve N-body equations of motion o n an unstructured mesh is described. Poisson's equation is solved usin g the conjugate gradient method. A gas-kinetic scheme based on the BGK model to solve Euler equations is used to evolve the hydrodynamic equ ations. We apply these algorithms to solve cosmological settings, whic h involve both dark and baryonic matter. Various cooling and heating p rocesses for primordial baryonic matter are included in the code. The numerical results show that the N-body and hydrodynamic algorithms bas ed on unstructured meshes with mesh refinement are well suited for hie rarchical structure formation problems.