Numerical simulation of evolution of a gas bubble in a liquid near a wall

A numerical technique based on application of the boundary element method is proposed for studying the axially symmetric dynamics of a bubble in a liquid near a solid wall. It is assumed that the fluid is ideal incompressible, its flow is potential. The process of expansion and contraction of a spheroidal bubble is considered, including the toroidal phase of its movement. The velocity and pressure fields in the liquid surrounding the bubble are evaluated along with the shape of the bubble surface and the velocity of its displacement. The numerical convergence of the algorithm with increasing the number of the boundary elements and refining the time step is shown, a comparison with experimental and numerical results of other authors are performed. The capabilities of the technique are illustrated by solving a problem of collapse, in water, of a spheroidal bubble located a short distance from the wall.