Evolution of the density distribution in the orbital plane of Cygnus X-1 showing gradual decay of the high-density flow in the proximity of L₁ point. The left-hand side panel corresponds to the quasi-stationary solution representing the low/hard X-ray state of Cygnus X-1. The right-hand panel shows the outcome of the simulation when the new equilibrium is reached after adjusting the X-ray luminosity of the compact object to the level corresponding to the high/soft state. The central panel represents a transient state roughly in the middle of the transition. The time index in the upper right corner of each panel is expressed in units of P_orb. (This figure is available in colour in the electronic version of the paper.)