  Gas bubbles immersed in a liquid and flowing through a large pressure
gradient undergoes volumetric deformation in addition to possible deviatoric
deformation. While the high density liquid phase can be assumed to be an
incompressible fluid, the gas phase needs to be modelled as a compressible
fluid for such bubble flow problems. The Rayleigh--Plesset (RP) equation
describes such a bubble undergoing volumetric deformation due to changes in
pressure in the ambient incompressible fluid, assuming axisymmetric dynamics.
We propose a compressible-incompressible coupling of Smoothed Particle
Hydrodynamics (SPH) and validate this coupling against the RP model in two
dimensions. For different density ratios, a sinusoidal pressure variation is
applied to the ambient incompressible liquid and the response of the bubble is
observed and compared with the solutions of the axisymmetric RP equation.
