Numerical Simulations of Shock-Bubble Interactions Using an Improved Ghost Fluid Method

The present work is concerned with numerical simulations for the shock-bubble interactions using the Ghost Fluid Method (GFM) in which the interface is captured with level set methods. The GFM is applied to the interactions between an air shock wave and a cylindrical or spherical helium bubble to investigate the numerical diffusion in the reinitialization procedure of the level set function. It is shown that the interface is not captured accurately using the GFM without the reinitialization of the level set function. The numerical diffusion in the reinitialization procedure affects the formation of a re-entrant jet and vortex structures after a shock wave impacts the bubble. It is also shown that the results with the hybrid particle level set method agree with the experiments by Haas and Sturtevant. The hybrid particle level set method is superior in the mass conservation. Also, we have improved the GFM by correcting velocities, pressure and density at boundary nodes using the Riemann solutions to avoid numerical oscillations near the gas-liquid interface. We have succeeded in capturing the sharp interface for the shock-air bubble interaction in water by using the improved GFM coupling with the hybrid particle level set method. Mass conservation in the hybrid particle level set method is better than that in the standard level set method with high order discretization scheme.