The bubble radii within a bubble cluster typically distribute over a wide range, and bubble dynamics under acoustic excitation are strongly dependent on the radius. To accurately predict the oscillation behaviour of the bubble cluster and the propagation of acoustic waves, it is necessary to divide the bubble cluster into groups and calculate the dynamics of each group separately. Increasing the number of groups improves the prediction accuracy at the expense of greater computational cost. In this study, bubble clusters were categorized based on three criteria: equal radius intervals per group (Equal-ΔR method), equal scattering cross-section coefficients (Equal-σs method), and equal scattering pressure (Equal-ps method). The prediction accuracy of these three grouping methods was compared using a grouped homogeneous model. Furthermore, for linear oscillations, the equivalent radius and number density of each group were determined by incorporating the linear solution of the bubble dynamics equation, based on which the grouping method was improved. For nonlinear oscillations, the grouping method was improved using fitting solutions derived from numerical results of the bubble dynamics equation. Simulation results demonstrate that the Equal-ps method achieves the highest accuracy among the three methods. For linear oscillations, the relative root mean square error (RRMSE) for a 5-group division is between 2–3%, which drops below 0.42% after the improvement. For nonlinear oscillations, the RRMSE were respectively below 0.88% and 0.63% for 3-group and 5-group divisions. This study provides an efficient grouping method for the numerical prediction and theoretical analysis of bubble cluster dynamics and acoustic scattering.
Ye et al. (Tue,) studied this question.