INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng (2011) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nme.3149 Numerical modeling of Kelvin–Helmholtz instability using smoothed particle hydrodynamics M. S. Shadloo and M. Yildiz ∗, † Faculty of Engineering and Natural Sciences, Advanced Composites and Polymer Processing Laboratory, Sabanci University, 34956 Tuzla, Istanbul, Turkey SUMMARY This paper presents a Smoothed Particle Hydrodynamics (SPH) solution for the Kelvin–Helmholtz Insta- bility (KHI) problem of an incompressible two-phase immiscible fluid in a stratified inviscid shear flow with interfacial tension. The time-dependent evolution of the two-fluid interface over a wide range of Richardson number ( Ri ) and for three different density ratios is numerically investigated. The simulation results are compared with analytical solutions in the linear regime. Having captured the physics behind KHI, the effects of gravity and surface tension on a two-dimensional shear layer are examined inde- pendently and together. It is shown that the growth rate of the KHI is mainly controlled by the value of the Ri number, not by the nature of the stabilizing forces. It was observed that the SPH method requires a Richardson number lower than unity (i.e. Ri ∼ = 0.8) for the onset of KHI, and that the artificial viscosity plays a significant role in obtaining physically correct simulation results that are in agreement with analytical solutions. The numerical algorithm presented in this work can easily handle two-phase fluid flow with various density ratios. Copyright  2011 John Wiley & Sons, Ltd. Received 28 May 2010; Revised 4 January 2011; Accepted 11 January 2011 KEY WORDS: smoothed particle hydrodynamics (SPH); shear flow; two-phase flow; interfacial flows; surface tension; Kelvin–Helmholtz instability (KHI) 1. INTRODUCTION Flow instability at the interface between two horizontal parallel streams of different velocities and densities, with the heavier fluid at the bottom, is called the Kelvin–Helmholtz Instability (KHI). The KHI is induced by either velocity shear within a continuous fluid or a sufficiently large velocity difference across the interface of a multiphase fluid. The instability kicks in when the destabilizing effect of shear across the interface overcomes the stabilizing effect of stratification due to gravity and/or surface tension if it exists. The KHI manifests itself as a row of horizontal eddies (in the form of waves) aligned across the interface. These eddies or waves are referred to as main billows. There are several well-known natural situations where the KHI can be observed such as wind blowing over the ocean or water surface, a meteor entering the Earth’s atmosphere, the interface between the tails of comets and solar wind, or the interface between a liquid layer and a compressible gas, among others. ∗ Correspondence to: M. Yildiz, Faculty of Engineering and Natural Sciences, Sabanci University, 34956 Tuzla, Istanbul, Turkey. † E-mail: meyildiz@sabanciuniv.edu Copyright  2011 John Wiley & Sons, Ltd.