LAUSR

The formation of molecular hydrogen (H$_2$) and carbon monoxide (CO) is sensitive to the volume and column density distribution of the turbulent interstellar medium. In this paper, we study H$_2$ and CO formation in a large set of hydrodynamical simulations of periodic boxes with driven supersonic turbulence, as well as in colliding flows with the \textsc{Flash} code. The simulations include a non-equilibrium chemistry network, gas self-gravity, and diffuse radiative transfer. We investigate the spatial resolution required to obtain a converged H$_2$ and CO mass fraction and formation history. From the numerical tests we find that H$_2$ converges at a spatial resolution of $\lesssim0.2$~pc, while the required resolution for CO convergence is $\lesssim 0.04$~pc in gas with solar metallicity which is subject to a solar neighbourhood interstellar radiation field. We derive two critical conditions from our numerical results: the simulation has to at least resolve the densities at which (1) the molecule formation time in each cell in the computational domain is equal to the dissociation time, and (2) the formation time is equal to the the typical cell crossing time. For both H$_2$ and CO, the second criterion is more restrictive. The formulae we derive can be used to check whether molecule formation is converged in any given simulation.