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 “approximate projection” 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.