Original Moving Particle Semi-implicit Research Articles

Improved MPS models for simulating free surface flows

Two improved Laplacian models are introduced in this study for more accurate simulation of free surface flows in the context of the moving particle semi-implicit (MPS) method, a well-known mesh-less approach. The Euler equations are the governing equations of these flows without considering viscous forces which are solved in the Lagrangian frame by the MPS and two-step projection methods for spatial and temporal discretization, respectively. Considering the similarity between the MPS and SPH (smoothed particle hydrodynamics) methods, one of the introduced Laplacian models is formulated by a corrective matrix firstly proposed in an improved SPH method [28]. The other modified Laplacian model is also derived from the divergence of a newly developed MPS gradient model proposed for solving elasticity problems [33]. The higher accuracy of these methods compared to the classic SPH, MPS and even three modified SPH and MPS Laplacian models [7, 34, 44] is verified by solving 2D Poisson equations. Moreover, the excellent performance of the Laplacian models and the improved gradient model in obtaining smooth pressure field is validated by solving three benchmark free surface flows. Furthermore, the problem of wave damping in the original MPS computations can be resolved by using the applied models.

Solving 2-D Slamming Problems by an Improved Higher-Order Moving Particle Semi-Implicit Method

Abstract A higher-order moving particle semi-implicit (MPS) method was further developed to solve 2-D water entry problems. To overcome the inconsistency in the original MPS methods, a pressure gradient correction was implemented to guarantee the first-order consistency of the gradient. The corrective matrix was modified by using the derivative of the kernel function. A particle shifting technique was also applied to improve the numerical stability. Validation studies were carried out for water entry of a rigid wedge with the tilting angles of 0, 10, and 20, and two rigid ship sections. Convergence studies were conducted on domain size, particle spacing, and time step. A particle convergence index method was proposed to evaluate numerical uncertainties in the improved MPS method. Uncertainties in numerical solutions due to spatial discretization were calculated. The predicted impact pressures and forces by the present method are in good agreement with experimental data. Introduction Slamming can cause local structural deformation and damages. It is important to solve highly nonlinear water-entry problems involving breaking free surfaces. Many studies on the impact of pressures/ loads during water entry or slamming have been performed using experiments, analytical solutions, and numerical simulations. Extensive drop tests have been conducted. For example, Bisplinghoff and Doherty (1952) carried out a series of experiments for free-fall wedges. Because ship motions in waves can lead to asymmetric water entry, wedges with different tilt angles were tested by Barjasteh et al. (2016). A more detailed review of studies based on theoretical, potential-flow, and computational fluid dynamics (CFD) methods is presented in the work of Peng and Qiu (2018).

An improved higher-order moving particle semi-implicit method for simulations of two-dimensional hydroelastic slamming

An improved higher-order moving particle semi-implicit (MPS) method has been developed to solve the problem of fluid–structure interactions for an elastic wedge entering calm water. The structural responses of the wedge with a reinforced tip were computed during the water entry. In the present method, the pressure gradient is corrected to guarantee the first-order consistency and to satisfy the conservation of momentum. Different particle spacings are used for the fluid and the structure. Convergence studies were carried out on particle spacings for the fluid and the structure and on a time step. A particle convergence index method was applied to evaluate numerical uncertainties in the improved MPS method. Validation studies were carried out on two elastic wedges with deadrise angles of 30° and 20° entering water at various velocities. Numerical solutions were compared with the results from the original higher-order MPS method and experimental data. The improved higher-order MPS methods led to better agreement with experimental data than the original one and significantly reduced the oscillations in numerical solutions.

Numerical analysis of the nonlinear free surface flow around an advancing ship using moving particle semi-implicit method

This paper presents a methodology to simulate the nonlinear free surface flow around an advancing ship. This methodology is based on the Moving Particle Semi-implicit (MPS) method, which is widely used to simulate the incompressible fluid flow. In this paper, the original MPS method is modified in order to analyze effectively the nonlinear free surface flow around an advancing ship. Several treatment techniques are newly proposed, and the original MPS method is modified by combining these techniques with other previous research studies. The proposed techniques include the Laplacian compensation model in the region near the body boundary, the collision model between fluid particles and wall particles, and some treatments for the opened boundary. The accuracy of the modified MPS method is verified through the numerical simulations on two benchmark problems for the performance evaluation of the particle methods and on the flows around both the wedged body and model ship. The numerical results demonstrate that the modified MPS method can be effectively applied to the simulation of nonlinear free surface flow around an advancing ship in marine engineering.

Numerical simulation of solitary waves overtopping on a sloping sea dike using a particle method

Sea dikes, as a commonly used type of coastal protection structures, are often attacked or damaged by violent waves overtopping under tsunamis and storm surges. In this study, the behavior of solitary waves traveling on a sloping sea dike is simulated, and solitary wave overtopping characteristics are analyzed using a complete Lagrangian numerical method, the moving particle semi-implicit (MPS) method. To better describe the complicated fluid motions during the wave overtopping process, the original MPS method is modified by introducing a new free surface detection method, i.e., the area filling rate identification method, and a modified gradient operator to provide higher precision. Meanwhile, the approximation method for sloping boundaries in particle methods is enhanced, and a smooth slope approximation method is proposed and recommended. To verify the improved MPS method, a solitary wave traveling over a steep sloping bed is studied. The entire solitary wave run-up and run-down processes and exquisite water movements are reproduced well by the present method, and are consistent with the corresponding experimental results. Subsequently, the improved MPS method is applied to investigate the overtopping process of a single solitary wave over a sloping sea dike. The results show that the hydraulic jump phenomenon is also possible to occur during the run-down motion of the solitary wave overtopping. Finally, the characteristics of the propagation and overtopping of two successive solitary waves on a sloping sea dike are discussed. The result manifests that the interaction between adjacent solitary waves affects wave overtopping patterns and overtopping velocities.

The truncation and stabilization error in multiphase moving particle semi-implicit method based on corrective matrix: Which is dominant?

The Lagrangian nature of the moving particle semi-implicit (MPS) method brings two challenges: disordered particle distribution and particle clumping. The former can cause large random discretization error for the original MPS models while corrective matrix can effectively reduce such large error to the high-order truncation error. The latter can trigger instability easily and thus some adjustment strategies for stability are indispensable, thereby causing non-negligible stabilization error. The purpose of this paper is to compare the relative magnitude of the truncation and stabilization error, which is of great significance for future improvements. An indirect approach is developed because of the difficulty of separating different error from total error in dynamic simulations. The basic idea is to check whether the total error decreases significantly after the truncation error is further reduced. First, a second order corrective matrix (SCM) is proposed for MPS to reduce the truncation error further, as demonstrated by theoretical error analysis. Second, error analysis reveals that the first order gradient model produces less numerical diffusion than the second order gradient model in interpolation after particle shifting. Then, several numerical examples, including Taylor-Green vortex, elliptical drop deformation, excited pressure oscillation flow and continuous oil spill flow, are simulated to test the variance of total error after SCM is applied. It is found that the SCM schemes basically did not remarkably decrease the total error for incompressible free surface flow, implying that truncation error is not dominant compared to the stabilization error. Therefore, reducing the stabilization error is of more significance in future.

Three-dimensional numerical simulation of the HECLA-4 transient MCCI experiment by improved MPS method

The molten corium-concrete interaction (MCCI) is an important phenomenon after the failure of pressure vessel in a severe accident of nuclear reactor. It has been verified that the original Moving Particle Semi-implicit (MPS) method has the capacity to simulate some MCCI experiments. In this study, the original MPS method has been improved by including the explicit pressure calculation model to reduce the computational cost and enhance the computational speed. Then, the improved MPS method was validated by simulating the classical dam break problem, and the results agreed well with that of the original MPS method. Afterwards, the HECLA-4 transient MCCI test performed by VTT was simulated by the improved MPS method with a three dimensional particle configuration of about one million particles. The basemat and sidewall ablation fronts, melt pool temperature and concrete temperature at different positions predicted by MPS were in good agreement with the experimental results. All the above-mentioned simulations proved that MPS method using explicit pressure model is capable of simulating MCCI and related heat and mass transfer in multicomponent phase flow.

A novel multiphase MPS algorithm for modeling crust formation by highly viscous fluid for simulating corium spreading

Corium (lava-like mixture of fissile material) spreading prediction is of great significance in the severe accidents of nuclear power plants. Crust formation due to solidification distinguishes corium spreading from common isothermal spreading. The Lagrangian moving particle semi-implicit (MPS) method is potential for such spreading flow with both free surface and crust-melt interface. Crust formation is usually represented by viscosity escalation, but crust creeping is an associated problem. In the original MPS algorithm, creeping velocity cannot be reduced steadily by the continuous increase of viscosity, owing to the numerical creeping. A new solution algorithm is proposed for particle methods to eliminate such numerical creeping, so that creeping velocity decreases proportionally with viscosity rise. In this situation, high enough viscosity can effectively represent crust behaviors. Three numerical examples, leakage flow with high viscosity, dam break flow with low viscosity and the VULCANO VE-U7 corium spreading experiment with both high and low viscosities simultaneously, are investigated to contrast the performance difference between the original and new algorithms. It is demonstrated that the current algorithm is suitable for crust formation in corium spreading.

Analysis of hemispherical vessel ablation failure involving natural convection by MPS method with corrective matrix

In a severe accident of a light water reactor, the reactor pressure vessel (RPV) lower head may fail due to ablation at the vessel wall boundary involving natural convection of molten core materials. Accurate prediction of RPV lower head failure is essential for assessing severe accident progression and improving accident management because it greatly influences the subsequent ex-vessel accident progressions. However, there have been still large uncertainties about RPV lower head failure mode in the Fukushima Daiichi Nuclear Accident in 2011. The Lagrangian based MPS (moving particle semi-implicit) method has advantage of analyzing such phenomena involving complex interfaces and liquid-solid phase changes over other Eulerian mesh-based method. In the preceding study, small-scale Pb–Bi hemisphere vessel ablation experiment, with silicone oil as simulated molten core, was reproduced qualitatively by original MPS method. However, ablation mechanism associated with natural convection of the high temperature liquid could not be discussed because of significant influence of numerical discretizing error. In this study, the improved MPS method coupling corrective matrix in the particle interaction model which largely suppress the numerical fluctuation was adopted to analyze the experiment. The results show that the ablated metal relocation may enhance convective heat transfer in the downstream. As a result, ablation of the vessel wall extends from the level, close to the silicone oil surface down to the bottom of the vessel rather than previously simulated localized ablation near the silicone oil surface.

Large deformation simulations of geomaterials using moving particle semi-implicit method

Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit (MPS) method, which is a Lagrangian gridless particle method, and investigated its performance and stability to simulate large deformation of geomaterials. A calculation method was developed using geomaterials modeled as Bingham fluids to improve the original MPS method and enhance its stability. Two numerical tests showed that results from the improved MPS method was in good agreement with the theoretical value. Furthermore, numerical simulations were calibrated by laboratory experiments. It showed that the simulation results matched well with the experimentally observed free-surface configurations for flowing sand. In addition, the model could generally predict the time-history of the impact force. The MPS method could be a useful tool to evaluate large deformation of geomaterials.

A numerical study of violent sloshing problems with modified MPS method

A numerical study on violent liquid sloshing phenomenon in a partially filled rectangular container is carried out by using moving particle semi-implicit (MPS) method. The present study deals with the implementation of five modifications all together over the original MPS method. The modifications include improved source terms for pressure Poisson equation, special approximation technique for the representation of gradient differential operator, collective action of mixed free surface particle identification boundary conditions, effecting Neumann boundary condition on solving the PPE and fixing judiciously the parting distance among particles to prevent collision. The suitability of the kernel function used in the original MPS method along with these five modifications is investigated for violent sloshing problems. The present model ensures a good agreement between numerical results with the existing experimental observations. The model is successfully applied to a partially filled tank undergoing horizontal sinusoidal excitation to compute the sloshing wave amplitudes and pressure on tank walls. The assessment of dynamic behaviour manifested in terms of base shear, overturning moment and impact pressure load exerted on tank ceiling induced by violent sloshing motion using MPS method is not reported in the open literature and has been efficiently carried out in the present study.

Improvement of moving particle semi‐implicit method for simulation of progressive water waves

SummaryPrecise simulation of the propagation of surface water waves, especially when involving breaking wave, takes a significant place in computational fluid dynamics. Because of the strong nonlinear properties, the treatment of large surface deformation of free surface flow has always been a challenging work in the development of numerical models. In this paper, the moving particle semi‐implicit (MPS) method, an entirely Lagrangian method, is modified to simulate wave motion in a 2‐D numerical wave flume preferably. In terms of consecutive pressure distribution, a new and simple free surface detection criterion is proposed to enhance the free surface recognition in the MPS method. In addition, a revised gradient model is deduced to diminish the effect of nonuniform particle distribution and then to reduce the numerical wave attenuation occurring in the original MPS model. The applicability and stability of the improved MPS method are firstly demonstrated by the calculation of hydrostatic problem. It is revealed that these modifications are effective to suppress the pressure oscillation, weaken the local particle clustering, and boost the stability of numerical algorithm. It is then applied to investigate the propagation of progressive waves on a flat bed and the wave breaking on a mild slope. Comparisons with the analytical solutions and experimental results indicate that the improved MPS model can give better results about the profiles and heights of surface waves in contrast with the previous MPS models. Copyright © 2017 John Wiley & Sons, Ltd.

Modified MPS method for the 2D fluid structure interaction problem with free surface

As a Lagrangian mesh-free method, the Moving Particle Semi-implicit (MPS) method is very suitable for simulating violent flows, such as breaking waves on free surface. However, despite its wide range of applicability, the original MPS algorithm suffers from some inherent difficulties in obtaining an accurate fluid pressure in both spatial and time domain. Different modifications to improve the method have been proposed in the literature. In this paper, we propose the following modifications to improve the accuracy of pressure calculations and the stability of the method: (i) A mixed source term in the pressure Poisson equation with no artificial term in the formulation, (ii) New solid and free surface boundary handling methods, (iii) Particle position shifting and collision handling, and (iv) A new version of “cell-link” neighbour particle searching strategy, which reduces about 6.5/9 (∼72%) of the searching area compared with traditional “cell-linked” algorithm.The proposed modifications are verified and validated by some model free-surface flow problems, such as a two-dimensional dam break (with rigid and flexible structures on the impacting end—FSI model), liquid sloshing and ship cross section dropping problems. The numerical results obtained are found to be in good agreement with the available numerical or experimental results. With the proposed modifications, the stability and accuracy of the pressure field are improved in spatial and time domains.

Analysis of wall boundary in moving particle semi-implicit method and a novel model of fluid–wall interaction

Wall boundary modelling is one of the key factors that affect the accuracy of the moving particle semi-implicit (MPS) method. In most implementations of the MPS method, wall boundaries are modelled by discrete wall particles and corresponding phantom particles. In this work, a systematic analysis is performed to demonstrate that the discretised representation of wall boundaries can numerically cause unphysical ‘frictional force’ and ‘bouncing movement’ to nearby fluid particles. This can significantly influence the accuracy of the MPS method. To address these issues, a new fluid–wall interaction model is proposed which replaces the discrete wall particles with a continuous, smooth mathematical description of the particle number density. With the new fluid–wall interaction model, solid boundaries are modelled to retain their physical shapes. Numerical examples demonstrate that the new method generates more accurate and physical results than the original MPS method. In addition to the improved results, the new method also features reduced complexity of MPS modelling and more efficient computation. The method is also envisioned to be applicable to problems with arbitrarily shaped boundaries.

An Improved Moving Particle Semi-Implicit Method for Free Surface Flows

The objective of this study is to make some improvements to the original Moving Particle Semi-implicit method (MPS) for free surface flows. Compared to traditional mesh methods, MPS is feasible to simulate surface flows with large deformation, however, during the simulation; the pressure oscillation is quite violent, duo to misjudgment of surface particles as well as particles gathering together. To modify this problem, a new arc method is applied to judge free surface particles, and a collision model is introduced to avoid particles from gathering together. Hydrostatic pressure and classical dam break are investigated by original and improved MPS. The results verify that improved MPS method is more effective for free surface flows.

Simulation of flow slides in municipal solid waste dumps using a modified MPS method

Flow slides in municipal solid waste (MSW) dumps have caused serious damage to structures and casualties all over the world. Therefore, much attention should be paid to this type of disaster to elucidate the flow mechanisms and fluidization characteristics of MSW, which are essential for the assessment and prevention of flowlike hazards. To bypass the deficiencies of the traditional analysis methods that use the mesh method and are based on a framework of solid mechanics, the moving particle semi-implicit (MPS) method, which is a purely Lagrangian meshless method and proposed for incompressible flow, is introduced to study flow slides in MSW landfills. Considering the no-physical pressure fluctuation that affects the simulation accuracy in the original MPS, the original MPS is revised in three ways: the kernel function, the source term of the Poisson equation and the search for free surface particles. Two benchmark problems, the dam break problem and the static pressure problem, are computed to illustrate the improvement of the pressure stability of the modified MPS. The Bingham constitutive model combined with the Mohr–Coulomb failure criterion is adopted to depict the dynamic features of MSW flow slides, and the equivalent viscosity is employed to bridge the gap between Bingham fluid models and Newtonian fluid models. This method, ultimately, is applied to simulate real flow slides in the Umraniye–Hekimbashi landfill and the Payatas waste dump. The numerical results show good consistency with the field data, indicating that the modified MPS method is capable of capturing the essential dynamic behavior and reproducing the entire process of complicated flow slides in MSW dumps.

Research on numerical wave tank based on the improved moving-particle semi-implicit method with large eddy simulation

Moving-particle semi-implicit (MPS) method is a new mesh-free numerical method based on Lagrangian particle. In this paper, MPS method is applied to the study on numerical wave tank. For the purpose of simulating numerical wave, we combine the MPS method with large eddy simulation (LES) which can simulate the turbulence in the flow. The intense pressure fluctuation is a significant shortcoming in MPS method. So, we improve the original MPS method by using a new pressure Poisson equation to ease the pressure fluctuation. Divergence-free condition representing fluid incompressible is used to calculate pressure smoothly. Then, area-time average technique is used to deal with the calculation. With these improvements, the modified MPS-LES method is applied to the simulation of numerical wave. As a contrast, we also use the original MPS-LES method to simulate the wave in a numerical wave tank. The result shows that the new method is better than the original MPS-LES method.

Experiments and MPS analysis of stratification behavior of two immiscible fluids

Stratification behavior is of great significance in the late in-vessel stage of core melt severe accident of a nuclear reactor. Conventional numerical methods have difficulties in analyzing stratification process accompanying with free surface without depending on empirical correlations. The Moving Particle Semi-implicit (MPS) method, which calculates free surface and multiphase flow without empirical equations, is applicable for analyzing the stratification behavior of fluids. In the present study, the original MPS method was improved to simulate the stratification behavior of two immiscible fluids. The improved MPS method was validated through simulating classical dam break problem. Then, the stratification processes of two fluid columns and injected fluid were investigated through experiments and simulations, using silicone oil and salt water as the simulant materials. The effects of fluid viscosity and density difference on stratification behavior were also sensitively investigated by simulations. Typical fluid configurations at various parametric and geometrical conditions were observed and well predicted by improved MPS method.

Enhancement of performance and stability of MPS mesh-free particle method for multiphase flows characterized by high density ratios

The paper presents an enhanced stabilized MPS (Moving Particle Semi-implicit) method for simulation of multiphase flows characterized by high density ratios. The developed method benefits from four previously developed schemes [1] as well as a novel one proposed for accurate, consistent modeling of density at the phase interface. The new scheme can be considered as an extended version of a commonly applied density smoothening scheme and is shown to keep the sharpness of spatial density variations while enhancing the stability and performance of simulations. Further, the paper highlights the importance of applying a Taylor series consistent scheme for calculation of pressure gradient in multiphase MPS-based simulations. By presenting a simple perturbation analysis, it is shown that some commonly applied MPS-based pressure gradient models are prone to increase the level of unphysical perturbations at the phase interface leading to numerical instabilities. The original MPS gradient model with a Gradient Correction [1] is shown to provide stable and accurate results even in case of violent multiphase flows characterized by high density ratios.

Numerical simulation of sloshing with large deforming free surface by MPS-LES method

Moving particle semi-implicit (MPS) method is a fully Lagrangian particle method which can easily solve problems with violent free surface. Although it has demonstrated its advantage in ocean engineering applications, it still has some defects to be improved. In this paper, MPS method is extended to the large eddy simulation (LES) by coupling with a sub-particle-scale (SPS) turbulence model. The SPS turbulence model turns into the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. Although MPS method has the advantage in the simulation of the free surface flow, a lot of non-free surface particles are treated as free surface particles in the original MPS model. In this paper, we use a new free surface tracing method and the key point is “neighbor particle”. In this new method, the zone around each particle is divided into eight parts, and the particle will be treated as a free surface particle as long as there are no “neighbor particles” in any two parts of the zone. As the number density parameter judging method has a high efficiency for the free surface particles tracing, we combine it with the neighbor detected method. First, we select out the particles which may be mistreated with high probabilities by using the number density parameter judging method. And then we deal with these particles with the neighbor detected method. By doing this, the new mixed free surface tracing method can reduce the mistreatment problem efficiently. The serious pressure fluctuation is an obvious defect in MPS method, and therefore an area-time average technique is used in this paper to remove the pressure fluctuation with a quite good result. With these improvements, the modified MPS-LES method is applied to simulate liquid sloshing problems with large deforming free surface. Results show that the modified MPS-LES method can simulate the large deforming free surface easily. It can not only capture the large impact pressure accurately on rolling tank wall but also can generate all physical phenomena successfully. The good agreement between numerical and experimental results proves that the modified MPS-LES method is a good CFD methodology in free surface flow simulations.