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Simulation of single mode Rayleigh–Taylor instability by SPH method

Abstract

A smoothed particle hydrodynamics (SPH) solution to the Rayleigh–Taylor instability (RTI) problem in an incompressible viscous two-phase immiscible fluid with surface tension is presented. The present model is validated by solving Laplace’s law, and square bubble deformation without surface tension whereby it is shown that the implemented SPH discretization does not produce any artificial surface tension. To further validate the numerical model for the RTI problem, results are quantitatively compared with analytical solutions in a linear regime. It is found that the SPH method slightly overestimates the border of instability. The long time evolution of simulations is presented for investigating changes in the topology of rising bubbles and falling spike in RTI, and the computed Froude numbers are compared with previous works. It is shown that the numerical algorithm used in this work is capable of capturing the interface evolution and growth rate in RTI accurately.

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Correspondence to M. Yildiz.

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Shadloo, M.S., Zainali, A. & Yildiz, M. Simulation of single mode Rayleigh–Taylor instability by SPH method. Comput Mech 51, 699–715 (2013). https://doi.org/10.1007/s00466-012-0746-2

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Keywords

  • Smoothed particle hydrodynamics (SPH)
  • Mesh free method
  • Projection method
  • Multi-phase flow
  • Interfacial flow
  • Rayleigh–Taylor instability (RTI)