A method to calculate a length and a shape of two--dimensional unsteady
supercavities past
slender wedges and around slender hydrofoils is developed. In case of
arbitrary time--dependence, the finite difference time discretization
is used. In each time step, the solution is constructed by the method of
integral equations. The variable supercavity length is found
by numerical solving the equation of the mass of gas in the cavity balance.
Examples of calculation of evolution of both the natural supercavity and
the ventilated cavity in cases of aperiodic time--dependence and sinusoidal
oscillation of hydrofoil are presented
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