Investigation on the dynamics of air-gun array bubbles based on the dual fast multipole boundary element method

• A dual fast multipole boundary element method (FMBEM) was used to simulate air-gun array bubbles.
• The efficiency of dual FMBEM exceeds the conventional BEM greatly with almost no accuracy lost.
• The details of each bubble in the air-gun array are simulated precisely in large-scale problems.
• New dynamic behavior of the 3-D air-gun array bubbles subjected to the gravity effect is analyzed.

The air-gun array has important applications in ocean engineering. In this work, new dynamic behaviors of the air-gun array bubbles were investigated. The new adaptive fast multipole boundary element method (FMBEM) was implemented to accelerate the calculation of large scale moving boundary problems. The dual boundary integral equation (BIE) with an optimal linear combination of the regular BIE and the gradient BIE was used to facilitate a faster convergent FMBEM. It has been verified that the accuracy of the present numerical model was satisfactory for the dynamic simulation and the overall computational cost was scaled to O(N1.1)O(N1.1) with N being the number of unknowns, which surpassed the conventional BEM largely. The behavior of air-gun array bubbles was studied for different distribution forms of the air-guns with the gravity effect considered. By increasing the dimensions of the bubble array, it can be seen that the “shield effect” of outer bubbles on inner bubbles was more evident. Pressure gradient was the dominant factor that determined the re-entrant jet's direction. The period of bubble array was longer if array scale increased. The distance between bubbles versus the intensity of interaction effect has been studied. In addition, the evolutions and the movements of the bubbles are quite different in this kind of large scale problem.