To meet the design requirements for lightning protection on hypersonic vehicles, a numerical simulation method for lightning strike processes was developed. Under local thermodynamic equilibrium conditions, the thermodynamic and transport properties of air were calculated using the free energy minimization method. The effects of Joule heating, viscous radiation, short-wavelength thermal radiation, and the Lorentz force on the magnetic confinement of the lightning channel were considered. The development of the lightning channel, variations in the thermodynamic parameters of the channel, and the shock wave development process were investigated. The results show that the shock wave development process obtained from the numerical method aligns with experimental measurements. The shock wave velocity decay rate and overpressure decay rate match the theoretical predictions, with clear distinctions in shock wave attenuation characteristics before and after the transition point between strong and weak shocks. Additionally, the effects of thermal radiation, magnetic confinement, lightning discharge power, and discharge time on the lightning strike process were studied based on this method.