A high-order projection method for tracking fluid interfaces in variable density incompressible flows

We present a numerical method for computing solutions of the incompressible Euler or Navier-Stokes equations when a principal feature of the flow is the presence of an interface between two fluids with different fluid properties. The method is based on a second-order projection method for variable density flows using an open-quotes approximate projectionclose quotes formulation. The boundary between the fluids is tracked with a second-order, volume-of-fluid interface tracking algorithm. We present results for viscious Rayleigh-Taylor problems at early time with equal and unequal viscosities to demonstrate the convergence of the algorithm. We also present computational results for the Rayleigh-Taylor instability in air-helium and for bubbles and drops in an air-water system without surface tension to demonstrate the behavior of the algorithm on problems with large density and viscosity contrasts. 64 refs., 5 figs