Boundary element simulation of fully three-dimensional bubble dynamics.

Abstract

A three‐dimensional boundary element method is presented for simulating bubble dynamics in incompressible, inviscid fluids (such that the fluid velocity is the gradient of a potential). The method is applied to simulate the migration and collapse of bubbles near rigid boundaries. The motivation is to model multiple cavitation bubble interactions near the hard surfaces of kidney stones that occur in shock‐wave lithotripsy. In order to accurately compute the fluid velocity, the method employs a novel curvilinear representation of the bubble geometry that enforces the global continuity of the unit normal vector. Contrary to the axisymmetric setting, the global continuity of the derivative of the parametrization, known as C1 continuity, cannot be enforced. Enforcing the continuity of the unit normal, known as G1 continuity, guarantees that the surface gradient of the velocity potential is orthogonal to the normal vector and enables a more accurate computation of the total gradient. The presentation concludes with several movies showing the simulated bubble migration and collapse, which are in good agreement with other known simulations (that assume axisymmetry) and experimentally obtained photographs. Results for multiple‐bubble scenarios in non‐axisymmetric configurations will also be presented. [Work supported by the ARL:UT Postdoctoral Fellow Program and NIH DK070618.]