Ultrasonic horn transducers are frequently used in applications of acoustic cavitation in liquids. It has been observed that if the horn tip is sufficiently small and driven at high amplitude, cavitation is very strong, and the tip can be covered entirely by the gas/vapor phase for longer time intervals. A peculiar dynamics of the attached cavity can emerge with expansion and collapse at a self-generated frequency in the subharmonic range, i.e. below the acoustic driving frequency. The term "acoustic supercavitation" was proposed for this type of cavitation Žnidarčič et al. (2014) [1]. We tested several established hydrodynamic cavitation models on this problem, but none of them was able to correctly predict the flow features. As a specific characteristic of such acoustic cavitation problems lies in the rapidly changing driving pressures, we present an improved approach to cavitation modeling, which does not neglect the second derivatives in the Rayleigh-Plesset equation. Comparison with measurements of acoustic supercavitation at an ultrasonic horn of 20kHz frequency revealed a good agreement in terms of cavity dynamics, cavity volume and emitted pressure pulsations. The newly developed cavitation model is particularly suited for simulation of cavitating flow in highly fluctuating driving pressure fields.