Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 66, Issue 8, Pages 1466-1474Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2013.08.021
Keywords
Rayleigh-Taylor instability; Phase-field method; Projection method; Time-dependent pressure boundary condition
Categories
Funding
- National Research Foundation of Korea (NRF)
- Ministry of Education [2009-0093827, 2012R1A6A3A01019827]
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The Rayleigh Taylor instability is a fundamental instability of an interface between two fluids of different densities, which occurs when the light fluid is pushing the heavy fluid. During the nonlinear stages, the growth of the Rayleigh Taylor instability is greatly affected by three-dimensional effects. To investigate three-dimensional effects on the Rayleigh Taylor instability, we introduce a new method of computation of the flow of two incompressible and immiscible fluids and implement a time-dependent pressure boundary condition that relates to a time-dependent density field at the domain boundary. Through numerical examples, we observe the two-layer roll-up phenomenon of the heavy fluid, which does not occur in the two-dimensional case. And by studying the positions of the bubble front, spike tip, and saddle point, we show that the three-dimensional Rayleigh Taylor instability exhibits a stronger dependence on the density ratio than on the Reynolds number. Finally, we perform a long time three-dimensional simulation resulting in an equilibrium state. (C) 2013 Elsevier Ltd. All rights reserved.
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