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 rt 1 = ? (ru) 5 0, (1) feature of the flow is the presence of an interface between two fluids with different fluid properties. The method is based on a where u denotes the fluid velocity. To obtain high-order second-order projection method for variable density flows using an accuracy one typically approximates solutions of (1) with ‘‘approximate projection’’ formulation. The boundary between the fluids is tracked with a second-order, volume-of-fluid interface an advection algorithm that is high-order in smooth regions tracking algorithm. We present results for viscious Rayleigh–Taylor and subject to some sort of monotonicity constraint (e.g., problems at early time with equal and unequal viscosities to demonsee [6, 14, 30]). This approach has been successfully used strate the convergence of the algorithm. We also present computaby Bell and Marcus to study a variety of problems [7, 32]. tional results for the Rayleigh–Taylor instability in air-helium and for The primary advantages of this approach are that it is easy bubbles and drops in an air–water system without surface tension to demonstrate the behavior of the algorithm on problems with large to implement and no additional algorithmic details are density and viscosity contrasts. Q 1997 Academic Press required to model topological changes of the interface. However, the front diffuses over several computational zones, resulting in a corresponding loss of accuracy (see,