Unstructured Moving-Mesh Hydrodynamic Simulation

We present a new hydrodynamic simulation code based on the Voronoi tessellation for estimating the density precisely. The code employs both of Lagrangian and Eulerian description by adopting the movable mesh scheme, which is superior to the conventional SPH (smoothed particle hydrodynamics) and AMR (adaptive mesh refinement) schemes. The code first generates unstructured meshes by the Voronoi tessellation at every time step, and then solves the Riemann problem for all surfaces of each Voronoi cell so as to update the hydrodynamic states as well as to move current meshes. Besides, the IEM (incremental expanding method) is devised to compute the Voronoi tessellation to desired degree of speed, thereby the CPU time is turned out to be just proportional to the number of particles, i.e., O(N). We discuss the applications of our code in the context of cosmological simulations as well as numerical experiments for galaxy formation.