Oldroyd-B黏弹性液滴弹跳行为的改进SPH模拟

基于光滑粒子流体动力学SPH(Smoothed Particle Hydrodynamics)方法对Oldroyd-B黏弹性液滴撞击固壁面产生的弹跳行为进行了模拟与分析。首先,为了解决SPH模拟黏弹性自由表面流出现的张力不稳定性问题,联合粒子迁移技术提出了一种改进SPH方法。然后,对Oldroyd-B黏弹性液滴撞击固壁面产生的铺展行为进行了改进SPH模拟,与文献结果的比较验证了方法的有效性。最后,通过降低Reynolds数捕捉到了液滴的弹跳行为;并在此基础上,分析了液滴黏度比、Weissenberg数和Reynolds数对液滴弹跳行为的影响。结果表明,改进SPH方法可有效地模拟黏弹性自由表面流问题;液滴黏度比、Weissenberg数和Reynolds数对液滴最大回弹高度均有显著的影响。     

An SPH model for free surface flows with moving rigid objects

This paper presents a computational model for free surface flows interacting with moving rigid bodies. The model is based on the SPH method, which is a popular meshfree, Lagrangian particle method and can naturally treat large flow deformation and moving features without any interface/surface capture or tracking algorithm. Fluid particles are used to model the free surface flows which are governed by Navier–Stokes equations, and solid particles are used to model the dynamic movement (translation and rotation) of moving rigid objects. The interaction of the neighboring fluid and solid particles renders the fluid–solid interaction and the non‐slip solid boundary conditions. The SPH method is improved with corrections on the SPH kernel and kernel gradients, enhancement of solid boundary condition, and implementation of Reynolds‐averaged Navier–Stokes turbulence model. Three numerical examples including the water exit of a cylinder, the sinking of a submerged cylinder and the complicated motion of an elliptical cylinder near free surface are provided. The obtained numerical results show good agreement with results from other sources and clearly demonstrate the effectiveness of the presented meshfree particle model in modeling free surface flows with moving objects. Copyright © 2013 John Wiley & Sons, Ltd.     

An improved KGF‐SPH with a novel discrete scheme of Laplacian operator for viscous incompressible fluid flows

The kernel gradient free (KGF) smoothed particle hydrodynamics (SPH) method is a modified finite particle method (FPM) which has higher order accuracy than the conventional SPH method. In KGF‐SPH, no kernel gradient is required in the whole computation, and this leads to good flexibility in the selection of smoothing functions and it is also associated with a symmetric corrective matrix. When modeling viscous incompressible flows with SPH, FPM or KGF‐SPH, it is usual to approximate the Laplacian term with nested approximation on velocity, and this may introduce numerical errors from the nested approximation, and also cause difficulties in dealing with boundary conditions. In this paper, an improved KGF‐SPH method is presented for modeling viscous, incompressible fluid flows with a novel discrete scheme of Laplacian operator. The improved KGF‐SPH method avoids nested approximation of first order derivatives, and keeps the good feature of ‘kernel gradient free’. The two‐dimensional incompressible fluid flow of shear cavity, both in Euler frame and Lagrangian frame, are simulated by SPH, FPM, the original KGF‐SPH and improved KGF‐SPH. The numerical results show that the improved KGF‐SPH with the novel discrete scheme of Laplacian operator are more accurate than SPH, and more stable than FPM and the original KGF‐SPH. Copyright © 2015 John Wiley & Sons, Ltd.     

An integrated smoothed particle hydrodynamics model for complex interfacial flows with large density ratios

In this paper, an integrated smoothed particle hydrodynamics (SPH) model for complex interfacial flows with large density ratios is developed. The discrete continuity equation and acceleration equation are obtained by considering the time derivative of the volume of particle and Eckart's continuum Lagrangian equation. A continuum surface force model is used to meet the fact that surface force may not be distributed uniformly on each side of the interface. An improved boundary condition is imposed to model wall free-slip and no-slip condition for interfacial flows with large density ratios. Particle shifting algorithm (PSA) is added for interfacial flows by imposing the normal correction near the interface, called as Interface-PSA. Then four representative numerical examples, including droplet deformation, Rayleigh-Taylor instability, dam breaking, and bubble rising, are presented and compared well with reference data. It is demonstrated that inherent interfacial flow physics can be well captured, including surface tension and the dynamic evolution of the complex interfaces.     

Simulating surface tension with smoothed particle hydrodynamics

A method for simulating two‐phase flows including surface tension is presented. The approach is based upon smoothed particle hydrodynamics (SPH). The fully Lagrangian nature of SPH maintains sharp fluid–fluid interfaces without employing high‐order advection schemes or explicit interface reconstruction. Several possible implementations of surface tension force are suggested and compared. The numerical stability of the method is investigated and optimal choices for numerical parameters are identified. Comparisons with a grid‐based volume of fluid method for two‐dimensional flows are excellent. The methods presented here apply to problems involving interfaces of arbitrary shape undergoing fragmentation and coalescence within a two‐phase system and readily extend to three‐dimensional problems. Boundary conditions at a solid surface, high viscosity and density ratios, and the simulation of free‐surface flows are not addressed. Copyright © 2000 John Wiley & Sons, Ltd.     

Coupling finite difference method with finite particle method for modeling viscous incompressible flows

A hybrid approach to couple finite difference method (FDM) with finite particle method (FPM) (ie, FDM-FPM) is developed to simulate viscous incompressible flows. FDM is a grid-based method that is convenient for implementing multiple or adaptive resolutions and is computationally efficient. FPM is an improved smoothed particle hydrodynamics (SPH), which is widely used in modeling fluid flows with free surfaces and complex boundaries. The proposed FDM-FPM leverages their advantages and is appealing in modeling viscous incompressible flows to balance accuracy and efficiency. In order to exchange the interface information between FDM and FPM for achieving consistency, stability, and convergence, a transition region is created in the particle region to maintain the stability of the interface between two methods. The mass flux algorithm is defined to control the particle creation and deletion. The mass is updated by N-S equations instead of the interpolation. In order to allow information exchange, an overlapping zone is defined near the interface. The information of overlapping zone is obtained by an FPM-type interpolation. Taylor-Green vortices and lid-driven shear cavity flows are simulated to test the accuracy and the conservation of the FDM-FPM hybrid approach. The standing waves and flows around NACA airfoils are further simulated to test the ability to deal with free surfaces and complex boundaries. The results show that FDM-FPM retains not only the high efficiency of FDM with multiple resolutions but also the ability of FPM in modeling free surfaces and complex boundaries.     

A correction for balancing discontinuous bed slopes in two‐dimensional smoothed particle hydrodynamics shallow water modeling

In this paper, a smoothed particle hydrodynamics (SPH) numerical model for the shallow water equations (SWEs) with bed slope source term balancing is presented. The solution of the SWEs using SPH is attractive being a conservative, mesh‐free, automatically adaptive method without special treatment for wet‐dry interfaces. Recently, the capability of the SPH–SWEs numerical scheme with shock capturing and general boundary conditions has been used for predicting practical flooding problems. The balance between the bed slope source term and fluxes in shallow water models is desirable for reliable simulations of flooding over bathymetries where discontinuities are present and has received some attention in the framework of Finite Volume Eulerian models. The imbalance because of the source term resulting from the calculation of the the water depth is eradicated by means of a corrected mass, which is able to remove the error introduced by a bottom discontinuity. Two different discretizations of the momentum equation are presented herein: the first one is based on the variational formulation of the SWEs in order to obtain a fully conservative formulation, whereas the second one is obtained using a non‐conservative form of the free‐surface elevation gradient. In both formulations, a variable smoothing length is considered. Results are presented demonstrating the corrections preserve still water in the vicinity of either 1D or 2D bed discontinuities and provide close agreement with 1D analytical solutions for rapidly varying flows over step changes in the bed. The method is finally applied to 2D dam break flow over a square obstacle where the balanced formulation improves the agreement with experimental measurements of the free surface. Copyright © 2012 John Wiley & Sons, Ltd.     

含液颗粒材料液固耦合分析的离散颗粒模型及特征线SPH法

对含液颗粒材料流固耦合分析建议了一个基于离散颗粒模型与特征线SPH法的显式拉格朗日-欧拉无网格方案。在已有的用以模拟固体颗粒集合体的离散颗粒模型[1]基础上,将颗粒间间隙内的流体模型化为连续介质,对其提出并推导了基于特征线的SPH法。数值例题显示了所建议方案在模拟颗粒材料与间隙流相互作用的能力和性能以及间隙流体对颗粒结构承载能力及变形的影响。     

An assessment of particle methods for approximating anisotropic dispersion

We derive a smoothed particle hydrodynamics (SPH) approximation for anisotropic dispersion that only depends upon the first derivative of the kernel function and study its numerical properties. In addition, we compare the performance of the newly derived SPH approximation versus an implementation of the particle strength exchange (PSE) method and a standard finite volume method for simulating multiple scenarios defined by different combinations of physical and numerical parameters. We show that, for regularly spaced particles, given an adequate selection of numerical parameters such as kernel function and smoothing length, the new SPH approximation is comparable with the PSE method in terms of convergence and accuracy and similar to the finite volume method. On other hand, the performance of both particle methods (SPH and PSE) decreases as the degree of disorder of the particle increases. However, we demonstrate that in these situations the accuracy and convergence properties of both particle methods can be improved by an adequate choice of some numerical parameters such as kernel core size and kernel function. Copyright © 2012 John Wiley & Sons, Ltd.     

三维溃坝流的光滑粒子动力学方法模拟

采用光滑粒子动力学SPH(Smoothed Particle Hydrodynamics)方法对三维溃坝流问题进行了数值模拟。为了逼真地模拟出坝内水体与壁面间相互作用而产生的水花飞溅、融合以及近壁面流动等现象,加入了混合长度形式的湍流模型。为了有效地防止粒子穿透固壁,提出了一种新型的适合三维数值模拟的固壁边界处理方法。应用SPH方法对三维溃坝流进行了数值模拟,并分别考虑了未添加障碍物和添加圆柱障碍物两种情形。计算结果表明,改进SPH方法能够精细地捕捉溃坝流在不同时刻的自由液面,并获得稳定而精确的数值结果。     

固体介质中SPH方法的拉伸不稳定性问题研究进展

光滑粒子流体动力学法(smoothed particle hydrodynamics, SPH)是一种基于核估计的无网格Lagrange数值方法.它用粒子方程离散流体动力学的连续方程, 既可以处理有限元难于处理的大变形和严重扭曲问题, 又可以处理有限差分法不易处理的自由边界和材料界面的问题, 在固体力学中的冲击、爆炸和裂纹模拟中具有广阔的发展前景.但是, 该算法的拉伸不稳定性(tensile instability)问题是它在固体力学领域中应用的最大障碍.对SPH稳定性分析表明, 算法不稳定性的条件仅与应力状态和核函数的2阶导数有关.目前, 应力点法(stress points)、Lagrange核函数法、人工应力法(artificialstress)、修正光滑粒子法(corrective smoothed particle method, CSPM)和守恒光滑法(conservativesmoothing)以及其他一些方法成功地改善了SPH的拉伸不稳定性, 但是每一种方法都不能彻底解决SPH的拉伸不稳定性问题.本文介绍了SPH法的方程和Von Neumann稳定性分析的思想, 以及国内外在这几个方面的研究成果及其最新进展, 同时指出目前研究中存在的问题和研究的方向.      

A corrected particle method with high-order Taylor expansion for solving the viscoelastic fluid flow

In this paper, a corrected particle method based on the smoothed particle hydrodynamics (SPH) method with high-order Taylor expansion (CSPH-HT) for solving the vis-coelastic flow is proposed and investigated. The validity and merits of the CSPH-HT method are first tested by solv-ing the nonlinear high order Kuramoto-Sivishinsky equation and simulating the drop stretching, respectively. Then the flow behaviors behind two stationary tangential cylinders of polymer melt, which have been received little attention, are investigated by the CSPH-HT method. Finally, the CSPH-HT method is extended to the simulation of the filling process of the viscoelastic fluid. The numerical results show that the CSPH-HT method possesses higher accuracy and stability than other corrected SPH methods and is more reliable than other corrected SPH methods.     

A critical investigation of smoothed particle hydrodynamics applied to problems with free‐surfaces

In this paper, an in‐depth study of SPH method, in its original weakly compressible version, is achieved on dedicated 2D and 3D free‐surface flow test cases. These rather critical prototype problems shall constitute suitable test cases to get through when building a free‐surface SPH model. The present work aims at investigating various numerical aspects of this method, often little mentioned in literature. In particular, a great care is paid to the dynamic part of the solution, which is critical to the local hydrodynamic load prediction. The role of numerical errors in the development of acoustic frequencies in the pressure signals is discussed, as well as the influence of the choice of the sound velocity. On the shown test problems, it is also evidenced that some numerical tools are crucial to ensure the robustness and accuracy of the standard SPH method. The convergence of our model is heuristically proved on these nonlinear prototype tests, showing at the same time the very satisfactory level of accuracy reached. Through these tests, some other numerical specificities of the SPH method are discussed, such as the self‐redistribution of the particles occurring during the Lagrangian evolution. A higher order model is also proposed, and its advantages and drawbacks are discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Enhancement of the accuracy of the finite volume particle method for the simulation of incompressible flows

A finite volume particle (FVP) method for simulation of incompressible flows that provides enhanced accuracy is proposed. In this enhanced FVP method, a dummy neighbor particle is introduced for each particle in the calculation and used for the discretization of the gradient model and Laplacian model. The error‐compensating term produced by introducing the dummy neighbor particle enables higher order terms to be calculated. The proposed gradient model and Laplacian model are applied in both pressure and pressure gradient calculations. This enhanced FVP scheme provides more accurate simulations of incompressible flows. Several 2‐dimensional numerical simulations are given to confirm its enhanced performance.     

Incompressible smoothed particle hydrodynamics simulation of multifluid flows

This paper presents an incompressible SPH (ISPH) technique to simulate multifluid flows. The SPH method is a mesh‐free particle modeling approach that can treat free surfaces and multi‐interfaces in a simple and efficient manner. The ISPH method employs an incompressible hydrodynamic formulation to solve the fluid pressure that ensures a stable pressure field. Two multifluid ISPH models are proposed following different interface treatments: the coupled ISPH model does not distinguish the different fluid phases and applies the standard ISPH technique across the interface, whereas the decoupled ISPH model first treats each fluid phase separately and then couples the different phases by applying pressure and shear stress continuities across the interface. The two proposed models were used to investigate a gravity underflow with a low density ratio in a Generalized Reservoir Hydrodynamics (GRH) flume and a horizontal lock exchange flow with a high density ratio. Comparisons with data and relevant numerical error analysis indicated that the decoupled model performed well in cases of both low and high density ratios because of the accurate treatment of interface boundaries. Copyright © 2011 John Wiley & Sons, Ltd.     

An incompressible SPH method for simulation of unsteady viscoelastic free-surface flows

In this paper, an incompressible smoothed particle hydrodynamics (SPH) method is presented to solve unsteady free-surface flows. Both Newtonian and viscoelastic fluids are considered. In the case of viscoelastic fluids, both the Maxwell and Oldroyd-B models are investigated. The proposed SPH method uses a Poisson pressure equation to satisfy the incompressibility constraints. The solution algorithm is an explicit predictor-corrector scheme and employs an adaptive smoothing length based on density variations. To alleviate the numerical difficulties encountered when fluid is highly stretched, an artificial stress term is incorporated into the momentum equation which reduces the risk of unrealistic fractures in the material. Two challenging test cases, the impacting drop and the jet buckling problems, are solved to demonstrate the capability of the proposed scheme in handling viscoelastic flows with complex free surfaces. The jet buckling test case was solved for a wide range of Weissenberg numbers. It was shown that in all cases the method is stable and fairly accurate and agrees well with the available data.     

SPH computation of plunging waves using a 2‐D sub‐particle scale (SPS) turbulence model

The paper presents a 2‐D large eddy simulation (LES) modelling approach to investigate the properties of the plunging waves. The numerical model is based on the smoothed particle hydrodynamics (SPH) method. SPH is a mesh‐free Lagrangian particle approach which is capable of tracking the free surfaces of large deformation in an easy and accurate way. The Smagorinsky model is used as the turbulence model due to its simplicity and effectiveness. The proposed 2‐D SPH–LES model is applied to a cnoidal wave breaking and plunging over a mild slope. The computations are in good agreement with the documented data. Especially the computed turbulence quantities under the breaking waves agree better with the experiments as compared with the numerical results obtained by using the k–ε model. The sensitivity analyses of the SPH–LES computations indicate that both the turbulence model and the spatial resolution play an important role in the model predictions and the contributions from the sub‐particle scale (SPS) turbulence decrease with the particle size refinement. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical modelling of complex turbulent free‐surface flows with the SPH method: an overview

The gridless smoothed particle hydrodynamics (SPH) method is now commonly used in computational fluid dynamics (CFD) and appears to be promising in predicting complex free‐surface flows. However, increasing flow complexity requires appropriate approaches for taking account of turbulent effects, whereas some authors are still working without any turbulence closure in SPH. A review of recently developed turbulence models adapted to the SPH method is presented herein, from the simplistic point of view of a one‐equation model involving mixing length to more sophisticated (and thus realistic) models like explicit algebraic Reynolds stress models (EARSM) or large eddy simulation (LES). Each proposed model is tested and validated on the basis of schematic cases for which laboratory data, theoretical or numerical solutions are available in the general field of turbulent free‐surface incompressible flows (e.g. open‐channel flow and schematic dam break). They give satisfactory results, even though some progress should be made in the future in terms of free‐surface influence and wall conditions. Recommendations are given to SPH users to apply this method to the modelling of complex free‐surface turbulent flows. Copyright © 2006 John Wiley & Sons, Ltd.     

Space potential particles to enhance the stability of projection-based particle methods

Particle methods have been seldom verified by a Karman vortex simulation, which is commonly performed as a typical benchmark in computational fluid dynamics. This is mainly due to a difficulty in suppression of occurrence of unphysical voids manifested usually in a strong vortex on account of definition of free surface by the Lagrangian tracking framework with inconsistency in volume conservation. This paper presents a simple and effective scheme as a free-surface boundary condition of projection-based particle methods, namely the MPS (moving particle semi-implicit) and Incompressible SPH (ISPH) methods to handle the free surface with consistency in volume conservation. The new scheme is introduced into the Poisson pressure equation (PPE) with consideration of a potential in void space as space potential particle (SPP), to reproduce physical motions of particles around free surface through a particle–void interaction. The enhancing effect of the newly proposed SPP scheme is shown by simulating a few numerical tests, including a whirling water flow, a two-phase surfacing flow, and a set of Karman vortex simulations.     

A one-dimensional meshfree particle formulation for simulating shock waves

In this paper, a one-dimensional meshfree particle formulation is proposed for simulating shock waves, which are associated with discontinuous phenomena. This new formulation is based on Taylor series expansion in the piecewise continuous regions on both sides of a discontinuity. The new formulation inherits the meshfree Lagrangian and particle nature of SPH, and is a natural extension and improvement on the traditional SPH method and the recently proposed corrective smoothed particle method (CSPM). The formulation is consistent even in the discontinuous regions. The resultant kernel and particle approximations consist of a primary part similar to that in CSPM, and a corrective part derived from the discontinuity. A numerical study is carried out to examine the performance of the formulation. The results show that the new formulation not only remedies the boundary deficiency problem but also simulates the discontinuity well. The formulation is applied to simulate the shock tube problem and a 1-D TNT slab detonation. It is found that the proposed formulation captures the shock wave at comparatively lower particle resolution. These preliminary numerical tests suggest that the new meshfree particle formulation is attractive in simulating hydrodynamic problems with discontinuities such as shocks waves.Received: 8 October 2002, Accepted: 10 May 2003, Published online: 15 August 2003