On the SPH tensile instability in forming viscous liquid drops

Smoothed Particle Hydrodynamics (SPH) simulations of elastic solids and viscous fluids may suffer from unphysical clustering of particles due to the tensile instability. Recent work has shown that in simulations of elastic or brittle solids the instability can be removed by an artificial stress whose form is derived from a linear perturbation analysis of the full set of governing SPH equations. While a linear analysis cannot be used to derive the corresponding form of the artificial stress for a viscous fluid, here we show that the same construction which applies to elastic solids may also work for viscous fluids provided that the constant parameter ? entering in the definition of the artificial stress is properly chosen. As a suitable test case, we model the formation of a circular van der Waals liquid drop and show that the tensile instability is removed when an artificial viscous force and energy generation term are added to the standard SPH equations of motion and energy, respectively. The optimal value of the constant ? is constrained by the ability of the model simulation to reproduce both a sufficiently smoothed density profile and the van der Waals phase diagram.     

基于GPU的无网格流体实时渲染

提出基于平滑粒子流体力学的自由界面流体模拟方法,采用了范德瓦尔斯方程与粒子间短距离排斥力和长距离吸引力作用的表面张力,设计出基于GPU的粒子泼溅算法。渲染算法完全消除了时间离散假象,具有交互式的高质量渲染效果。与传统拉格朗日算法相比,该方法具有简化的表面张力模型,快速的渲染方式,减小了运算的复杂性,有效提高了系统的运行速度。     

Particle Monte Carlo and lattice-Boltzmann methods for simulations of gas-particle flows

A numerical solution concept is presented for simulating the transport and deposition to surfaces of discrete, small (nano-)particles. The motion of single particles is calculated from the Langevin equation by Lagrangian integration under consideration of different forces such as drag force, van der Waals forces, electrical Coulomb forces and not negligible for small particles, under stochastic diffusion (Brownian diffusion). This so-called particle Monte Carlo method enables the computation of macroscopic filter properties as well the detailed resolution of the structure of the deposited particles. The flow force and the external forces depend on solutions of continuum equations, as the Navier-Stokes equations for viscous, incompressible flows or a Laplace equation of the electrical potential. Solutions of the flow and potential fields are computed here using lattice-Boltzmann methods. Essential advantage of these methods are the easy and efficient treatment of three-dimensional complex geometries, given by filter geometries or particle covered surfaces. A number of numerical improvements, as grid refinement or boundary fitting, were developed for lattice-Boltzmann methods in previous studies and applied to the present problem. The interaction between the deposited particle layer and the fluid field or the external forces is included by recomputing of these fields with changed boundaries. A number of simulation results show the influence of different effects on the particle motion and deposition.     

An Enskog based Monte Carlo method for high Knudsen number non-ideal gas flows

A Monte Carlo method based on the Enskog equation for dense gas is developed by considering high density effect on collision rates and both repulsive and attractive molecular interactions for a Lennard-Jones fluid. The appropriate internal energy exchange model is introduced with consistency with the collision model. The equation of state for a non-ideal gas is therefore derived involving the finite density effect and the van der Waals intermolecular force, changing from the Clapeyron equation to the van der Waals equation. In contrast to previous Monte Carlo approaches, the present predictions agree better with experimental data for the gas transport properties at high densities and in a wide temperature region. The numerical modeling of non-ideal gas flow in micro and nanochannels show that the high gas density affects greatly flow behavior and heat transfer characteristics. The high density of gas leads to a lower skin friction coefficient on the wall surfaces than the predictions by the perfect gas assumption.     

SPH simulation of selective withdrawal from microcavity

The selective withdrawal of weakly compressible fluids is investigated by smoothed particle hydrodynamics (SPH) with a revised model of surface tension. In our model problem, fluid is withdrawn from a two-dimensional microcavity through a narrow outlet above the interface of two immiscible fluids. The outflow boundary is implemented by a particular zone of fluid particles with prescribed velocity, together with the introduction of artificial boundary particles. Based on the average number density of fluid particles, the effective contribution of boundary particles is corrected for the compressible context. It is found that there exists a critical withdrawal rate for each initial interface height, beyond which the lower phase becomes entrained in a thin spout along with the upper phase. Besides, the Froude number with redefinition for this kind of multiphase flow could serve as a criterion of flow behavior. Furthermore, larger surface tension, smaller dynamical viscosity and density of the upper phase all lead to longer threshold time of formation of the spout state, and thus are favorable to the withdrawal of upper phase both in terms of higher efficiency and larger quantity.     

Modeling fibrin aggregation in blood flow with discrete-particles

Excessive clotting can cause bleeding over a vast capillary area. We study the mesoscopic dynamics of clotting by using the fluid particle model. We assume that the plasma consists of fluid particles containing fibrin monomers, while the red blood cells and capillary walls are modeled with elastic mesh of "solid" particles. The fluid particles interact with each other with a short-ranged, repulsive dissipative force. The particles containing fibrin monomers have a dual character. The polymerization of fibrin monomers into hydrated fibrins is modeled by the change of the interactions between fluid particles from repulsive to attractive forces. This process occurs with a probability being an increasing function of the local density. We study the blood flow in microscopic capillary vessels about 100 microm long and with diameters in order of 10 microm. We show that the model of polymerization reflects clearly the role played by fibrins in clotting. Due to the density fluctuations caused the by the high acceleration, the fibrin chains are produced within a very short time (0.5 ms). Fibrin aggregation modifies the rheological properties of blood, slows down the incipient flow, and entraps the red blood cells, thus forming dangerous clots.     

MPM simulation of interacting fluids and solids

The material point method (MPM) has attracted increasing attention from the graphics community, as it combines the strengths of both particle‐ and grid‐based solvers. Like the smoothed particle hydrodynamics (SPH) scheme, MPM uses particles to discretize the simulation domain and represent the fundamental unknowns. This makes it insensitive to geometric and topological changes, and readily parallelizable on a GPU. Like grid‐based solvers, MPM uses a background mesh for calculating spatial derivatives, providing more accurate and more stable results than a purely particle‐based scheme. MPM has been very successful in simulating both fluid flow and solid deformation, but less so in dealing with multiple fluids and solids, where the dynamic fluid‐solid interaction poses a major challenge. To address this shortcoming of MPM, we propose a new set of mathematical and computational schemes which enable efficient and robust fluid‐solid interaction within the MPM framework. These versatile schemes support simulation of both multiphase flow and fully‐coupled solid‐fluid systems. A series of examples is presented to demonstrate their capabilities and performance in the presence of various interacting fluids and solids, including multiphase flow, fluid‐solid interaction, and dissolution.     

Mesoscale SPH modeling of fluid flow in isotropic porous media

A novel numerical technique—Smoothed Particle Hydrodynamics (SPH) is used to model the fluid flow in isotropic porous media. The porous structure is resolved in a mesoscopic-level by randomly assigning certain portion of SPH particles to fixed locations. A repulsive force, similar in form to the 12-6 Lennard-Jones potential between atoms, is set in place to mimic the interactions between fluid and porous structure. This force is initiated from the fixed porous material particle and may act on its nearby moving fluid particles. In this way, the fluid is directed to pass through the porous structure in physically reasonable paths. For periodic porous systems formed by intersecting solid material with straight parallel fluid channels, the Kozeny formula of permeability was reproduced successfully, which, to a great extent, validates the reliability of the developed SPH model. Further, SPH simulations for the fluid flows induced by an applied streamwise body force in two-dimensional porous structures of different porosities are performed. The macroscopic Darcy's law is confirmed to be valid only in the creeping flow regime. The derived relationship of permeability versus porosity is compared with some existing numerical results/experimental data, which demonstrates that the present SPH model is able to capture the essential features of the fluid flow in porous media.     

Volume preserving viscoelastic fluids with large deformations using position-based velocity corrections

We propose a particle-based hybrid method for simulating volume preserving viscoelastic fluids with large deformations. Our method combines smoothed particle hydrodynamics (SPH) and position-based dynamics (PBD) to approximate the dynamics of viscoelastic fluids. While preserving their volumes using SPH, we exploit an idea of PBD and correct particle velocities for viscoelastic effects not to negatively affect volume preservation of materials. To correct particle velocities and simulate viscoelastic fluids, we use connections between particles which are adaptively generated and deleted based on the positional relations of the particles. Additionally, we weaken the effect of velocity corrections to address plastic deformations of materials. For one-way and two-way fluid-solid coupling, we incorporate solid boundary particles into our algorithm. Several examples demonstrate that our hybrid method can sufficiently preserve fluid volumes and robustly and plausibly generate a variety of viscoelastic behaviors, such as splitting and merging, large deformations, and Barus effect.     

Dynamics modeling and analysis of inkjet technology-based oligo DNA microarray spotting

Oligo deoxyribonucleic-acid (DNA) microarrays are fabricated through in-situ chemical synthesis. Contact and fluid dynamics contribute to this process. To produce high-quality oligo DNA microarrays, it is important to well understand the dynamics of the fabrication process. Much work has been done in understanding the chemistry principles. However, few studies have been conducted from the mechanics point of view. This paper proposes a contact dynamics model of inkjet technology-based oligo DNA microarray spotting process. The proposed dynamics model can reasonably well explain the dynamics of the oligo DNA microarray spotting process. Note to Practitioners-This research was motivated by the need to develop a dynamics model for analyzing the inkjet technology-based oligo deoxyribonucleic-acid (DNA) microarray spotting process. Modeling techniques for micro/nanoscale dynamics have not been well established in the open literature. This case study shows how this can be done for DNA spotting dynamics. Contact dynamics, electrostatic forces, viscous forces, and van der Waals forces have all been considered in this study. The method may be extended to model and analyze the dynamics of other biological particle spotting processes as well.     

Effect of relative particle size on large particle detachment from a microchannel

The detachment of a single rigid sphere in a cylindrical PDMS microchannel has been investigated for systems where the particle occupies greater than 50% of the channel cross-sectional area. The fluid velocity required to detach a particle adhering to a microchannel wall is a function of many variables; however, only the effect of particle size is considered in this paper. Experiments were performed for Reynolds numbers less than 0.1, and the ratio of particle diameter, d _p, to channel dimension, D, was varied from 0.50 to 0.95 in a 230 μm channel. A nonionic surfactant (Tween 80) was used to minimize the effect of adhesive forces other than van der Waals forces. In addition, a simple force-balance model based on particle lift, buoyancy, drag, gravitational forces, and adhesion due to van der Waals forces has been developed to predict the velocity required for particle detachment. The predicted and experimentally measured velocities agree relatively well within the limit of experimental error. The detachment velocity was qualitatively found to increase with decreasing d _p /D.     

Lattice Boltzmann simulation of the dispersion of aggregated particles under shear flows

The lattice Boltzmann method (LBM) for multicomponent immiscible fluids is applied to simulations of the deformation and breakup of a particle-cluster aggregate in shear flows. In the simulations, the solid particle is modeled by a droplet with strong interfacial tension and large viscosity. The van der Waals attraction force is taken into account for the interaction between the particles. The ratio of the hydrodynamic drag force to cohesive force, I, is introduced, and the effect of I on the aggregate deformation and breakup in shear flows is investigated. It is found that the aggregate is easier to deform and to be dispersed when I is over 100.     

Realistic and stable simulation of turbulent details behind objects in smoothed‐particle hydrodynamics fluids

This paper presents a novel realistic and stable turbulence synthesis method to simulate the turbulent details generated behind objects in smoothed particle hydrodynamics (SPH) fluids. Firstly, by approximating the boundary layer theory on the fly in SPH fluids, we propose a vorticity production model to identify which fluid particles shed from object surfaces and which are seeded as vortex particles. Then, we employ an SPH‐like summation interpolant formulation of the Biot–Savart law to calculate the fluctuating velocities stemming from the generated vorticity field. Finally, the stable evolution of the vorticity field is achieved by combining an implicit vorticity diffusion technique and an artificial dissipation term. Moreover, in order to efficiently catch turbulent details for rendering, we propose an octree‐based adaptive surface reconstruction method for particle‐based fluids. The experiment results demonstrate that our turbulence synthesis method provides an effect way to model the obstacle‐induced turbulent details in SPH fluids and can be easily added to existing particle‐based fluid–solid coupling pipelines. Copyright © 2014 John Wiley & Sons, Ltd.     

范德华力作用下粗糙表面静态粘附的研究

通过在硅微接触表面上涂覆低表面能的憎水性OTS膜以除去接触面间的表面张力,把两表面均接地以除去接触面间的静电力,研究了仅有范德华力作用时硅微结构接触表面的粘附.根据实际粗糙表面凸峰自相似的高度分布,计算了发生粘附后,微观接触表面产生弹性和塑性变形的两种情况下的范德华粘附能,分析了表面形貌对其影响.     

GPU‐assisted real‐time coupling of blood flow and vessel wall

The vessel wall and the blood flow interact and influence each other, and real‐time coupling between them is of great importance to the virtual surgery as well as the research and diagnosis of vascular disease. On the basis of smoothed particle hydrodynamics (SPH), we present a new approach to solve non‐Newtonian viscous force of blood and a parallel mixed particles‐based coupling method for blood flow and vessel wall. Meanwhile, we also design a proxy particle‐based vessel wall force visualization method. Our method is as follows. Firstly, we solve the non‐Newtonian viscous forces of blood through the SPH method to discretize the Casson equation. Secondly, in each time step, we combine blood particles and sampling proxy particles on the blood vessel wall to form mixed particles and calculate the interaction forces through the SPH method between every pair of the neighboring mixed particles inside the graphics processing unit. Thirdly, the forces of the proxy particles will be mapped to the color display of the proxy particle. Experimental results demonstrate that our method is able to implement real‐time sizeable coupling of blood flow and vessel wall while mainly ensuring physical authenticity and it can also provide real‐time and obvious information about vessel wall force distribution. Copyright © 2015 John Wiley & Sons, Ltd.     

Interaction of flexible multibody systems with fluids analyzed by means of smoothed particle hydrodynamics

The present work deals with a computational approach to fluid-structure interaction (FSI) problems by coupling of flexible multibody system dynamics and fluid dynamics. Since the methods for the numerical modeling are well known, both for the structural and the fluid part, the focus of this work lies on the coupling formalism. Moreover, the applicability of the presented approach to arbitrary geometries and high structural stiffness is studied, as well as an easy model setup. No restriction should be made on the topology of the structure or the complexity of motion.For the fluid part a meshless method, known as smoothed particle hydrodynamics (SPH) is applied, which fulfills the above requirements. While an explicit time integration scheme in SPH provides a fast simulation of the fluid dynamics, advanced methods from flexible multibody dynamics provide a variety of benefits for the simulation of the solid part. Amongst these are specialized structural finite elements for both small and large deformation bodies, joints, stable implicit time-integration schemes, and model reduction techniques.A rule for the interaction between fluids and structures is derived from imposing a distributed potential over boundary segments of the structures, which the fluid particles respond to. The work is concluded by illustrative examples, demonstrating the successful coupling of flexible multibody systems with fluids.     

Insight into the micro scale dynamics of a micro fluidic wetting-based conveying system by particle based simulation

We simulate a microfluidic conveying system using the many-body dissipative particle dynamics method (MDPD). The conveying system can transport micro parts to a specified spot on a surface by letting them float inside or on top of a droplet, which is pumped by changing the wetting behaviour of the substrate, e.g., with electrowetting on dielectrics. Subsequent evaporation removes the fluid; the micro part remains on its final position, where a second substrate can pick it up. In this way, the wetting control can be separate from the final device substrate. The MDPD method represents a fluid by particles, which are interpreted as a coarse graining of the fluid’s molecules. The choice of interaction forces allows for free surfaces. To introduce a contact angle model, non-moving particles beyond the substrate interact with the fluid particles by MDPD forces such that the required contact angle emerges. The micro part is simulated by particles with spring-type interaction forces.     

基于物理模型的实时喷泉水流运动模拟

本文基于流体动力学和粒子系统给出了一个模拟实时喷泉水流运动的方法。     

SPH particle boundary forces for arbitrary boundaries

This paper is concerned with approximating arbitrarily shaped boundaries in SPH simulations. We model the boundaries by means of boundary particles which exert forces on a fluid. We show that, when these forces are chosen correctly, and the boundary particle spacing is a factor of 2 (or more) less than the fluid particle spacing, the total boundary force on a fluid SPH particle is perpendicular to boundaries with negligible error. Furthermore, the variation in the force as a fluid particle moves, while keeping a fixed distance from the boundary, is also negligible. The method works equally well for convex or concave boundaries. The new boundary forces simplify SPH algorithms and are superior to other methods for simulating complicated boundaries. We apply the new method to (a) the rise of a cylinder contained in a curved basin, (b) the spin down of a fluid in a cylinder, and (c) the oscillation of a cylinder inside a larger fixed cylinder. The results of the simulations are in good agreement with those obtained using other methods, but with the advantage that they are very simple to implement.