A numerical method for three-dimensional gas–liquid flow computations

A numerical method for multiphase flow computations based on a finite-difference formulation with a fixed grid is described. The method combines ideas from front tracking and the Ghost Fluid Method, with a numerical technique for velocity extrapolation near the interface. It is shown that the method is able to solve three-dimensional free-surface flow problems with an incompressible liquid and a compressible gas maintaining the interface sharp. Numerical results are compared with numerical solutions of the Rayleigh–Plesset equation for the free oscillation of a gas bubble, and independent front-tracking results for buoyant bubbles. Finally, the effects of an imposed sinusoidal liquid flow on a gas bubble are investigated.