The dynamics of three-dimensional underwater explosion bubble

The fluid is assumed to be inviscid and incompressible and the flow irrotational. A time-integration boundary-integral method is used to solve the Laplace equation for the velocity potential to calculate the shape and position of the bubble. To improve the accuracy of the solution, the high-order triangular elements with curved sides and surfaces defined by six nodes are used to discretize the boundary surface in this investigation. Meanwhile, the singularity of the double-layer potential is eliminated by recasting the principal-value integral of the double-layer potential when the influence coefficient matrix is calculated. The material velocity vector at any node can be obtained by the potential of adjacent nodes with an appropriate weighted method. Elastic mesh technique (EMT), which is a new mesh regulation technique, is further applied to maintain the regularity of the triangular-element mesh used to discretize the dynamic boundary surface during the evolution of explosion bubble(s). All these efforts make the present approach viable and robust, and which is validated by computations of several bubble dynamics problems. Numerical analyses are carried out for the evolution of a bubble near a free surface and the interaction of two bubbles with a floating structure near a free surface. The robustness of the algorithm is demonstrated through simulating bubble jets near a free surface producing sharp free surface spikes and bubble(s) collapsing nearby a floating structure close to a free surface.