In this paper, a numerical wave tank with open relaxation boundary for wave simulation is presented under the framework of weakly compressible Smoothed Particle Hydrodynamics (SPH). The open relaxation boundary consists of open boundaries and relaxation particles. A relaxation function is applied for the relaxation particles which are placed between the inflow/outflow zone and the fluid domain. Open particles lie in the inflow/outflow regions to avoid kernel truncation. The open particles and relaxation particles can be created and deleted depending on the fluid motion around the open boundaries, and the properties of these particles can be obtained from theoretical resolution or by extrapolating within the domain. The model is validated by simulating a 2nd Stokes wave and wave runup on a beach. The results demonstrate that the present SPH model with open relaxation boundary works well in wave generation and absorption.


Smoothed particle hydrodynamics (SPH) is a numerical method originally developed for astrophysical modeling (Gingold and Monaghan, Lucy, 1977) and later adapted for free-surface flow simulations (Monaghan, 1994). In recent years, the application of SPH to engineering problems has had a steady increase. SPH is a Lagrangian and mesh-less method, which uses a series of particles carrying physical properties to describe computational fluid dynamics (Liu and Liu, 2010). The Lagrangian reference frame of SPH makes it useful in solving problems with large deformations and complex free surfaces (Ye et al., 2019).

In this regard, SPH has been successfully applied to a number of free-surface problems that involve wave simulation and wave structure interaction (Liu and Zhang, 2019, Gotoh etal., 2018). Bouscasse et al. (2013) described a complete algorithm able to compute fully coupled viscous water wave and solid interactions using a δ-SPH solver. Altomare et al (2017) presented a fully comprehensive SPH implementation of wave generation and active wave absorption for long-crested monochromatic and random waves using a piston-type wavemaker. Crespo et al. (2017) applied a GPU–accelerated SPH code ( DualSPHysics ) to simulate wave interaction with a floating offshore moored OWC device. It was demonstrated that the model was able to reproduce the water surface correctly inside the chamber. Meringolo et al. (2018) presented an analysis of the variation with time of mechanical and internal energies during wave generation, propagation and absorption. Zhang et al. (2018) applied SPH in the simulations of an oscillating wave surge converter (OWSC). The results demonstrated that the active power of a land hinged OWSC strongly depends on both the power take off damping coefficients and the wave periods. He et al. (2020) presented a numerical investigation of the solitary wave breaking over a slope by using a enhanced SPH model. Brito et al. (2020) presented a SPH model with nonlinear mechanical constraints for OWSC and analyzed the effect of the flap inertia.

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