Abstract A two-dimensional cylindrically symmetric model is developed to study the streamer-less spark formation in a short gap on the timescale of ion motion. It incorporates the coupling between the electric discharge and the gas through the heat generated by the discharge and the consecutive gas expansion. The model is employed to study electrical breakdown in supercritical N 2 . We present the simulation results of gas heating by the electrical discharge and the effect of gas expansion on the electrical discharge.