Numerical modeling of Kelvin-Helmholtz instability using smoothed particle hydrodynamics

This paper presents a Smoothed Particle Hydrodynamics (SPH) solution for the Kelvin-Helmholtz Instability (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 independently 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 congruent to 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 (C) 2011 John Wiley & Sons, Ltd.