Behind the iconic “pop!" accompanying the uncorking of a champagne bottle hides a gas flow of surprising complexity. Its modeling is made delicate by its supersonic nature, its interaction with the cork stopper, the eminently unsteady character of the flow escaping from the bottle, and the continuous change of the geometry of the computational flow domain due to the displacement of the cork. Our numerical simulations reveal the formation, evolution and dissipation of shock wave patterns during the first millisecond following cork popping. A first crown-shaped shock wave pattern develops radially, then followed by the formation of a detached shock wave, or bow shock, induced by the presence of the cork in the axial path of the supersonic gas. The numerical simulations correctly reproduce the position of the bow shock previously observed through high-speed imaging.