Optimal Network (ON) method - A robust and accurate technique for Lagrangian tracking of bubbles and detecting fragmentation and coalescence

Bubbles play an important role in many natural phenomena and engineering applications. Tracking a large number of bubbles and detecting their fragmentation or coalescence are important and challenging for investigating bubble trajectories, residence times, and generation mechanisms.  In this work, we developed a novel technique called the Optimal Network (ON) method for the Lagrangian tracking of bubbles and detecting their time-evolution behaviors in multiphase flow simulations. The ON method is based on establishing a network of mappings between bubbles identified at adjacent time instants. The mappings are determined by selecting the minimum from a set of pseudo-distance errors, which are themselves based on constraints imposed on bubble position, velocity, and volume between adjacent time instants. The ON method is proven to be accurate and robust through extensive tests, including numerical inspection of the pseudo-distance errors and visual verification of over 16000 bubble events identified in simulated breaking waves. The accuracies for continuity, binary fragmentation, and binary coalescence are estimated to be 99.5%, 90%, 95%, respectively. The ON method is extensible to other dispersed structures, such as sea spray droplets or oil droplets.