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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.

Tsunamis produce a wealth of quantitative data that can be used to improve tsunami hazard awareness and to increase the preparedness of the population at risk. These data also allow for a performance evaluation of the coastal infrastructure and observations of sediment transport, erosion, and deposition. The interaction of the tsunami with coastal infrastructures and with the movable sediment bed is a three-dimensional process. Therefore, for runup and inundation prediction, three-dimensional numerical models must be employed. In this study, we have employed Smoothed Particle Hydrodynamics (SPH) to simulate tsunami runup on idealized geometries for the validation and exploration of three-dimensional flow structures in tsunamis. We make use of the canonical experiments for long-wave runup for breaking and nonbreaking waves. The results of our study prove that SPH is able to reproduce the runup of long waves for different initial and geometric conditions. We have also investigated the applicability and the effectiveness of different viscous terms that are available in the SPH literature. Additionally, a new breaking criterion based on numerical experiments is introduced, and its similarities and differences with existing criteria are discussed.

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.