BEM-based numerical study of three-dimensional compressible bubble dynamics in stokes flow

The dynamics of compressible gas bubbles in a viscous shear flow and an acoustic field at low Reynolds numbers is studied. The numerical approach is based on the boundary element method (BEM), which is effective as applied to the three-dimensional simulation of bubble deformation. However, the application of the conventional BEM to compressible bubble dynamics faces difficulties caused by the degeneration of the resulting algebraic system. Additional relations based on the Lorentz reciprocity principle are used to cope with this problem. Test computations of the dynamics of a single bubble and bubble clusters in acoustic fields and shear flows are presented.