Moving Particle Semi-implicit Method Research Articles

Hydrodynamic Performance of Wave Interaction with Curtain-Wall Breakwater: Using the MPS Model

Iddy, I.; Jiang, Q., and Zhang, C., 2020. Hydrodynamic performance of wave interaction with curtain-wall breakwater: Using the MPS model. In: Hu, C. and Cai, M. (eds.), Geo-informatics and Oceanography. Journal of Coastal Research, Special Issue No. 105, pp. 76–80. Coconut Creek (Florida), ISSN 0749-0208.This paper examines the hydrodynamic performance of wave interactions with double curtain-wall breakwater by the laboratory experiment and numerical model. A vertical two-dimensional moving particle semi-implicit (MPS) numerical model is developed and verified by comparison of the simulated and experimental results. Then it is applied to investigate wave interaction with partially immersed double curtain walls at different immersion depths, porosity of perforated front wall, and chamber width. A good agreement is shown between the numerical results and the experimental data, indicating that the proposed MPS numerical model can successfully capture the essential aspects of wave interactions with breakwater structure and can be a useful predictive tool.

Investigation of single bubble behavior under rolling motions using multiphase MPS method on GPU

Study of single bubble behavior under rolling motions can prove useful for fundamental understanding of flow field inside the modern small modular nuclear reactors. The objective of the present study is to simulate the influence of rolling conditions on single rising bubble in a liquid using multiphase Moving Particle Semi-implicit (MPS) method. Rolling force term was added to 2D Navier-Stokes equations and a computer program was written using C language employing OpenACC to port the code to GPU. Computational results obtained were found to be in good agreement with the results available in literature. The impact of rolling parameters on trajectory and velocity of the rising bubble has been studied. It has been found that bubble rise velocity increases with rolling amplitude due to modification of flow field around the bubble. It has also been concluded that the oscillations of free surface, caused by rolling, influence the bubble trajectory. Furthermore, it has been discovered that smaller vessel width reduces the impact of rolling motions on the rising bubble. The effect of liquid viscosity on bubble rising under rolling was also investigated and it was found that effects of rolling became more pronounced with the increase of liquid viscosity.

Numerical simulation of Rayleigh-Bénard convection and three-phase Rayleigh-Taylor instability using a modified MPS method

The main objective of the current work is to enhance consistency and capabilities of Moving Particle Semi-implicit (MPS) method for simulating a wide range of free-surface flows and convection heat transfer. For this purpose, two novel high-order gradient and Laplacian operators are derived from the Taylor series expansion and are applied for the discretization of governing equations. Furthermore, the combination of the explicit Third-order TVD Runge-Kutta scheme and two-step projection algorithm is employed to approximate transient terms in the Navier-stokes and energy equations. To further improve the accuracy and performance of the method, a new kernel function is constructed by a combination of the Gaussian and cosine functions and then implemented for modeling the 1D Sod shock tube problem. Validation and verification of the proposed model are conducted through the simulations of several canonical test cases such as: dam break, rotation of a square patch of fluid, two-phase Rayleigh-Taylor instability, oscillating concentric circular drop and good agreement are achieved. The proposed model is then employed to simulate three-phase Rayleigh-Taylor instability and entropy generation due to natural convection heat transfer (Differentially Heated Cavity and Rayleigh-Bénard convection). The obtained results reveal that, the newly constructed kernel function provides more reliable results in comparison with two frequently used kernel functions namely; quartic spline and Wendland. Furthermore, it is found that, the enhanced MPS model is capable of handling multiphase flow problems with low and high density contrast.

A coupled 3D isogeometric/least-square MPS approach for modeling fluid–structure interactions

A two-way coupling method of the three-dimensional (3D) isogeometric approach and the least-square moving particle semi-implicit method (LSMPS) is presented for handling the fluid–structure interaction problems. This method takes advantages of isogeometric analysis (IGA) for structure deformation, e.g. the exact representation of the structure geometry and high accuracy for solution fields with relatively few elements, and that of the LSMPS method for fluid flow, e.g. its consistent discretization for both internal particles and boundary conditions. When the fluid is solved by the LSMPS method, the NURBS (Non-Uniform Rational B-Splines) surfaces provide boundary conditions for the LSMPS method. Afterward, the pressure on the NURBS surface is first evaluated from the pressure and the corresponding derivatives at the LSMPS particles by using the Taylor series expansion, and then integrated to determine the pressure force at the virtual points on the NURBS surface by using the Newton–Cotes method. Subsequently, the pressure forces at the virtual points are distributed onto the control nodes (i.e. control points) of the IGA elements so that the structure deformation can be analyzed by using the IGA method. The coupling algorithm is based on a Lagrangian framework and can handle the boundary conditions and the fluid–structure interactions accurately and easily. Finally, three examples, i.e. fluid flowing in a rigid pipe, fluid-tank, and fluid-torus interactions in the elastic regime, are simulated to demonstrate the accuracy and validity of the proposed coupling method.

Direct numerical simulation of incompressible multiphase flow with vaporization using moving particle semi-implicit method

In this paper, the moving particle semi-implicit (MPS) method is developed towards the simulation of multiphase incompressible flows with mass transfer due to vaporization. Traditional MPS method assumes particle volume to be constant and encounters difficulty in modeling vapor-liquid phase change due to abrupt volume change in vaporization process. In the proposed model, particle volume is assumed variable and volume change due to vaporization is considered. Particle splitting technique is developed to avoid large volume difference among particles. Source term accounting for mass transfer rate in vaporization process is developed in the pressure Poisson equation (PPE). Combined with enhanced MPS schemes developed in our previous studies, the numerical method is tested on single rising bubble, one-dimensional Stefan problem, vapor film growth around a sphere without gravity and then used in simulations of two-dimensional film boiling on both horizontal surface and cylindrical surface.

A numerical and experimental investigation of wave generated by submerged landslides

The Weakly-Compressible Moving Particle Semi-implicit (WC-MPS) approach is applied to investigate the wave propagation and the flow fields induced by sliding blocks. Since there are already studies focusing on an inclination slope of 45°, two slope angles, 40° and 50°, are used to obtain the additional experimental results. Sliding blocks are released under water, where the top edges are parallel to the water surface. The simulation results are compared to the experimental measurements both on the water surface and the velocity distribution at specific locations. To analyze the flow fields, contour and vector plots illustrate the flow characteristics for the entire velocity distribution in the simulation domain along with the vortex movements from the sliding block. Two case scenarios are presented to investigate the velocity distribution of the sliding block. For the first case scenario, seven cross-sections, including the front edge, the top edge, and the back edge of the sliding block were selected to further identify the characteristics of the horizontal and vertical velocity distributions. The second case scenario has five specific locations at the front, top and back edge of the block. A good agreement was obtained between the WC-MPS simulated results to the experimental data.

An incompressible–compressible Lagrangian particle method for bubble flows with a sharp density jump and boiling phase change

Modeling the boiling phase change is particularly challenging for Lagrangian particle methods due to a high density ratio and dramatic volume expansion. In this study, the incompressible moving particle semi-implicit (MPS) method and the weakly compressible smoothed particle hydrodynamics (SPH) method are coupled to develop an incompressible–compressible particle method for modeling a multiphase flow with boiling. The coupling strategies developed by Lind et al. (JCP, 2016) are adopted. A high speed of sound must be employed in SPH for incompressible bubbles in a heavy liquid under gravity, which can cause severe spurious pressure fluctuations. In this situation, a technique for detecting bubble connectivity is developed to average the pressure inside each bubble for stable coupling. This pressure averaging strategy is physically consistent due to the high density ratio. Because the pressure coupling strategy tends to break the force balance between the surface tension and the pressure jump across the interface, the surface tension model must be based only on the liquid particles near the interface. The boiling mass transfer is modeled in a straightforward manner by injecting gas particles towards the gas phase from the liquid interface particles. The gas volume expansion is naturally considered by the coupling method, as the gas particle distribution can be automatically regulated in the SPH calculation. Rising bubble simulations with different surface tension coefficients and density ratios verify the proposed method for a bubble flow. The Stefan and sucking problems as well as a horizontal film boiling flow are simulated to verify the boiling model and to demonstrate its straightforward capability to handle gas volume expansion.

Numerical analysis of dam-break waves propagating over dry and wet beds by the mesh-free method

Climate change increases the probability of dam-break flooding, making the prediction of flooding zone and dam-break wave crucial for the evacuation of people in hazardous areas. However, the propagation of dam-break waves can be affected by different downstream bed conditions such as obstacles, dry and wet beds. In this study, a mesh-free method is employed to simulate dam-break wave spreading in different bed configurations. The mesh-free method is good at capturing the free surface in the dam-break flow. In the numerical method, an explicit calculation for the pressure field is used and the spatial operators are based on the Moving Particle Semi-implicit method (MPS). The mesh-free method is validated to simulate the dam-break flow by comparing to available experimental measurements. The validated method is then used to simulate the dam-break wave propagating over the downstream wet beds with different depths. The effect from the combination of dry and wet bed for the dam-break wave is also investigated by the mesh-free method. In the simulations, the flow characteristics including free surface, flow pattern, and wavefront movement, and bed shear stress are presented and discussed.

Quadric SFDI for Laplacian Discretisation in Lagrangian Meshless Methods

In the Lagrangian meshless (particle) methods, such as the smoothed particle hydrodynamics (SPH), moving particle semi-implicit (MPS) method and meshless local Petrov-Galerkin method based on Rankine source solution (MLPG_R), the Laplacian discretisation is often required in order to solve the governing equations and/or estimate physical quantities (such as the viscous stresses). In some meshless applications, the Laplacians are also needed as stabilisation operators to enhance the pressure calculation. The particles in the Lagrangian methods move following the material velocity, yielding a disordered (random) particle distribution even though they may be distributed uniformly in the initial state. Different schemes have been developed for a direct estimation of second derivatives using finite difference, kernel integrations and weighted/moving least square method. Some of the schemes suffer from a poor convergent rate. Some have a better convergent rate but require inversions of high order matrices, yielding high computational costs. This paper presents a quadric semi-analytical finite-difference interpolation (QSFDI) scheme, which can achieve the same degree of the convergent rate as the best schemes available to date but requires the inversion of significant lower-order matrices, i.e. 3 × 3 for 3D cases, compared with 6 × 6 or 10 × 10 in the schemes with the best convergent rate. Systematic patch tests have been carried out for either estimating the Laplacian of given functions or solving Poisson’s equations. The convergence, accuracy and robustness of the present schemes are compared with the existing schemes. It will show that the present scheme requires considerably less computational time to achieve the same accuracy as the best schemes available in literatures, particularly for estimating the Laplacian of given functions.

A fluid simulation system based on the MPS method

Fluid flow simulation is a highly active area with applications in a wide range of engineering problems and interactive systems. Meshless methods like the Moving Particle Semi-implicit (MPS) are a great alternative to deal efficiently with large deformations and free-surface flow. However, mesh-based approaches can achieve higher numerical precision than particle-based techniques with a performance cost. This paper presents a numerically stable and parallelized system that benefits from advances in the literature and parallel computing to obtain an adaptable MPS method. The proposed technique can simulate liquids using different approaches, such as two ways to calculate the particles’ pressure, turbulent flow, and multiphase interaction. The method is evaluated under traditional tests cases presenting comparable results to recent techniques. This work integrates the previously mentioned advances into a single solution, which can switch on improvements, such as better momentum conservation and less spurious pressure oscillations, through a graphical interface. The code is entirely open-source under the GPLv3 free software license. The GPU-accelerated code reached speedups ranging from 3 to 43 times, depending on the total number of particles. The simulation runs at one fps for a case with approximately 200,000 particles. Program summaryProgram Title: Voxar MPSCPC Library link to program files:http://dx.doi.org/10.17632/49f6djvhjk.1Licensing provisions: GNU General Public License version 3Programming language: C++ and CUDANature of problem: The Voxar MPS code has been developed to study the flow of incompressible fluids that requires high computational cost.Solution method: Voxar MPS is an implementation of the Moving Particle Semi-implicit, a Lagrangian meshless particle method for incompressible fluids.

MPS eutectic reaction model development for severe accident phenomenon simulation

During the postulated severe accident of nuclear reactor, eutectic reaction leads to low-temperature melting of fuel cladding and early failure of core structure. In order to model eutectic melting with the moving particle semi-implicit (MPS) method, the eutectic reaction model is developed to simulate the eutectic reaction phenomenon. The coupling of mass diffusion and phase diagram is applied to calculate the eutectic reaction with the uniform temperature. A heat transfer formula is proposed based on the phase diagram to handle the heat release or absorption during the process of eutectic reaction, and it can combine with mass diffusion and phase diagram to describe the eutectic reaction with temperature variation. The heat transfer formula is verified by the one-dimensional melting simulations and the predicted interface position agrees well with the theoretical solution. In order to verify the eutectic reaction models, the eutectic reaction of uranium and iron in two semi-infinite domains is simulated, and the profile of solid thickness decrease over time follows the parabolic law. The modified MPS method is applied to calculate Transient Reactor Test Facility (TREAT) experiment, the penetration rate in the simulations are agreeable with the experiment results. In addition, a hypothetical case based on the TREAT experiment is also conducted to validate the eutectic reaction with temperature variation, the results present continuity with the simulations of TREAT experiment. Thus the improved method is proved to be capable of simulating the eutectic reaction in the severe accident.

Verification and validation of MPS potential force interface tension model for stratification simulation

The moving particle semi-implicit (MPS) method is employed to simulate the density stratification of immiscible fluids. For the sake of accurate prediction of immiscible fluids, the potential-force surface tension model is extended to calculate the interface tension. The interface tension model is verified by the simulation of a floating droplet and shows accurate prediction of the contact angle between immiscible fluids. In order to demonstrate the validity of the interface tension model at the solid surface, the wall contact angle with immiscible fluids is simulated and the predicted value agrees well with the theoretical value. In order to further validate the modified MPS method, the two-dimensional dam-break stratification experiment is simulated. The validation shows that the interface deformation can be accurately reproduced by the interface tension model. Finally, three-dimensional injection stratification is simulated to prove the effectiveness of implemented modification.

Proposal of Novel Icing Simulation Using a Hybrid Grid- and Particle-Based Method

ABSTRACTIcing on aircraft can drastically reduce aerodynamic performance and lead to serious accidents. Therefore, prediction of the accreted ice shape and area and its effects on aerodynamic performance is crucial during the design phase of an aircraft. However, numerical simulations based on conventional grid-based methods such as the finite volume method cannot accurately reproduce the complex ice shapes, which involve horn growth, feather growth, air voids, and severe surface roughness. In the present study, instead of the grid-based method, a hybrid grid- and particle-based method was newly proposed and applied to the icing problem on a NACA0012 airfoil. The explicit moving particle semi-implicit method was employed as the particle-based method due to its short computing time. The numerical simulations effectively reproduced feather-shaped ice, air voids, and surface roughness. Finally, by computing the flow around the iced airfoil, it was confirmed that flow separation around the leading edge occurred due to the ice layer, which resulted in a thicker boundary layer and wake and an increase in the drag coefficient of approximately 70% after a residence time of only 60 seconds.

CFD simulations of three-dimensional violent sloshing flows in tanks based on MPS and GPU

For violent sloshing, the flow field becomes complicated and 3-D effect is non-negligible. In addition to the excitation direction, the wave can also propagate perpendicular to the excitation direction. Due to the superposition of waves from different directions, the impact pressure imposed on the wall of the tank may increase. In this paper, our in-house solver MPSGPU-SJTU based on moving particle semi-implicit (MPS) method coupled with GPU techniques is employed for the liquid sloshing simulation, to study the factors leading to the 3-D effect. Firstly, a series of sloshing simulations are carried out to validate the reliability of present solver. Then, the sensitivity of 3-D effect against some parameters, such as excitation frequency, dimensions of the tank and filling ratio, is checked through numerical simulations. Time histories of pressure obtained by 2-D and 3-D simulations are compared to judge the occurrence of 3-D effect. It concludes that effects of those parameters are all significant.

Numerical simulation of free-surface flow and convection heat transfer using a modified Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method

A novel Kernel Derivative-Free (KDF) Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) model is developed for simulation of free-surface flows and convection heat transfer. A high-order Laplacian operator is developed and then applied for the approximation of the diffusion terms (e.g., viscous term, thermal diffusion, and newly additional diffusion term in the continuity equation). The transient term in Navier–Stokes equation is discretized using the third-order TVD Runge-Kutta scheme, while a stiff equation of state is employed to predict pressure field. To increase numerical accuracy, a new high-order smoothing operator in the context of the MPS description (Moving Particle Semi-implicit) is also proposed and then applied for the treatment of the buoyancy force term in the momentum equation. Furthermore, a new high-order smoothing kernel is constructed and tested via simulation of the 1D Sod shock tube problem. A series of numerical benchmark cases such as: dam break, stretching of a circular water drop, rotating square patch of fluid and natural convection heat transfer in a square enclosure are used to verify and evaluate the feasibility of the proposed models. It is found that all simulation results are in excellent agreement with the available experimental and numerical data. Capability and performance of KDF-WCSPH method in handling particulate flows with thermal convection are further demonstrated through analysis of entropy generation due to natural convection heat transfer in the three different well-known geometries including: Differentially Heated Cavity, L-shaped enclosure and horizontal annuli. Comparison with the past Finite-Volume results demonstrates that the present model can maintain stability and accuracy, which makes it a very useful tool for simulation of thermo-hydraulic problems.

Simulation of Nonlinear Heat Conduction in Perforated Material by Improved Moving Particle Semi-Implicit Method

Abstract An improved moving particle semi-implicit (MPS) method is presented to simulate heat conduction with temperature-dependent thermal conductivity. Based on Taylor expansion, a modified Laplacian operator is proposed, and its accuracy in irregular particle distributions is verified. Two problems are considered: (1) heat conduction in a one-dimensional (1D) slab and (2) heat conduction in a perforated sector with different boundary conditions. Consistent results with a mesh-based method are obtained, and the feasibility of the proposed method for heat conduction simulation with temperature-dependent conductivity is demonstrated.

Consistent Robin boundary enforcement of particle method for heat transfer problem with arbitrary geometry

Enforcing accurate and consistent boundary conditions is a difficult issue for particle methods, due to the lack of information outside boundaries. Recently, consistent Neumann boundary condition enforcement is developed for the least squares moving particle semi-implicit method (LSMPS). However, the Robin boundary cannot be straightforwardly considered by that method because no computational variables are defined on the wall boundary. In this paper, a consistent Robin boundary enforcement for heat transfer problem is proposed. Based on the Taylor series expansion, the Robin boundary condition for temperature is converted to the fitting function of internal rather than boundary particles and incorporated into least squares approach for discretization schemes. Arbitrary geometric wall as well as free surface boundary can be easily treated due to the adoption of polygon and moving surface mesh, respectively. A convergence study is firstly carried out to verify the consistency. Then, numerical tests of 1-D, 2-D, and 3-D heat conduction problems subject to mixed boundary conditions are performed for verification. Good agreements with theoretical solutions are observed. Natural convection problems with different boundary conditions in an annulus are carried out for further validations of heat-fluid coupling. Excellent agreements between the present and literature results are presented. Finally, problem of heat convection in a square droplet oscillation is demonstrated to show the capability of dealing with moving free surface.

Fiber Orientation Predictions—A Review of Existing Models

Fiber reinforced polymers are key materials across different industries. The manufacturing processes of those materials have typically strong impact on their final microstructure, which at the same time controls the mechanical performance of the part. A reliable virtual engineering design of fiber-reinforced polymers requires therefore considering the simulation of the process-induced microstructure. One relevant microstructure descriptor in fiber-reinforced polymers is the fiber orientation. This work focuses on the modeling of the fiber orientation phenomenon and presents a historical review of the different modelling approaches. In this context, the article describes different macroscopic fiber orientation models such as the Folgar-Tucker, nematic, reduced strain closure (RSC), retarding principal rate (RPR), anisotropic rotary diffusion (ARD), principal anisotropic rotary diffusion (pARD), and Moldflow rotary diffusion (MRD) model. We discuss briefly about closure approximations, which are a common mathematical element of those macroscopic fiber orientation models. In the last section, we introduce some micro-scale numerical methods for simulating the fiber orientation phenomenon, such as the discrete element method (DEM), the smoothed particle hydrodynamics (SPH) method and the moving particle semi-implicit (MPS) method.

Numerically simulated flooding of a freely-floating two-dimensional damaged ship section using an improved MPS method

An improved Moving-Particle Semi-Implicit (MPS) method was used to numerically simulate the transient flooding process of a freely floating two-dimensional damaged ship section. First, a near-wall particle search technique was developed to support the computations using the improved MPS method. This technique was verified via sloshing simulations. Then, numerical flooding simulations were performed for various models of this ship section, where a hole was located at different positions to represent broadside and bottom damage. In addition, flooding simulations were carried out with baffles located inside the damaged ship section. The damaged hole and the internal baffles affected flooding and motion characteristics of the damaged ship section. Greater distance of the hole from the calm water surface and the ship section's center caused larger motions. Vertical baffles had a greater influence on flooding than that from the horizontal baffles.

Turbulence models evaluation in MPS Lagrangian simulation of marine waters

ABSTRACT An advanced and well-equipped Moving Particle Semi-implicit which is a Lagrangian method is employed to simulate hydrodynamic behaviour of water wave evolution. Unlike most recently developed MPS models that consider inviscid or laminar flow, the present developed model is based on the turbulent nature of the fluid flow. In order to consider the turbulence stresses, three turbulence closures are included in the model, which are constant eddy viscosity, mixing length and k-ε model. The developed model was applied to different case studies including wave run-up on an inclined wall, wave train induced by wavemaker and landslide-generated wave. The model results were compared with analytical, empirical and experimental data cited in the literature and a good agreement was found. The results also showed that deploying a turbulence model could improve the stability of the MPS model. Results obtained through this research reveal that the application of k-ε model in combination with MPS method produces accurate and reliable results in addition to a stable solution for free surface prediction in wave mechanics.