Kelvin-Helmholtz instability by SPH
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In this paper, we have modeled the Kelvin-Helmholtz Instability (KHI) problem of an incompressible two-phase immiscible ﬂuid in a stratiﬁed inviscid shear ﬂow with interfacial tension using Smoothed Particle Hydrodynamics (SPH) method. 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. 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 a two-phase ﬂuid ﬂow with various density ratios.