The direct numerical simulations are conducted for the backscattering of incident pressure waves from a bubble with the ghost fluid method in order to understand the formation of secondary cavitation in the high intensity focused ultrasound (HIFU). It is shown that the ratio of a bubble collapse time
t_{0} to a characteristic time of wave propagation
t_{s},
η =
t_{0}/
t_{s}, is an important determinant for generating negative pressure region by backscattering. When
η is of the order of 0.1, no negative pressures are generated around the bubble and the bubble collapses by the pressure increase due to the incident pressure wave. When
η is of the order of 1, negative pressures are generated and an impulse per unit area with negative values takes the minimum although the positive pressure wave by the bubble collapse, which arrives at the negative pressure region, would reduce the growth of incepted cavitation. Also, the collapse time of a bubble takes the minimum when
η = 0.733. When
η is of the order of 10, high negative pressures are generated in a relatively smaller volume during shorter duration, which may cause the inception of the secondary cavitation. We also evaluate a negative pressure volume
V_{th} and a duration of negative pressure
τ_{th} associated with cavitation inception. The results also show that the product of
V_{th} and
τ_{th}, which is an indicator of probability of cavitation inception in the classical homogeneous nucleation theory, takes the local maximum in terms of
η: A larger
V_{th}τ_{th} suggests a higher probability of cavitation inception.
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