Moving Particle Semi-implicit Method Research Articles

MPS-FEM Coupled Method for Study of Wave-Structure Interaction

Nowadays, an increasing number of ships and marine structures are manufactured and inevitably operated in rough sea. As a result, some phenomena related to the violent fluid-elastic structure interactions (e.g., hydrodynamic slamming on marine vessels, tsunami impact on onshore structures, and sloshing in liquid containers) have aroused huge challenges to ocean engineering fields. In this paper, the moving particle semi-implicit (MPS) method and finite element method (FEM) coupled method is proposed for use in numerical investigations of the interaction between a regular wave and a horizontal suspended structure. The fluid domain calculated by the MPS method is dispersed into fluid particles, and the structure domain solved by the FEM method is dispersed into beam elements. The generation of the 2D regular wave is firstly conducted, and convergence verification is performed to determine appropriate particle spacing for the simulation. Next, the regular wave interacting with a rigid structure is initially performed and verified through the comparison with the laboratory experiments. By verification, the MPS-FEM coupled method can be applied to fluid-structure interaction (FSI) problems with waves. On this basis, taking the flexibility of structure into consideration, the elastic dynamic response of the structure subjected to the wave slamming is investigated, including the evolutions of the free surface, the variation of the wave impact pressures, the velocity distribution, and the structural deformation response. By comparison with the rigid case, the effects of the structural flexibility on wave-elastic structure interaction can be obtained.

Analysis of stenosis effect on blood pressure using moving particle semi-implicit method

Computational fluid dynamics are developed by scientists in the last few decades. Computing is used to explain the physical problem which is using a numerical method. In this paper, the phenomenon of stenosis inhibited blood flow is simulated and observed using the Moving Particle Semi-Implicit Method. The simulation was built using the Navier-Stokes equation. This simulation does not use data with quantitative units because it only aims to observe the phenomenon of blockage of stenosis in the bloodstream, so the value was obtained without units. The velocity profile of the blood particles which are located between the rigid stenosis will be fastest if the percentage of stenosis is higher. The velocity profile shows a fluctuation in the direction of the radial position = 0 when the horizontal position is 1.5 ⩽ x ⩽ 2.5 with the maximum velocity when the stenosis is 60% i.e 9.2 units. This shows that there are obstacles that cause the velocity profile to be higher than the blood flow without stenosis, and the greater the percentage of stenosis, the greater the fluctuations occurring in the area so that it has a higher velocity.

Use of the Mps method to estimate the energy conversion efficiency of the owc-wec (first report)

In recent years, ocean renewable energy has been increasingly in the spotlight due to global warming and energy issues etc. Research on ocean renewable energy devices is being carried out by many researchers, companies and countries. Additionally, many sea tests are being carried out by countries with real sea test sites. Ocean renewable energy devices still need to research about a power generation method, an energy conversion efficiency and costs etc. In this paper, Authors focus on the oscillating water column type wave energy converter (called below OWC-WEC). It is considered that the OWC-WEC is useful because a movable part which becomes a cause of trouble is few and can also be used as a breakwater device. In this study, the MPS (Moving Particle Semi-implicit) method is applied to the performance analysis of the OWC-WEC. It is because the performance analysis by various parameters and the reduction of an experimental cost is needed. In this paper, these following items are shown; 1) the development of analysis program code which can simulate the multiphase flow by three phases of gas, liquid and solid, 2) the development of air duct model, 3) verification of the usefulness of the improved MPS program code and 4) verification of the applicability to the performance analysis of the OWC-WEC. This program code was applied to the simulation of the fixed type OWC-WEC. Following this, the reproducibility of the primary conversion efficiency of the fixed type OWC-WEC by this program code was verified and discussed. Finally, the usefulness and applicability of this program code were discussed and recommendations for future work were made.

Numerical Study of 3-D Liquid Sloshing in an Elastic Tank by MPS-FEM Coupled Method

The sloshing phenomenon in a partially loaded oil tanker or liquid natural gas ship is a typical fluid-structure interaction problem involving multi-physics, violent free-surface flow, and nonlinear structural response. In the past decades, the complex phenomenon has been commonly investigated without consideration of the hydro-elastic behaviors of the bulkheads. In our previous work, the liquid sloshing phenomenon in a two-dimensional (2-D) elastic tank was numerically studied. However, the bulkheads of the tank will deform within the three-dimensional (3-D) space in reality. So, it is necessary to study the 3-D sloshing problem in an elastic tank. In this article, a hybrid approach is developed within the Lagrangian system. The moving particle semiimplicit (MPS) method is used to simulate the evolution of 3-D flow with a violent free surface, and the finite element method (FEM) is used for the numerical analysis of structural response due to the impact loads of the sloshing flow. To couple the MPS method and the FEM method, an interpolation scheme based on the kernel function of the particle method is proposed for the communication on the isomerous interface between the fluid and structure domains. The reliability of force and deformation interpolation modules is validated by two tests. Then, the sloshing phenomenon in a 3-D elastic tank is numerically investigated and compared against the previous published 2-D results. By varying the Young's modulus of the tank walls, characteristics regarding the evolutions of free surface, variation of impact pressures, and dynamic responses of the structures are presented. 1. Introduction To support the transportation demands of natural resources, more and more vessels, such as the very large crude carriers and the liquid natural gas carriers, are manufactured. For these huge structures, risks such as local deformation or even damage of cargo-containment systems resulting from sloshing phenomena subsequently increase. Therefore, it is necessary to take the elasticity of the tank walls into account in the research of sloshing phenomena (Dias & Ghidaglia 2018). However, the phenomena involving the vibrations of the tank walls are complex. In the process of sloshing wave interacting with elastic bulkheads, the fragmentation, splash, and fusion of water are observed. Meanwhile, the structures vibrate nonlinearly under the impact loads resulting from the sloshing wave. These phenomena are hard to simulate realistically by the traditional mesh-based methods.

Study on fracture morphology of water film on the wall of vertical corrugated plate under shear of the air flow

Corrugated plate is a main steam-water separation device, and the water film cracking mechanism has a great influence on the steam-water separation efficiency. Based on high-speed photography method, the rupture morphology of the water film is experimentally studied. Rupture morphology of the water film under the shearing of the air flow is numerically simulated according on the improved moving particle semi-implicit (MPS) method, and the initial distribution of the air flow velocity in the corrugated plate channel is obtained. The relationship between critical air flow velocity when the water film is broken and the water film width is given. Comparison between experimental results and numerical results shows that improved MPS method can simulate location of film rupture, the rupture pattern, the droplet splash direction, and flight speed of the droplet after rupture, respectively. There is a positive correlation between critical air flow velocity and water film width on the wall.

Improvement of Pressure Calculations in the Moving Particle Semi-Implicit Method for Free-Surface Flows

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.

Numerical Simulation of the water-exit process of the missile based on Moving Particle Semi-Implicit method

The phenomenon of a water mound can show up in the process of water-exit of the missile [1], and the a water mound will break and splash in a very short time, which will exert an extra force on the missile and therefore will affects the movement of the missile as well as the gesture when the missile comes out the water. Therefore, investigation into the water-exit process of the missile is of great significance to the launch of the underwater missiles. The traditional grid methods always fail to simulate the whole the water-exit process because of the large deformation of the mesh. The paper adopts a meshless method, called Moving Particle Semi-Implicit method (MPS), to study the water-exit process of the missile. Based on verifying it by the dam break simulation, MPS is applied to simulate the water mound during the water-exit process, which is aiming at providing some reference for the relevant theoretical research.

Bucket-based multigrid preconditioner for solving pressure Poisson equation using a particle method

The execution time for incompressible particle methods is dominated by solving large sparse linear systems. In this study, a novel simple bucket-based multigrid (BMG) preconditioner is presented to retrieve linear scaling. In the algorithm, the domain is decomposed into cubic boxes, to enable recursive aggregation of the closest neighboring particles. Under a moving particle semi-implicit (MPS) discretization scheme, parametric, verification, and performance studies were conducted for basic problems. From the parametric study, the BMG preconditioner was accompanied with a Krylov subspace accelerated multigrid cycle strategy and incorporated into a generalized conjugate residual method. Regardless of dimension and degree of particle distribution irregularity, the method significantly outperformed a conjugate gradient (CG), an incomplete Cholesky CG, and a conventional plain aggregation-based algebraic multigrid preconditioned solver. For a dam-break problem with 1.3 M and 2.3 M particles in 2D and 3D, the proposed method, as a linear solver for the MPS method, was 27 and 5.4 times faster than the CG method.

Implementation of the moving particle semi-implicit method for free-surface flows on GPU clusters

The moving particle semi-implicit (MPS) method performs well in simulating incompressible flows with free surfaces. Despite its applicability, the MPS method suffers from the fundamental instability problem and high computational cost in its practical application. Substantial research has been conducted on improving the stability and accuracy of the MPS method. Moreover, graphics processing units (GPUs), which are multi-processors that execute many three-dimensional geometric processes at high speed, provide unprecedented capability for scientific computations. However, the usage of a single GPU card is not sufficient for engineering applications that require several million particles that predict the desired physical processes, because the available memory space is insufficient. In this work, the dynamic stability (DS) algorithm and particle shifting (PS) algorithm have been used to overcome the instability and inaccuracies caused by tensile instability and non-uniform particle distribution, respectively. Based on the stable MPS method, a GPU-based MPS code that uses the compute unified device architecture (CUDA) language has been developed. An efficient neighborhood particle search is performed using an indirect method, and the matrix for the pressure Poisson equation (PPE) is assembled in parallel. Based on the single-GPU version, a multi-GPU MPS code has been developed. The approach uses a non-geometric dynamic domain decomposition method that provides homogeneous load balancing whereby different portions (subdomains) of the physical system under study are assigned to different GPUs. Communication between devices is achieved with the use of a message passing interface (MPI). Based on the neighborhood particle search, the techniques for building and updating the “halo” are described in detail. The speed-up of the single-GPU version is analyzed for different numbers of particles, and the scalability of the multi-GPU version is analyzed for different numbers of particles and different numbers of GPUs. Last, an application with more than 107 particles is presented to show the capability of the code in handling large-scale simulations.

A stable moving particle semi-implicit method with renormalized Laplacian model improved for incompressible free-surface flows

We present a stable and accurate moving particle semi-implicit (MPS) for free-surface flows. For simulating free-surface flows, previous formulations using renormalized procedure is only applicable to interior particles. Poor accuracy of the free-surface particle in turn contaminate the overall solution accuracy. In this study, dummy particle is introduced to stabilize the renormalized Laplacian model on free surface and to enforce the free-surface condition. The proposed renormalized Laplacian model enables accurate pressure calculation for both internal and free-surface particles. Modification also includes a modified gradient model in which linear consistency is guaranteed and stability is enhanced by introducing dummy particle. The proposed MPS scheme provides a more accurate and stable simulation of incompressible free surface flows. Several two-dimensional numerical simulations are presented to demonstrate the enhanced performance of the proposed MPS method.

A fully Lagrangian method for fluid–structure interaction problems with deformable floating structure

A fully Lagrangian meshless method was developed to solve the nonlinear fluid–structure interaction (FSI) problem. The improved moving particle semi-implicit (MPS) method was applied to simulate the incompressible fluid flow, and the bonded-particle model (BPM) was introduced in the discrete element method (DEM) to predict the structure deformation. The coupled MPS–DEM method was established based on the refined interface force calculation and time steps matching. In addition, a new dimensionless parameter, the deformation coefficient (DC), was proposed to quantitatively evaluate the deformation and displacement changes for the deformable structure. The oscillation of the DC would show the position fluctuation on the structure due to the deformation, and it makes the stability analysis of the deformable structure more comprehensive and reasonable. The proposed MPS–DEM(BPM) method was developed to study the motion of the moored deformable structure under solidary wave, and the effect of the Young’s modulus on the stability of the deformable structure was discussed.

A conservative finite volume-particle hybrid method for simulation of incompressible interfacial flow

Coupling the finite volume method (FVM) and the moving-particle semi-implicit (MPS) method, a conservative hybrid method is proposed for simulation of incompressible interfacial flow. In this hybrid method, bulk flow is resolved using the multi-moment constrained interpolation profile (CIP) FVM while the interface region is rendered using moving particles calculated by several enhanced MPS schemes. A new boundary condition is developed for particles located on the boundary of the interface. Numerical particles in the MPS method are used to determine the density of each mesh cell and the conservation of mass is guaranteed by a volume-fraction remedy procedure. The approach allows accurate interface tracking without diminishing numerical efficiency. Several benchmark simulations are conducted to demonstrate the accuracy and efficiency of the proposed hybrid method.

Improvement of a projection-based particle method in free-surface flows by improved Laplacian model and stabilization techniques

This paper incorporates an improved Laplacian model for the pressure Poisson equation, a stabilization technique and a newly proposed advanced conditional collision force model in a projection-based particle method of the Moving Particle Semi-implicit (MPS) method. The Laplacian model is used to calculate pressure field and is able to predict more accurate results. The stabilization technique is used to eliminate density variation, which is developed from the continuity equation and transport theorem. The conditional collision force model is developed to handle approaching particles in simulations. With the conditional collision force model and the stabilization technique, the density calculation is improved in the dam-breaking flow and the number of separate jumping particles in the flow is greatly reduced due to the stabilization technique. By using the conditional collision force model, the Laplacian model can calculate the rotation of a square fluid patch. The stabilization technique further enhances the calculation, allowing the method to predict the evolution of the fluid patch in long duration. Including the three techniques, the present MPS is able to predict accurate pressure in the dam-breaking flow and rotation of the fluid patch. The energy variation in the impact of two rectangular fluid patches is also reproduced by the implemented techniques.

MR-WC-MPS: A Multi-Resolution WC-MPS Method for Simulation of Free-Surface Flows

A Multi-Resolution Weakly Compressible Moving-Particle Semi-Implicit (MR-WC-MPS) method is presented in this paper for simulation of free-surface flows. To reduce the computational costs, as with the multi-grid schemes used in mesh-based methods, there is also a need in particle methods to efficiently capture the characteristics of different flow regions with different levels of complexity in different spatial resolutions. The proposed MR-WC-MPS method allows the use of particles with different sizes in a computational domain, analogous to multi-resolution grid in grid-based methods. To evaluate the accuracy and efficiency of the proposed method, it is applied to the dam-break and submarine landslide tests. It is shown that the MR-WC-MPS results, while about 15% faster, are in good agreement with the conventional single-resolution MPS results and experimental results. The remarkable ability of the MR-WC-MPS method in providing robust savings in computational time for up to 60% is then shown by applying the method for simulation of extended submarine landslide test.

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.

Numerical simulation of zircaloy-water reaction based on the moving particle semi-implicit method and combined analysis with the MIDAC code for the nuclear-reactor core melting process

During the severe accident in PWR (Pressurized Water Reactor), local phenomena (e.g., eutectic reaction, candling effect, zircaloy-water reaction) occurring in the core have a significant impact on the core melting process. However, the traditional severe accident analysis codes cannot simulate the local phenomena accurately. To solve this problem, the Computational Fluid Dynamics (CFD) method is considered. By coupling CFD method with traditional severe accident codes, the accident sequence in the core melting process can be simulated accurately. In this study, considering the complexity of physical and chemical phenomena involved in the core melting process, the zircaloy-water reaction is selected for analysis. The zircaloy-water reaction kinetics models in the Module In-vessel Degradation Analysis Code (MIDAC) are summarized. The correlations for zircaloy temperature below 1800K are compared and the results show that the Cathcart-Pawel correlation induces a considerable overestimation of the reaction rates above 1460 K. Then based on the Moving Particle Semi-implicit (MPS) method, a numerical analysis model is developed to simulate zircaloy-water reaction. A zircaloy-water reaction kinetics correlation with higher accuracy is obtained by simulations and added to MIDAC. The TMI-2 accident is selected to evaluate the newly developed correlation by comparing with other correlations in MIDAC. The results indicate that different correlations can greatly influence the structure of corium pool in the core and the melt behaviors during reflooding and long-term cooling stage. However, it can hardly influence the relocation of debris bed to the lower plenum and behaviors of debris bed in the lower plenum.

Lagrangian simulation of three-dimensional macro-scale melting based on enthalpy method

Melting and solidification are encountered or utilized in industrial applications. Based on the moving particle semi-implicit (MPS) method a robust numerical approach is developed for simulation of macroscopic melting. In the approach the passively moving solid model, which accounts for liquid-solid interaction force, is introduced to facilitate simultaneous solution in the liquid and solid part for all the governing equations. An enthalpy-based viscosity model is utilized to realize smooth transition of viscosity on the liquid-solid interface. The potential-force surface tension and contact angle model are also employed to ensure realistic simulation of free surface motion during melting. To suppress possible numerical instability and ensure robustness of numerical solution, the viscosity term in the momentum equation is solved implicitly. In the meanwhile, the blended source term is utilized in the pressure Poisson equation. Verification of the developed simulation approach is carried out with a one-dimensional conduction-induced melting problem. The liquid-solid interface can be sharply predicted in the simulation. And the interface position and temperature profile are accurately calculated. The approach is further validated with the three-dimensional cube melting. Pressure oscillation is observed in the simulation when the melt starts. The oscillation can be dampened when enough liquid exists under the solid cube. Comparison with experimental data shows that the simulation can properly capture the motion of solid cube and spreading of liquid film during melting.

CFD Analysis of Effective Human Motion for Whipping Heavy Cream by Hand

This study observed human motions of whipping conducted by five expert confectionery hygiene mistresses, because mixing performance can be easily estimated by change of physical properties in heavy cream. Mixing state of heavy cream was evaluated by an overrun which indicates the amount of gas phase in the cream. Rheological properties of the cream were also measured for mixing state estimation. Agitating behaviors were recorded by a high-speed camera. Fluid flow motion was numerically observed by the Moving Particle Semi-implicit (MPS) method. The experts' motions were classified into two patterns, i.e. vertically elliptical rotation and horizontally reciprocating. Numerical analysis suggested that these motions with large amplitude produced large disturbances and high shear on the liquid surface and consequently enhanced the uptake of air as fine bubbles. It is considered that elliptical and reciprocating motions are effective for whipping because the shearing on fluid and efficient air uptake improve the whipping performance.

Convergence study and optimal weight functions of an explicit particle method for the incompressible Navier–Stokes equations

To increase the reliability of simulations by particle methods for incompressible viscous flow problems, convergence studies and improvements of accuracy are considered for a fully explicit particle method for incompressible Navier--Stokes equations. The explicit particle method is based on a penalty problem, which converges theoretically to the incompressible Navier--Stokes equations, and is discretized in space by generalized approximate operators defined as a wider class of approximate operators than those of the smoothed particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) methods. By considering an analytical derivation of the explicit particle method and truncation error estimates of the generalized approximate operators, sufficient conditions of convergence are conjectured.Under these conditions, the convergence of the explicit particle method is confirmed by numerically comparing errors between exact and approximate solutions. Moreover, by focusing on the truncation errors of the generalized approximate operators, an optimal weight function is derived by reducing the truncation errors over general particle distributions. The effectiveness of the generalized approximate operators with the optimal weight functions is confirmed using numerical results of truncation errors and driven cavity flow. As an application for flow problems with free surface effects, the explicit particle method is applied to a dam break flow.

Updated Lagrangian Particle Hydrodynamics (ULPH) modeling and simulation of multiphase flows

In this paper, a weakly compressible updated Lagrangian particle hydrodynamics (ULPH) model [1] has been developed for multiphase flows with high density ratios and viscosity ratios. To enhance computation stability and prevent penetrations near the multiphase flow interface, a new surface tension resultant formulation based on the Continuum Surface Force (CSF) formulation [2], combined with the interface sharpness force, is also developed within the framework of ULPH method. The intermediate configuration is considered in the computational algorithm, and a modified predictor-corrector scheme is adopted to solve governing equations, which significantly improve the accuracy and efficiency of the ULPH model. Several numerical examples are presented to compare with either analytical or computational results obtained by using different numerical methods such as Smoothed Particle Hydrodynamics (SPH) method, Moving Particle Semi-implicit (MPS) method and Level Set (LS) method within the framework of Finite Element Method (FEM). The results indicate that the ULPH method has good accuracy, stability, and convergence properties in simulations of multiphase flows.