A new 3-D multi-fluid model with the application in bubble dynamics using the adaptive mesh refinement

Violent pulsating bubbles behave diversely in different circumstances. It is a multi-scale problem in both space and time. In 3-D problems, the numerical simulation is usually too expensive to implement in practice with a fixed grid. In this paper, a 3-D multi-fluid model is established based on the Eulerian finite element method and the adaptive mesh refinement technique to investigate the bubble evolution and its toroidal motion near a solid vertical wall. The mixture formula for compressible multi-fluid flow is adopted to ensure conservativeness. By means of the block-based adaptive mesh refinement, the accuracy and the efficiency of the simulation are well balanced. The present model is validated by comparing the results with an underwater explosion experiment and the existing numerical results. The results agree well and a fast convergence is observed. Then, several cases with different buoyancy parameters are simulated, and the toroidal bubble motion and their pressure load on the solid wall are analyzed. The bubble's motion exhibits complex physics, such as the formation of the crescent-shaped bubble, the air cushion effect during the jet penetration, and the nonlinear relationship between the jet impact pressure and the angle between the jet and the opposite bubble surface.