Solitary wave collisions by double-dam-broken simulations with the MPS method

Abstract

Purpose The paper aims to apply a modified version of the MPS method to a double-dam-breaking test in which high dispersion zones and high natural clusterization zones are present, such as when the water column collapses into two sides and the two solitary waves collide, respectively. Design/methodology/approach The work takes advantage of the mixed source term from the cheaper computational version of the moving particle semi-implicit (MPS) method to reduce one step from the MPS classical algorithm. The proposed test can be successfully simulated by applying modifications to the variance parameter in the Laplacian operator and gradient model. Findings The results show stable behavior in dispersion and clusterization zones. Also, the collision and merging produced by solitary waves was successfully simulated. Research limitations/implications The main limitation in this work was the development of a comparison between the obtained results and the simulations with the original cheaper computational version of the MPS, this limitation is due to the overestimation of inter particle repulsive forces from its gradient model. Practical implications The application of solitary waves is of paramount importance in a number of applications, and this stems from the fact that the interaction of solitary waves with ships and other floating structures could generate highly deformed and complex free surface flows. Social implications For future work, the modified version of the MPS method can be applied in flow over sill base simulations, in close and open channels, and in simulating breaking waves to determine impact pressures by using solitary wave propagation. Originality/value The simulation of interaction of large groups of particles as in the case when two solitary waves collide could cause severe instability problems in pressure, causing the computer analysis to stop. MPS classical algorithm takes into account an explicit step that, in this case, may provoke the problem. For this reason, the cheaper version of MPS method is used to correctly simulate solitary wave interactions.

Simulation of breaking waves on slope beaches integrating the MPS method into Iwagaki wave theory

“…The interaction radius used in this study is r 0 = 2.1l 0 , where l 0 is the initial distance between particles. The pressure gradient term used in this work is given by the formulation proposed by Sanchez-Mondragon [58], because it provides a stable approach for simulating solitary waves as it has been shown in Sanchez-Mondragon and Vazquez-Hernandez [59]. Moreover, in Sanchez-Mondragon [58], it is shown that this pressure gradient term reduces the overestimated interparticle pressure force magnitudes that are present in other pressure gradient (20) models.…”

“…The pressure gradient term used in this work is given by the formulation proposed by Sanchez-Mondragon [58], because it provides a stable approach for simulating solitary waves as it has been shown in Sanchez-Mondragon and Vazquez-Hernandez [59]. Moreover, in Sanchez-Mondragon [58], it is shown that this pressure gradient term reduces the overestimated interparticle pressure force magnitudes that are present in other pressure gradient (20) models. In the case of wavemakers, natural clusterization appears when the paddle moves forward to generate waves, so this pressure gradient term aids to maintain a stable simulation, that is, where d is the number of space dimensions, n 0 is the constant particle number density, and P i is the minimum value of P j neighboring particles, jmin =î .…”

“…The modified MPS method version by Sanchez-Mondragon and Vazquez-Hernandez [59] considers the mixed source term for the PPE developed by Tanaka and Masunaga [69] and Lee et al [44] (a schematic algorithm can be seen in Fig. 3), and an improved variance parameter of the Laplacian operator and a nonovervalued pressure gradient operator proposed by Sanchez-Mondragon [58]. This modified MPS method version was chosen since it demonstrated to be a simple yet where the symbol is the fluid density, t is the time, � ⃗ u is the fluid particle velocity vector, P is the fluid pressure, is the kinematic viscosity, and � ⃗ g is the external force, given by the gravitational acceleration body force vector term, � ⃗ g. The MPS method uses particle interaction models to represent differential operators from the governing equations (Eqs.…”

“…24 for the kernel function (Eq. 19) and the second term is the modification of the variance that depends on the velocity variance by Sanchez-Mondragon [58].…”

“…In this work, we make use of the version of the MPS method proposed by Sanchez-Mondragon and Vazquez-Hernandez [59] that has been tested previously on solitary waves interactions (also, model validations can be found on Sanchez-Mondragon [58]). The main goal of the work presented herein is to study cnoidal waves generation and their subsequent breaking into a slope beach, first by the linear wave approximation, where the piston, flap and hyperbolic wavemakers are taken into account.…”