ALTAI: computational code for the simulations of TeV air showers as observed with the ground-based imaging atmospheric Cherenkov telescopes

Ground-based atmospheric Cherenkov telescopes are proven to be effective instruments for observations of very high-energy (VHE) γ-radiation from celestial objects. For effective use of such technique one needs detailed Monte Carlo simulations of γ-ray- and proton/nuclei-induced air showers in the Earth atmosphere. Here we discuss in detail the algorithms used in the numerical code ALTAI developed particularly for the simulations of Cherenkov light emission from air showers of energy below 50 TeV. The specific scheme of sampling the charged particle transport in the atmosphere allows the performance of very fast and accurate simulations used for interpretation of the VHE γ-ray observations.