Abstract
A new numerical method based on the ghost fluid method was developed for compressible two-phase flows; the idea of adaptive mesh refinement with multigrid was implemented in the method. In the method, interpolation techniques between multiple grids near interfaces were also proposed. The present techniques are effective in diminishing the numerical instability caused by the discontinuity of physical variables across the interfaces. The bubble collapse induced by the interaction of an incident shock with a gas bubble in water was simulated with the present multigrid ghost fluid method. We have succeeded in capturing the fine interface and vortex structure during the collapsing and rebounding stage. The mass conservation is improved with the adaptive mesh refinement combined with the hybrid particle level set method. Also, the interaction of an incident shock wave with a gas bubble near a deformable boundary was simulated successfully with the method in which the motions of three phases, i.e., the gas inside the bubble, the ambient liquid, and the wall material, are taken into consideration.
