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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.

MSC:
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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