An improved boundary element formulation for the motion of spherical bubbles

We suggest a modified boundary element method for modeling the potential flow caused by the motion of many spherical bubbles. The problem for the fluid velocity potential is reduced to a Fredholm integral equation of the second kind. The kernel of that integral equation has no singularity; as a result, its numerical solution does not encounter any difficulties. The matrix representation of the integral equation is diagonally dominant and is well suited to handle multiple bubble system.