A method to simulate unsteady multi-fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described. The flow field is discretized by a conservative finite difference approximation on a stationary grid, and the interface is explicitly represented by a separate, unstructured grid that moves through the stationary grid. Since the interface deforms continuously, it is necessary to restructure its grid as the calculations proceed. In addition to keeping the density and viscosity stratification sharp, the tracked interface provides a natural way to include surface tension effects. Both two-and three-dimensional, full numerical simulations of bubble motion are presented.

A method to simulate unsteady multi-fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described. The flow field is discretized by a conservative finite difference approximation on a stationary grid, and the interface is explicitly represented by a separate, unstructured grid that moves through the stationary grid. Since the interface deforms continuously, it is necessary to restructure its grid as the calculations proceed. In addition to keeping the density and viscosity stratification sharp, the tracked interface provides a natural way to include surface tension effects. Both two-and three-dimensional, full numerical simulations of bubble motion are presented.

The fully three-dimensional deformation of an interface between two fluids resulting from a Rayleigh–Taylor instability is studied numerically in the limit of weak stratification. The Navier–Stokes equations are solved by a finite difference method, and the interface is kept sharp by front tracking. The difference between the large-amplitude stages of flows initiated by two- and three-dimensional perturbations is discussed.

Full numerical simulations of three-dimensional flows of two or more immiscible fluids of different densities and viscosities separated by a sharp interface with finite surface tension are discussed. The method used is based on a finite difference approximation of the full Navier-Stokes equations and explicit tracking of the interface between the fluids. Preliminary simulations of the Rayleigh-Taylor instability and the motion of bubbles are shown.

The two-dimensional Kelvin-Helmholtz instability of a sheared fluid interface separating immiscible fluids is studied by numerical simulations. The evolution is determined by the density ratio of the fluids, the Reynolds number in each fluid, and the Weber number. Unlike the Kelvin-Helmholtz instability of miscible fluids, where the sheared interface evolves into well-defined concentrated vortices if the Reynolds number is high enough, the presence of surface tension leads to the generation of fingers of interpenetrating fluids. In the limit of a small density ratio the evolution is symmetric, but for a finite density difference the large amplitude stage consists of narrow fingers of the denser fluid penetrating into the lighter fluid. The initial growth rate is well predicted by inviscid theory when the Reynolds numbers are sufficiently high, but the large amplitude behavior is strongly affected by viscosity and the mode that eventually leads to fingers is longer than the inviscidly most unstable one.