A High-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows
✍ Scribed by Elbridge Gerry Puckett; Ann S. Almgren; John B. Bell; Daniel L. Marcus; William J. Rider
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 415 KB
- Volume
- 130
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
density ) that satisfies an advection equation of the form
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
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. ᮊ 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, 269