Microbubble dynamics are associated with cavitation damage to pumps, turbines and propellers, as well as applications in biomedical ultrasonics, sonochemistry and cavitation cleaning. The compressible effects of liquid are essential, which are associated with acoustic radiation at the inception of a bubble and the end of collapse. Viscous effects are important for microbubbles. This thesis is concerned with microbubble dynamics in a viscous compressible liquid near a rigid boundary. The compressible effects are modelled by using the weakly compressible theory. The viscous effects are approximated using the viscous potential flow theory, because the flow field is characterised as being an irrotational flow in the bulk volume but with a thin viscous boundary layer at the bubble surface. Consequently, the phenomenon is modelled by using the boundary integral method. The numerical results are shown in good agreement with the Keller-Miksis equation, experiments and computations based on the Navier-Stokes equations. Numerical studies were carried out for microbubble dynamics near a rigid boundary as well as subject to an acoustic wave. The bubble oscillation, topological transform, jet development and penetration through the bubble and the energy of the bubble system are simulated and analysed regarding the compressible and viscous effects
