Hierarchical Numerical Cosmology with Hydrodynamics: Methods and Code Tests

We describe a two-level hierarchical three-dimensional numerical code designed to simulate the formation of galaxies and other larger scale structures in an expanding universe with Newtonian gravity and radiative cooling. The basis of the hierarchical code is a standard particle-mesh (PM) algorithm used to evolve the dark matter constituents and an ideal nonrelativistic MHD uid solver to evolve the gas components on a cubical Cartesian grid with variable timesteps. Within the parent cube we can construct a smaller subgrid ( xed in space) to resolve ner scale structures, providing a larger dynamical range over standard single grid codes without the enormous demand for memory and execution time. The elds from the parent grid are treated as external elds in the subgrid evolution and are passed down only as boundary