Analysis of the incompressibility constraint in the Smoothed Particle Hydrodynamics method

Smoothed particle hydrodynamics is a particle-based, fully Lagrangian, method for fluid-flow simulations. In this work, fundamental concepts of the method are first briefly recalled. Then, we present a thorough comparison of three different incompressibility treatments in SPH: the weakly compressible approach, where a suitably-chosen equation of state is used; and two truly incompressible methods, where the velocity field projection onto a divergence-free space is performed. A noteworthy aspect of the study is that, in each incompressibility treatment, the same boundary conditions are used (and further developed) which allows a direct comparison to be made. Problems associated with implementation are also discussed and an optimal choice of the computational parameters has been proposed and verified. Numerical results show that the present state-of-the-art truly incompressible method (based on a velocity correction) suffer from density accumulation errors. To address this issue, an algorithm, based on a correction for both particle velocities and positions, is presented. The usefulness of this density correction is examined and demonstrated in the last part of the paper

ISPH modeling of Rayleigh–Taylor instability

This paper presents a Smoothed Particle Hydrodynamics (SPH) solution to a Rayleigh-Taylor Instability (RTI) problem in an incompressible viscous two-phase immiscible fluid with an interfacial tension. The evolution of the fluid-fluid interface is numerically investigated for four different density ratios. The simulation outcomes are compared with existing results in literature. Three stages of instability, namely the exponential growth rate, the formation of circular form at the crest of spike and the appearance of the final shape of instability, are discussed for different density ratios. It is shown that the numerical algorithm used in this work is capable of capturing the complete physics behind the RTI, such as interface evolution, growth rate and secondary instability accurately, and successfully

Numerical simulation of single droplet dynamics in three-phase flows using ISPH

In this study, a new surface tension formulation for modeling incompressible, immiscible three-phase fluid flows in the context of incompressible smoothed particle hydrodynamics (ISPH) in two dimensions has been proposed. A continuum surface force model is employed to transform local surface tension force to a volumetric force while physical surface tension coefficients are expressed as the sum of phase specific surface tension coefficients, facilitating the implementation of the proposed method at triple junctions where all three phases are present. Smoothed color functions at fluid interfaces along with artificial particle displacement throughout the computational domain are combined to increase accuracy and robustness of the model. In order to illustrate the effectiveness of the proposed method, several numerical simulations have been carried out and results are compared to analytical data available in literature. Results obtained by simulations are compatible with analytical data, demonstrating that the ISPH scheme proposed here is capable of handling three-phase flows accurately