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The Rayleigh–Taylor instability (RTI) problem is one of the classic hydrodynamic instability cases in natural scenarios and industrial applications. For the numerical simulation of the RTI problem, this paper presents a multiphase method based on the moving particle semi-implicit (MPS) method. Herein, the incompressibility of the fluids is satisfied by solving a Poisson Pressure Equation (PPE) and the pressure fluctuation is suppressed. A single set of equations is utilized for fluids with different densities, making the method relatively simple. To deal with the mathematical discontinuity of density in the two-phase interface, a transitional region is introduced into this method. For particles in the transitional region, a density smoothing scheme is applied to improve the numerical stability. The simulation results show that the present MPS multiphase method is capable of capturing the evolutionary features of the RTI, even in the later stage when the two-phase interface is quite distorted. The unphysical penetration in the interface is limited, proving the stability and accuracy of the proposed method.

In the present study, the moving particle semi-implicit (MPS) method and finite element method (FEM) coupled method is developed for the 3D fluid–structure interaction (FSI) problems. Herein, the MPS method is employed for the simulation of fluid domain while the FEM approach is used for the analysis of structural domain. For the implementation of the coupled approach, we proposed a mapping algorithm to transfer quantity values between the particles of flow field and the elements of structural field. In this mapping algorithm, the nonmatching refinement levels of both domains are permitted, which implies that the much larger size of element can be used in the FSI simulation and the computational efficiency can be improved. With the benefit of the proposed MPS–FEM coupled method, the 3D FSI problem of dam-break flow impacting onto the flexible wall is numerically investigated. The evolutions of free surface and the impacting loads on the wall are compared against those regarding rigid tank. In addition, the deformation and the strength behaviors of the flexible wall are exhibited.

In this paper, numerical improvements are implemented for solving for the pressure in the moving particle semi-implicit (MPS) method for free-surface flow simulations. The tensile instability problem is solved using a dynamic stabilization (DS) algorithm. The low numerical diffusion of this algorithm is shown through numerical tests. A free-surface treatment that includes an accurate free-surface particle detection algorithm and the implicit application of a free-surface boundary condition is used. The solution of the Navier–Stokes equation is improved using a particle shifting (PS) algorithm. The proposed MPS method for free-surface flow simulations is successfully applied in several benchmark tests and two- and three-dimensional dam break problems. The numerical simulation results agree well with the analytical and empirical ones. It is shown that the proposed MPS method effectively improves the stability and accuracy of simulations of free-surface flows.

In this paper, the explicit solving of pressure Poisson equation and GPU parallelization were employed to improve the efficiency of MPS method, which is one of the mainstream particle methods. The performance of the explicit GPU parallel MPS method is discussed using two-dimensional dam-break and sloshing problems. The reliability and accuracy of the developed algorithm were validated against the results of traditional implicit solving method (based on GMRES) and experiment. In terms of efficiency improvement, compared with the traditional CPU-based serial solver, the explicit GPU-parallelized algorithm greatly reduces the computational time of the pressure Poisson equation. More specifically, the maximum acceleration ratios of 11.486 and 13.89 can be obtained by numerical simulation for 2D dam-break and sloshing problems with different particle numbers.

A particle method, or a gridless Lagrangian method, shows the high performance in describing the complicated behavior of water surface with the fragmentation and coalescence of water. In this paper, a wave overtopping process on a vertical seawall is numerically simulated on the basis of the Navier–Stokes equation with surface-tension term, which is discretized by the MPS (moving particle semi-implicit) method belonging to the category of the particle method. An improvement of the listing process of neighboring particle is introduced to reduce the computational load. Wave overtopping process in the experiments are well reproduced by the MPS method. The predictions of the MPS method of the overtopping volume agree well with the experimental results.

A Corrected Moving Particle Semi-implicit (CMPS) method is proposed for the accurate tracking of water surface in breaking waves. The original formulations of standard MPS method are revisited from the view point of momentum conservation. Modifications and corrections are made to ensure the momentum conservation in a particle-based calculation of viscous incompressible free-surface flows. A simple numerical test demonstrates the excellent performance of the CMPS method in exact conservation of linear momentum and significantly enhanced preservation of angular momentum. The CMPS method is applied to the simulation of plunging breaking and post-breaking of solitary waves. Qualitative and quantitative comparisons with the experimental data confirm the high capability and precision of the CMPS method. A tensor-type strain-based viscosity is also proposed to further enhanced CMPS reproduction of a splash-up.

A Lagrangian numerical simulation of breaking waves is performed by the moving particle semi-implicit (MPS) method, in which the Navier-Stokes equation is discritized based on the interaction of particles. The Eulerian numerical solvers of the Navier-Stokes equation with the volume of fluid (VOF) method have difficulties in the calculation of the free surface due to the existence of the numerical diffusion derived from the advection terms. To attenuate the numerical diffusion, the procedures of the calculation of the cells involving the free surface should be very complicated one in Eulerian models. While, the MPS method is free from the numerical diffusion, hence it can calculate the free surface clearly, even under the existence of the fragmentation and the coalescence of fluid. In this study, the breaking waves are simulated on the several bottom configurations, namely a uniform slope, a permeable uniform slope and a vertical wall with small step on its foot. The time series of the water surface profiles and the velocity fields are displayed to show the performance of the MPS method in the wave breaking simulations.