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A study of transient flows with interfaces using numerical solution of Navier-Stokes equations. (English. Russian original) Zbl 1475.76100

Fluid Dyn. 55, No. 3, 314-322 (2020); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2020, No. 3, 26-35 (2020).
Summary: Flows of two immisible fluids are considered taking into account the capillary and gravity forces. The flow is described using a viscous incompressible fluid model within a two-dimensional formulation. The Navier-Stokes equations are solved numerically by an extended finite-element method, which allows for the presence of a strong discontinuity on the interface. The interface location is tracked using the level set method. This approach makes it possible to study flows with a varying topology of the interface. The calculation results are presented for the problems of a rising 2D bubble, development of the Rayleigh-Taylor instability, and a film flowing down a vertical wall in an extended region.

MSC:

76T06 Liquid-liquid two component flows
76D05 Navier-Stokes equations for incompressible viscous fluids
76E17 Interfacial stability and instability in hydrodynamic stability
76A20 Thin fluid films
76M10 Finite element methods applied to problems in fluid mechanics
76M99 Basic methods in fluid mechanics
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