An Adaptive Hierarchical Particle-Mesh Code With Isolated Boundary Conditions

This article describes a new, fully adaptive particle-multiple-mesh (PM²) numerical simulation code developed primarily for cosmological applications. The code integrates the equations of motion of a set of particles subject to their mutual gravitational interaction and to an optional, arbitrary external field. The interactions between particles are computed using a hierarchy of nested grids constructed anew at each integration step to enhance the spatial resolution in high-density regions of interest. As the code is aimed at simulations of relatively small volumes of space (not much larger than a single group of galaxies) with independent control over the external tidal fields, significant effort has gone into supporting isolated boundary conditions at the top grid level. This makes our method also applicable to noncosmological problems, at the cost of some complications, which we discuss. We point out the implications of some differences between our approach and those of other authors of similar codes, in particular with respect to the handling of the interface between regions of different spatial resolution. We present a selection of tests performed to verify the correctness and performance of our implementation. The conclusion suggests possible further improvements in the areas of independent time steps and particle softening lengths.