Framework and computational model of bubble dynamics under water

Bubble dynamics under water is significant for both life and engineering applications since 71% of the Earth is covered by water. In this paper, the classical models of bubble dynamics are reviewed and analyzed, and we propose an advanced model, named the Adeba–Fan model; meanwhile, the framework and computational methods are illustrated. The Adeba–Fan model systematically incorporates the key physical mechanisms—shock wave propagation, thermal conduction, evaporation and condensation, viscosity, surface tension, compressibility, and gravitation—within a unified framework, ensuring applicability across all scenarios. A central feature of the model is the use of retarded time corrections, which refine the velocity potential and pressure formulations to consistently capture finite wave propagation effects. The theoretical formulation, based on the fundamental conservation laws of mass, momentum, and energy, ensures a consistent representation of the underlying physics, while detailed mathematical derivations and computational methods are presented. The model is capable of simulating spherical bubble behavior in an incompressible–compressible fluid across diverse input energy scales and fluid depths. Validation via experimental data and theoretical benchmarks, including laser-induced cavitation and underwater explosions at various water depths, demonstrates its superior accuracy in capturing bubble growth, collapse, rebound, shockwave interactions, and thermal effects. A Comparative analysis with existing models highlights its advantages in prediction accuracy, application range, and computational efficiency. Therefore, the Adeba–Fan model advances the study of bubble dynamics under water and provides a robust tool for applications in marine engineering, industrial cavitation, and underwater explosion analysis.