Cosmological hydrodynamics with adaptive mesh refinement

A new N-body and hydrodynamical code, called RAMSES, is presented. It has been designed to study structure formation in the universe with high spatial resolution. The code is based on Adaptive Mesh Refinement (AMR) technique, with a tree-based data structure allowing recursive grid refinements on a cell-by-cell basis. The N-body solver is very similar to the one developed for the ART code [CITE], with minor differences in the exact implementation. The hydrodynamical solver is based on a second-order Godunov method, a modern shock-capturing scheme known to compute accurately the thermal history of the fluid component. The accuracy of the code is carefully estimated using various test cases, from pure gas dynamical tests to cosmological ones. The specific refinement strategy used in cosmological simulations is described, and potential spurious effects associated with shock waves propagation in the resulting AMR grid are discussed and found to be negligible. Results obtained in a large N-body and hydrodynamical simulation of structure formation in a low density ΛCDM universe are reported, with 2563 particles and $4.1\times 10^7$ cells in the AMR grid, reaching a formal resolution of 81923. A convergence analysis of different quantities, such as dark matter density power spectrum, gas pressure power spectrum and individual haloe temperature profiles, shows that numerical results are converging down to the actual resolution limit of the code, and are well reproduced by recent analytical predictions in the framework of the halo model