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In this study, we have introduced two new iterative density-based Smoothed Particle Hydrodynamics (SPH) methods to model incompressible flows, namely, preconditioned dual time-stepping, and augmented Lagrangian method. The performance of these new methods are compared with each other and also with a modified version of the well-known weakly compressible SPH (WC-SPH) method through solving three carefully chosen incompressible flow problems: a laminar incompressible channel flow over a backward-facing step, a 2D stiff pressure decay problem and Taylor-Green vortices flow. For the first test problem, the results are compared with available data in literature. Moreover, it is observed that the two iterative methods provide a better accuracy in terms of smoother pressure field and also smaller magnitude of the velocity divergence across the computational domain. In the second test problem, it is shown that the preconditioned dual time-stepping and the augmented Lagrangian SPH methods yield rather smooth pressure fields, and converge to the exact solution, while the pressure field computed by the WC-SPH method oscillates even after very long time. As for the third test case, the iterative methods are compared with WC-SPH method for different iteration numbers and particle resolutions. (C) 2019 Elsevier Ltd. All rights reserved.

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.