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We investigate the effect of numerical magnetic diffusion inmagnetohydrodynamic simulations of magnetically supported molecular clouds. Tothis end, we have performed numerical studies on adaptive mesh isothermalsimulations of marginally sub-critical molecular clouds. We find thatsimulations with low and intermediate resolutions collapse, contrary to what istheoretically expected. However, the simulation with the highest numericalresolution oscillates around an equilibrium state without collapsing. In orderto quantify the numerical diffusion of the magnetic field, we ran a second suitof current-sheet simulations in which the numerical magnetic diffusioncoefficient can be directly measured, and computed the corresponding diffusiontimes at various numerical resolutions. On this basis, we propose a criterionfor the resolution of magnetic fields in MHD simulations based on requiringthat the diffusion time to be larger than the characteristic timescale of thephysical process responsible for the dynamic evolution of the structure.

A resolution criterion based on characteristic timescales for MHD simulations of molecular clouds