The effect of frequency on the characteristics of ac-driven breakdown processes in 0.7 bar argon is investigated by means of a two-dimensional fluid model. The geometry represents the high intensity discharge lamp burner with a pin–pin electrode system forming a 7mm electrode gap. The breakdown process is considered in the frequency range between 60 kHz and 1 MHz. The appearance of the discharge and the influence of the voltage frequency on its characteristics obtained in the simulations is in good agreement with the experimental data (accompanying paper—Sobota et al 2011 J. Phys. D: Appl. Phys. 44 224002, special issue on LS12/WLED3 symposium). The role of the secondary electron emission from the electrode surfaces is demonstrated and linked to the lowering of the threshold voltage with the increase in frequency observed both in experiment and model.