Comparison of frequency domain and time domain methods for the numerical simulation of contactless ultrasonic cavitation

Time-Dependent Numerical Modelling of Acoustic Cavitation in Liquid Metal Driven by Electromagnetic Induction

“…This is at least 10 times longer than the time interval in the presented example. One option for improving the computational performance of the time-dependent method is using a truncated, approximate calculation of the bubble collapse and simultaneously parallelising the ODE solution [9]. This is suit-able for obtaining also full three-dimensional results with more than 200,000 computational cells within comfortable parameter optimisation computing time and sufficient FFT accuracy.…”

“…This assumption is justified by the fact that the acoustic time step is already sufficiently small to resolve accurately both p and its temporal derivative. An alternative implementation where the bubble collapse is approximated in a way that avoids the need for extremely small timesteps has also provided useful results [9]. At the end of each ODE interval, the integral contribution of the Caflisch source term is calculated as…”

“…For three-dimensional domains (with many times more computational cells), the long running time may become an issue. An alternative approach to the ODE solution (with truncated bubble collapse resolution and parallel implementation) has been shown to provide useful results [9], and with that method the fuller 100 ms simulation for the examined two-dimensional case takes only 2 min. 1.…”

“…Mathematical, numerical, and computational modelling of electromagnetically induced acoustic cavitation is useful in two ways: it helps better understand the interrelations of the physical phenomena involved, and it can assist in tuning the multiple process parameters on which a successful application of the method depends. Traditionally, only the driving frequency is considered, and oscillation at any other frequency is assumed to be significantly attenuated by the action of the bubbles [7][8][9], which, indeed, is true for most practical cases and especially those where resonance at the driving frequency is sought. The alternative time-dependent modelling method attempts to include non-linearities and multiple frequencies in a single computation based on first principles-the governing equations of fluid motion in an acoustic approximation for liquid media.…”