  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-discretised meshless 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 timescales for gravitational collapse, and therefore impact star
formation activity in more complex galaxy disc simulations.
