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The instability of an interface between two media after the passage of two shocks that follow one after the other at a certain time interval is studied numerically. A simple formula suggested earlier (Charakhch'yan 2000 Prikl. Mekh. Tekh. Fiz. 41 28-37) for reshocking a free aluminum surface is confirmed for shocks from aluminum to deuterium ice, from air to helium and from freon to air. The formula describes reshocking at the non-linear stage of the instability evolution and is independent both of the wavelength of the initial perturbation and of the perturbation amplitude at the moment of reshocking. Both a sinusoidal initial perturbation and a perturbation in the form of a broken line are considered. It is demonstrated that the parameters of the second shock that ensure the freezeout phenomenon are determined using only the amplitude growth rate before reshocking.

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