SUMMARYIn this paper, pressure stability through the suppression of high-frequency pressure oscillations in the moving particle semi-implicit (MPS) method is presented. To obtain a stable pressure field, we improve the freesurface particle search algorithm. Pressure stability follows from the suppression of high-frequency pressure oscillations due to a correction in the Laplacian operator of the Poisson pressure equation and from the correction of the pressure gradient operator. The three proposed modifications are applied gradually and compared with the MPS method to show the improvements in the hydrostatic pressure and dam-breaking problems. To validate the suppression of the high-frequency numerical pressure oscillations, modified MPS methods with and without a removable wall are compared with published dam-breaking experiment pressure measurements.

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.

A model with interparticle inharmonic interaction under the 4 external potential is studied. Making use of the special relation of relevant parameters, in the continuous limit, it was possible to obtain various non-classical soliton solutions, specifically, compact and peak-like solutions. The solutions undergo a jump on their first derivatives at some points of the space-time manifold. These analytic solutions were obtained by considering strong restrictions on their velocities and on the jump conditions. The energy concentrated in these solutions shows in several cases a discrete spectrum.

No abstract

No abstract