A COSMOLOGICAL HYDRODYNAMIC CODE BASED ON THE TOTAL VARIATION DIMINISHING SCHEME

Abstract

We describe an explicit second-order finite difference code based on a total variation diminishing scheme for self-gravitating cosmological hydrodynamic systems. The code has been developed to follow correctly the adiabatic changes of extremely supersonic preshock flows with a Mach number larger than 100 as well as very strong shocks. In highly supersonic regions, we use an entropy-like variable switching to a more conventional total energy variable near to and interior to shocks. The self-gravity has been included in such a way that the numerical errors in calculating the gravitational force term do not induce the leakage of the gravitational energy into the thermal energy of the gas. Also, the gravitational force term has been corrected to take account of the mass diffusion around the shocks so the total energy can be conserved. Tests for the accuracy and performance of the code without gravity have proved that it can accurately handle supersonic flows with a Mach number larger than 10(4). In calculations of the formation of a one-dimensional Zel'dovich pancake, an energy accuracy of 1% is obtained for 32 cells per unit wavelength, and the accuracy reaches 0.01% as the number of cells approaching 1024. To further test the code with gravity, three-dimensional simulations of a purely baryonic universe but with the initial cold dark matter power-spectrum have been performed. The results have shown that shocks are well resolved and separate cleanly the hot, dense, collapsed peaks from the cold, low-density, expanding voids. The thermal energy in low-density regions can be orders of magnitude lower using this scheme than in some others due to very careful attention given to entropy in high Mach number regions. Various numerical experiments have proven that the code can handle the expanding low density regions very well as well as conserve the total energy very accurately