A multimass correction for multicomponent fluid flow simulation using smoothed particle hydrodynamics

In multicomponent fluid flow simulations using smoothed particle hydrodynamics, the Lagrangian particles used are mostly of equal mass. This is preferred over multimass particle setup (particles with different values of mass), as it resolves the fluid interfaces comparatively better. But the flip side of using uniform mass particle setup is that it may not be computationally economical in situations with large‐density ratios. Hence, using multimass particle setup is both economical and perhaps inevitable. An attractive feature of multimass particle setup is that it allows uniform resolution in regions with different values of density. To take advantage of the multimass setup, it is therefore imperative to reduce the error associated with its usage. In this work, we present suitable multimass correction terms and assess its effectiveness using the ?h–smooth particle hydrodynamics scheme. Standard benchmark problems, viz, shock tube test, triple‐point shock test, Rayleigh‐Taylor instability, and Kelvin‐Helmholtz instability were solved with multimass particle setup, where significant improvements could be achieved in resolving the associated contact discontinuities.     

Numerical study via total Lagrangian smoothed particle hydrodynamics on chip formation in micro cutting

Numerical simulation is an effective approach in studying cutting mechanism. The widely used methods for cutting simulation include finite element analysis and molecular dynamics. However, there exist some intrinsic shortcomings when using a mesh-based formulation, and the capable scale of molecular dynamics is extremely small. In contrast, smoothed particle hydrodynamics (SPH) is a candidate to combine the advantages of them. It is a particle method which is suitable for simulating the large deformation process, and is formulated based on continuum mechanics so that large scale problems can be handled in principle. As a result, SPH has also become a main way for the cutting simulation. Since some issues arise while using conventional SPH to handle solid materials, the total Lagrangian smoothed particle hydrodynamics (TLSPH) is developed. But instabilities would still occur during the cutting, which is a critical issue to resolve. This paper studies the effects of TLSPH settings and cutting model parameters on the numerical instability, as well as the chip formation process. Plastic deformation, stress field and cutting forces are analyzed as well. It shows that the hourglass coefficient, critical pairwise deformation and time step are three important parameters to control the stability of the simulation, and a strategy on how to adjust them is provided.The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-020-00297-z     

On the Galerkin formulation of the smoothed particle hydrodynamics method

In this paper, we propose a Galerkin‐based smoothed particle hydrodynamics (SPH) formulation with moving least‐squares meshless approximation, applied to free surface flows. The Galerkin scheme provides a clear framework to analyse several procedures widely used in the classical SPH literature, suggesting that some of them should be reformulated in order to develop consistent algorithms. The performance of the methodology proposed is tested through various dynamic simulations, demonstrating the attractive ability of particle methods to handle severe distortions and complex phenomena. Copyright © 2004 John Wiley & Sons, Ltd.     

Development of smoothed particle hydrodynamics method and its application in the hydrodynamics of condensed matter

An improved smoothed particle hydrodynamics (SPH) method is described; in this method, the solution to the Riemann problem in strength media is described. Generalization of this approach to solving heat conduction problems is performed. The improved SPH method is used to solve a wide range of problems. Problems of heat conduction and volume energy release accompanied by spallation effects, simulation of high speed perforation, and propagation of failure waves in brittle materials are considered. Shock wave compression of porous materials and diffraction of detonation waves in heterogeneous explosives are simulated on the mesostructure scale.     

Discrete-element modelling and smoothed particle hydrodynamics: potential in the environmental sciences

Particle-based simulation methods, such as the discrete-element method and smoothed particle hydrodynamics, have specific advantages in modelling complex three-dimensional (3D) environmental fluid and particulate flows. The theory of both these methods and their relative advantages compared with traditional methods will be discussed. Examples of 3D flows on realistic topography illustrate the environmental application of these methods. These include the flooding of a river valley as a result of a dam collapse, coastal inundation by a tsunami, volcanic lava flow and landslides. Issues related to validation and quality data availability are also discussed.     

3D numerical simulation of the behaviour of a spherical particle suspended in a Newtonian fluid and submitted to a simple shear

The 3D flow around a rigid spherical particle suspended in a Newtonian fluid and submitted to simple shear is numerically studied using Rem3D^® finite element code. The sphere motion is imposed by a sticking contact between the sphere and the fluid. The effect of the particle size as compared with the finite dimension of the shear cell was investigated. The direct calculations show that 3D modelling is necessary to correctly predict the sphere behaviour. The proximity of the particle and the cell walls strongly affects the flow velocities, the sphere motion (increase of the rotation period of the sphere) and the stress field (change of orientation angle and increase of maximal local stresses).     

Simulation of particle-laden flow in a Humphrey spiral concentrator using dust-liquid smoothed particle hydrodynamics

This paper demonstrates that our extended smoothed particle hydrodynamics (SPH) model can successfully simulate multiphase flow in a Humphrey spiral concentrator (HSC) with two phases: powder and water. The powder phase in the model was assumed to be a continuum, as the spacing between particles in this state is much smaller than the typical length scale of flow. Further investigation was conducted on the influences of various design factors of the HSC, including the descent angle and curvature profile of the trough, during the separation of a binary mineral particle mixture.The model was validated by comparing the simulated results with the experimental results of Loveday and Cilliers (1994) as well as those of a novel lab-scale-experiment using a miniature of the HSC. The proposed SPH model accurately simulated dusty liquid flow in the HSC in both cases with an acceptable degree of accuracy relative to the experimental results. These studies are expected to be useful in future optimizations of HSC design and operating conditions.     

A stabilized Runge–Kutta,Taylor smoothed particle hydrodynamics algorithm for large deformation problems in dynamics

Numerical simulation of large deformation and failure problems present a series of difficulties when solved using mesh based methods. Meshless methods present an interesting alternative that has been explored in the past years by researchers. Here we propose a Runge–Kutta Taylor SPH model based on formulating the dynamic problem as a set of first‐order PDEs. Two sets of nodes are used for time steps n and n + 1 ∕ 2, resulting on avoiding the classical tensile instability of some other SPH formulations. To improve the accuracy and stability of the algorithm, the Taylor expansion in time of the advective terms is combined with a Runge–Kutta integration of the sources. Finally, as boundaries change during the process, a free surface detection algorithm is introduced. Copyright © 2012 John Wiley & Sons, Ltd.     

基于二阶Godunov格式的SPH方法模拟弹塑性波的传播

针对一阶Godunov格式的SPH方法的计算精度和激波分辨率不高的问题,提出了二阶Godunov格式的SPH方法。新方法在求解相互作用的粒子间黎曼问题时,认为粒子内物理量呈线性分布,用线性插值后求得的值作为黎曼问题的初始值,然后把黎曼解和Taylor展开引入到SPH方法中。应用新方法对一维弹塑性应力波的传播进行了数值模拟,并与一阶Godunov格式的SPH方法进行比较.计算结果显示新方法有效地提高了计算精度和激波分辨率,同时验证了它的稳定性。     

Impact analysis of arbitrarily‐shaped bodies using a finite element method and a smoothed particle hydrodynamics method

We propose a new method to obtain contact forces under a non‐smoothed contact problem between arbitrarily‐shaped bodies which are discretized by finite element method. Contact forces are calculated by the specific contact algorithm between two particles of smoothed particle hydrodynamics, which is a meshfree method, and that are applied to each colliding body. This approach has advantages that accurate contact forces can be obtained within an accelerated collision without a jump problem in a discrete time increment. Also, this can be simply applied into any contact problems like a point‐to‐point, a point‐to‐line, and a point‐to‐surface contact for complex shaped and deformable bodies. In order to describe this method, an impulse based method, a unilateral contact method and smoothed particle hydrodynamics method are firstly introduced in this paper. Then, a procedure about the proposed method is handled in great detail. Finally, accuracy of the proposed method is verified by a conservation of momentum through three contact examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical simulation of the motion and deformation of a non-Newtonian shear-thinning drop suspended in a Newtonian circular Couette flow using DR-BEM

The motion and deformation of a non-Newtonian shear-thinning drop suspended in a Newtonian circular Couette flow is studied using a boundary element numerical simulation. Non-linear effects from the dependency of the viscosity on the velocity field are treated in an implicit manner and the resultant domain integral is transformed into an equivalent series of boundary integrals using the Dual Reciprocity Method. The non-homogeneous (non-linear) system of algebraic equations resulting from the discretization of the boundary element formulation is solved using a modified Newton–Raphson method for drops with values of the power law index of $n=0.8$ and $0.6$ and compared to the corresponding Newtonian cases ($n=1$). The viscosity of the fluid inside the drop follows the truncated power law model. By using this model, the shear-thinning behaviour of the viscosity is correctly represented while avoiding the shear thickening which can be observed using the standard power law in small gradient flows. The simulations showed that the non-Newtonian drops had larger deformations than the corresponding Newtonian drops due to a general decrease in the viscosity. The value of the local viscosities was found to be dependant not only on the velocity field created by the motion of the internal cylinder, but strongly dependant on the surface tension forces. The rate of deformation of the drops was greater in the beginning of the simulation and decreased toward the end showing the drops found a more or less stable shape.     

Smoothed particle hydrodynamics in a generalized coordinate system with a finite‐deformation constitutive model

This study proposes smoothed particle hydrodynamics (SPH) in a generalized coordinate system. The present approach allocates particles inhomogeneously in the Cartesian coordinate system and arranges them via mapping in a generalized coordinate system in which the particles are aligned at a uniform spacing. This characteristic enables us to employ fine division only in the direction required, for example, in the through‐thickness direction for a thin‐plate problem and thus to reduce computation cost. This study provides the formulation of SPH in a generalized coordinate system with a finite‐deformation constitutive model and then verifies it by analyzing quasi‐static and dynamic problems of solids. High‐velocity impact test was also performed with an aluminum target and a steel sphere, and the predicted crater shape agreed well with the experiment. Furthermore, the numerical study demonstrated that the present approach successfully reduced the computation cost with marginal degradation of accuracy. Copyright © 2015 John Wiley & Sons, Ltd.     

Simulation of high velocity impact in fluid-filled containers using finite elements with adaptive coupling to smoothed particle hydrodynamics

This paper presents a numerical study on the simulation of impacts of projectiles on fluid-filled containers. The type of impact investigated leads to hydrodynamic ram (HRAM) and complete failure of the container shell. Two different numerical approaches are compared which are both implemented in a research hydrocode: a pure Lagrangian discretization with Finite Elements (FE) and element erosion, and a coupled adaptive FE/SPH discretization. The numerical results are compared with two reference experiments. The principal phenomenology including the container deformation could be modeled well with both methods. The coupled FE/SPH approach was superior in the reproduction of the projectile’s observed residual velocity, it is, however, computationally more expensive.     

Torsional oscillations of a plane lamina in a buoyant fluid

The correction to the torque on a torsionally oscillating plane in a viscous, thermally conducting fluid due to its density variations is calculated when the thickness of the shear laters us small in comparison to the dimensions of the plane. The mechanism that drives the system away from strictly isothermal conditions is viscous dissipation. The corresponding variations in the mean (axial and radial) flow and the mean temperature are investigated for relatively strong and weak buoyancy-momentum coupling. Method of matched asymptotic expansions is employed to study the resulting fluid motion which exists as a double-decker structure and depends upon three physical parameters.     

高性能磁流变液悬浮相表面改性的研究

对悬浮相铁粉的表面进行镀镍和渗氮,从而改善磁流变液的性能。通过扫描电镜分析、热重分析、XRD分析、磁化特性分析,发现镀镍和渗氮可以提高铁粉的抗氧化性,渗氮后粒子表面形成1层Fe4N。摩擦性能的分析表明渗氮后提高了磁流变液的耐磨性。     

Analysis of liquid droplet deformation in a gas flow

The small perturbation method is used to obtain equations describing the dynamics of a liquid droplet in a flow of ideal incompressible gas. The stability criteria and droplet disintegration time are determined.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 5, pp. 743–748, May, 1986.     

Flow of a Newtonian fluid in the gap between conical permeable surfaces

The equations of motion of a viscous Newtonian fluid between rotating and stationary conical coaxial permeable surfaces have been obtained from the Navier-Stokes differential equations and have been solved by the numerical method. The analytical dependences confirmed experimentally for determination of the energy consumption in rotary apparatuses have been obtained. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 2, pp. 92–98, March–April, 2006.