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A high-order projection method for tracking fluid interfaces in variable density incompressible flows. (English) Zbl 0872.76065
Summary: We present a numerical method for computing solutions of the incompressible Euler or Navier-Stokes equations in 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.

76M20 Finite difference methods applied to problems in fluid mechanics
76V05 Reaction effects in flows
76B47 Vortex flows for incompressible inviscid fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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