Abstract
We examine how three fundamentally different numerical hydrodynamics codes follow the evolution of an isothermal galactic disc with an external spiral potential. We compare an adaptive mesh refinement code (ramses), a smoothed particle hydrodynamics code (sphng), and a volume-discretized mesh-less code (gizmo). Using standard refinement criteria, we find that ramses produces a disc that is less vertically concentrated and does not reach such high densities as the sphng or gizmo runs. The gas surface density in the spiral arms increases at a lower rate for the ramses simulations compared to the other codes. There is also a greater degree of substructure in the sphng and gizmo runs and secondary spiral arms are more pronounced. By resolving the Jeans length with a greater number of grid cells, we achieve more similar results to the Lagrangian codes used in this study. Other alterations to the refinement scheme (adding extra levels of refinement and refining based on local density gradients) are less successful in reducing the disparity between ramses and sphng/gizmo. Although more similar, sphng displays different density distributions and vertical mass profiles to all modes of gizmo (including the smoothed particle hydrodynamics version). This suggests differences also arise which are not intrinsic to the particular method but rather due to its implementation. The discrepancies between codes (in particular, the densities reached in the spiral arms) could potentially result in differences in the locations and time-scales for gravitational collapse, and therefore impact star formation activity in more complex galaxy disc simulations.