Numerical simulation of the three-dimensional Rayleigh-Taylor instability

Hyun Geun Lee, Junseok Kim

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1466-1474
Number of pages9
JournalComputers and Mathematics with Applications
Issue number8
Publication statusPublished - 2013 Nov


  • Phase-field method
  • Projection method
  • Rayleigh-Taylor instability
  • Time-dependent pressure boundary condition

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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