A COMPARISON OF BOUNDARY INTEGRAL METHODS FOR STUDYING THE MOTION OF A 2-DIMENSIONAL BUBBLE IN AN INFINITE FLUID

Boundary integral methods for solving the problem of a two-dimensional bubble in an infinite fluid are introduced and compared. It is found that there is very little difference between Green's formula, dipole and vortex methods, but that the source method breaks down very early on. By numerically calculating the growth of perturbations on a bubble, the stability of the methods is examined. This reveals a marked difference in stability between Green's method and the two other successful methods. The physical stability of the bubble is also studied and compared with the numerical findings.