Memory-friendly fixed-point iteration method for nonlinear surface mode oscillations of acoustically driven bubbles:...

Area of Science:

• Acoustics
• Fluid Dynamics
• Nonlinear Dynamics

Background:

• Microbubble dynamics are crucial in various applications, but their nonlinear oscillations are complex to model.
• Existing models often struggle with the implicit nature of governing equations, limiting computational efficiency.

Purpose of the Study:

• To develop and validate a fixed-point iteration technique for analyzing nonlinear surface mode oscillations in acoustically excited microbubbles.
• To provide an efficient computational method for studying microbubble behavior under acoustic excitation.

Main Methods:

• A fixed-point iteration technique is applied to solve the implicit ordinary differential equations governing microbubble dynamics.
• The model extends the Keller-Miksis equation and incorporates nonlinear coupling between mean radius and surface modes.
• Only implicit terms involving second derivatives are reevaluated iteratively.

Main Results:

• The fixed-point iteration method achieves high accuracy (10^-9 error) with minimal reevaluations in most cases.
• The technique demonstrates robustness across various parameter combinations.
• Despite higher arithmetic operations than Gauss elimination, its matrix-free nature is memory-efficient.

Conclusions:

• The presented fixed-point iteration technique offers an efficient and accurate solution for nonlinear microbubble surface mode oscillations.
• Its memory-friendly approach makes it suitable for high-performance GPU computations in extensive parameter studies.
• This method advances the modeling capabilities for acoustically driven microbubble systems.