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In this paper, Smoothed Particle Hydrodynamics (SPH) is used to simulate the propagation of waves in an intermediate depth water channel. The major advantage of using SPH is that no special treatment of the free surface is required, which is advantageous for simulating highly nonlinear flows with possible wave breaking. The SPH method has an option of different formulations with their own advantages and drawbacks to be implemented. Here, we apply the classical and Arbitrary Lagrange–Euler (ALE) formulation for wave propagation in a water channel. The classical SPH should come with an artificial viscosity which stabilizes the numerical algorithm and increases the accuracy. Here, we will show that the use of classical SPH with an artificial viscosity may cause the waves in the channel to decay. On the other hand, we will show that using the ALE-SPH algorithm with a Riemann solver is more stable, and in addition to producing the pressure fields with much less numerical noise, the waves propagate in the channel without dissipation.

This paper studies a two-dimensional incompressible viscous flow past a circular cylinder with in-line oscillation close to a free-surface. The sub-particle scale (SPS) turbulence model of a Lagrangian particle-based smoothed-particle hydrodynamics (SPH) method has been used to solve the full Navier–Stokes equations together with the continuity equation. The accuracy of numerical code has been verified using two cases consisting of an oscillating cylinder placed in the stationary fluid, and flow over a fixed cylinder close to a free-surface. Simulations are conducted for the Froude number of 0.3, the Reynolds numbers of 40 and 80, various gap ratios for fully-submerged and half-submerge cylinders. The dimensionless frequency and amplitude of oscillating have been chosen as 0.5, 0.8 and 10, 15, respectively. The selection of such a high oscillating frequency causes the flow regime to become turbulent. It is seen that the gap ratio defined as the ratio of cylinder distance from free-surface and its diameter, strongly affects the flow pattern and the magnitude of the drag and lift coefficients. The jet-like flow (the region above the cylinder and beneath the free-surface) creation is discussed in detail and showed that the strength of this jet-like flow is weakened when the gap ratio shrinks. It is seen that by decreasing the gap ratio, the lift and drag coefficients increase and decrease, respectively. It is found that the Reynolds number has an inverse effect on the drag and lift coefficients. Also, it is concluded that by increasing the amplitude of oscillation the drag coefficient increases.

Different permutations of the single and the two-fold dam-break flow have been investigated using the mesh-free smoothed-particle hydrodynamics and the experimental setup. The free-surface deformation in the case with the wet bed for five different downstream water heights has been investigated and respective numerical and experimental results were presented. The results demonstrate that the increase of the water height over the wet bed leads to the reduction of the flow front velocity. Effect of considering or omitting the dam gate during the numerical simulation has also been examined, which proves that the simulations including the dam gate show improved agreement with the experimental results. Influence of the three-dimensional cubic, triangular, circular and square cylindrical obstacles and their position on flow characteristics has been investigated. As the distance between the triangular obstacle and the gate increases, a bore is created at the position closer to the top of the triangle. In addition, it is found that larger force is exerted on the circular cylinder in comparison to the square cylinder.

The present work is dedicated to the modeling of viscous flow past a NACA0012 foil fixed in a current below a free surface. To this end, the ${\delta }^{+}$-smoothed-particle hydrodynamics (SPH) model has been adopted. This SPH model prevents the inception of the numerical tensile instability in the flow region characterized by negative pressure since a tensile instability control (TIC) has been included. In the TIC, a pressure differencing formulation (PDF) has been adopted for the momentum equation in the flow region characterized by negative pressure. In order to completely remove the numerical noise in the vorticity field, in this work, the PDF is also applied for the region with positive pressure, but except for the free-surface region in order to ensure the free surface stability when wave breaking occurs. The mechanism of PDF being able to eliminate the numerical noise in the vorticity field is also briefly analyzed. In order to reduce the nonconservation of total momentum induced by the PDF, a particle-shifting technique (PST) is implemented in each time step for regularizing the particle position. In the numerical results, ${\delta }^{+}$-SPH results are validated by the experimental data and other verified numerical results. Improvements of the results of ${\delta }^{+}$-SPH with PDF with respect to the ones without using PDF are demonstrated. Parametrical studies based on the ${\delta }^{+}$-SPH model regarding the breaking and non-breaking waves generated by the flow past a submerged foil are also carried out.