ar X iv : a st ro - p h / 98 07 12 1 v 1 1 3 Ju l 1 99 8 COSMOLOGICAL ADAPTIVE MESH REFINEMENT

We describe a grid-based numerical method for 3D hydrody-namic cosmological simulations which is adaptive in space and time and combines the best features of higher order–accurate Godunov schemes for Eulerian hydrodynamics with adaptive particle–mesh methods for collision-less particles. The basis for our method is the structured adaptive mesh refinement (AMR) algorithm of Berger & Collela (1989), which we have extended to cosmological hydro + N-body simulations. The resulting mul-tiscale hybrid method is a powerful alternative to particle-based methods in current use. The choices we have made in constructing this algorithm are discussed, and its performance on the Zeldovich pancake test problem is given. We present a sample application of our method to the problem of first structure formation. We have achieved a spatial dynamic range L box /∆x > 250, 000 in a 3D multispecies gas + dark matter calculation, which is sufficient to resolve the formation of primordial protostellar cloud cores starting from linear matter fluctuations in an expanding FRW universe .