SPH方法Delaunay三角刨分与自由液面重构

光滑粒子法(SPH)作为一种拉格朗日型无网格方法,兼具欧拉网格方法和拉格朗日网格方法的优势,已经成功应用于科学和工程的众多领域。SPH方法后处理一般基于无规则分布的粒子,不如网格类方法后处理简便、直接。另外,SPH方法模拟自由液面流动等问题时,通过粒子位置难以重构自由液面的准确位置。发展一种基于Delaunay三角刨分的SPH后处理方法,即先基于SPH粒子位置利用Delaunay三角刨分建立三角网格,然后将粒子信息转化成网格单元/节点信息,从而可以在三角网格上进行后处理,实现基于网格方法的后处理功能,并可以在三角网格上直接提取或重构自由液面。将本文的方法应用到液滴碰撞和溃坝流SPH模拟结果的后处理中,得到了非常好的结果,表明本文的方法有效可靠。     

A consistent incompressible SPH method for internal flows with fixed and moving boundaries

An improved incompressible smoothed particle hydrodynamics (ISPH) method is presented, which employs first‐order consistent discretization schemes both for the first‐order and second‐order spatial derivatives. A recently introduced wall boundary condition is implemented in the context of ISPH method, which does not rely on using dummy particles and, as a result, can be applied more efficiently and with less computational complexity. To assess the accuracy and computational efficiency of this improved ISPH method, a number of two‐dimensional incompressible laminar internal flow benchmark problems are solved and the results are compared with available analytical solutions and numerical data. It is shown that using smaller smoothing lengths, the proposed method can provide desirable accuracies with relatively less computational cost for two‐dimensional problems. Copyright © 2015 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.     

Conservation of circulation in SPH for 2D free‐surface flows

In this paper, we study how accurately the Smoothed Particle Hydrodynamics (SPH) scheme accounts for the conservation and the generation of vorticity and circulation, in a low viscosity, weakly compressible, barotropic fluid in the context of free‐surface flows. We consider a number of simple examples to clarify the processes involved and the accuracy of the simulations. The first example is a differentially rotating fluid where the integration path for the circulation becomes progressively more complicated, whereas the structure of the velocity field remains simple. The second example is the collision of two rectangular regions of fluid. We show that SPH accurately predicts the time variation of the circulation as well as the total vorticity for selected domains advected by the fluid. Finally, a breaking wave is considered. For such a problem we show how the dynamics of the vorticity generated by the breaking process is captured by the SPH model. Copyright © 2012 John Wiley & Sons, Ltd.     

An improved SPH model for multiphase flows with large density ratios

This paper presents a new smoothed particle hydrodynamics (SPH) model for simulating multiphase fluid flows with large density ratios. The new SPH model consists of an improved discretization scheme, an enhanced multiphase interface treatment algorithm, and a coupled dynamic boundary treatment technique. The presented SPH discretization scheme is developed from Taylor series analysis with kernel normalization and kernel gradient correction and is then used to discretize the Navier‐Stokes equation to obtain improved SPH equations of motion for multiphase fluid flows. The multiphase interface treatment algorithm involves treating neighboring particles from different phases as virtual particles with specially updated density to maintain pressure consistency and a repulsive interface force between neighboring interface particles into the pressure gradient to keep sharp interface. The coupled dynamic boundary treatment technique includes a soft repulsive force between approaching fluid and solid particles while the information of virtual particles are approximated using the improved SPH discretization scheme. The presented SPH model is applied to 3 typical multiphase flow problems including dam breaking, Rayleigh‐Taylor instability, and air bubble rising in water. It is demonstrated that inherent multiphase flow physics can be well captured while the dynamic evolution of the complex multiphase interfaces is sharp with consistent pressure across the interfaces.     

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.     

A coupled WC-TL SPH method for simulation of hydroelastic problems

A coupled weakly compressible (WC) and total Lagrangian (TL) smoothed particle hydrodynamics (SPH) method is developed for simulating hydroelastic problems. The fluid phase is simulated using WCSPH method, while the structural dynamics are solved using TLSPH method. Fluid and solid components of the method are validated separately. A sloshing water tank problem is solved to test the WCSPH method while oscillation of a thin plate and large deformation of a cantilever beam are simulated to test the TLSPH method. After validating each component, the coupled WC-TL SPH scheme is used to simulate two benchmark hydroelastic problems. The first test case shows the evolution of water column with an elastic boundary gate, and the second one investigates the breaking water column impact on elastic structures. The agreement between WC-TL SPH results and literature data shows the ability of the proposed method in simulating hydroelastic phenomena.     

A comparative study of truly incompressible and weakly compressible SPH methods for free surface incompressible flows

In this paper, the performance of the incompressible SPH (ISPH) method and an improved weakly compressible SPH (IWCSPH) method for free surface incompressible flows are compared and analyzed. In both methods, the Navier–Stokes equations are solved, and no artificial viscosity is used. The ISPH algorithm in this paper is based on the classical SPH projection method with common treatments on solid boundaries and free surfaces. The IWCSPH model includes some advanced corrective algorithms in density approximation and solid boundary treatment (SBT). In density approximation, the moving least squares (MLS) approach is applied to re‐initialize density every several steps to obtain smoother and more stable pressure fields. An improved coupled dynamic SBT algorithm is implemented to obtain stable pressure values near solid wall areas and, thus, to minimize possible numerical oscillations brought in by the solid boundaries. Three representative numerical examples, including a benchmark test for hydrostatic pressure, a dam breaking problem and a liquid sloshing problem, are comparatively analyzed with ISPH and IWCSPH. It is demonstrated that the present IWCSPH is more attractive than ISPH in modeling free surface incompressible flows as it is more accurate and more stable with comparable or even less computational efforts. Copyright © 2013 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 corrected symmetric SPH method to simulate viscoelastic free surface flows based on the PTT model

In this work, a corrected symmetric and periodic density reinitialized SPH (CSPDR‐SPH) method is proposed and extended to simulate the viscoelastic free surface flows based on the Phan–Thien–Tanner model. The improvements mainly lie in deriving a corrected symmetric kernel gradient, and combining it with a periodic density reinitialization procedure. In addition, a simple artificial viscosity and a simple artificial stress form are adopted. Thus, the CSPDR‐SPH method has higher accuracy and better stability than the SPH method, and conserves both linear and angular momentums. The consistency and convergence of the CSPDR‐SPH method are justified by approximating a function in one and two dimensions. The merits of CSPDR‐SPH method are demonstrated by several benchmarks. The simple flow in a two‐dimensional channel is investigated to show the capability of the CSPDR‐SPH method to simulate the viscoelastic free surface flow. Then the CSPDR‐SPH method is extended to simulate the impacting drop problem. Numerical results show that the CSPDR‐SPH method can precisely capture the viscoelastic free surface. The Reynolds number, Weissenberg number and elongation parameter have remarkable effect on the flows. Copyright © 2012 John Wiley & Sons, Ltd.     

An SPH multi‐fluid model based on quasi buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios

We introduce a smoothed particle hydrodynamics (SPH) concept for the stabilization of the interface between 2 fluids. It is demonstrated that the change in the pressure gradient across the interface leads to a force imbalance. This force imbalance is attributed to the particle approximation implicit to SPH. To stabilize the interface, a pressure gradient correction is proposed. In this approach, the multi‐fluid pressure gradients are related to the (gravitational and fluid) accelerations. This leads to a quasi‐buoyancy correction for hydrostatic (stratified) flows, which is extended to nonhydrostatic flows. The result is a simple density correction that involves no parameters or coefficients. This correction is included as an extra term in the SPH momentum equation. The new concept for the stabilization of the interface is explored in 5 case studies and compared with other multi‐fluid models. The first case is the stagnant flow in a tank: The interface remains stable up to density ratios of 1:1000 (typical for water and air), in combination with artificial wave speed ratios up to 1:4. The second and third cases are the Rayleigh‐Taylor instability and the rising bubble, where a reasonable agreement between SPH and level‐set models is achieved. The fourth case is an air flow across a water surface up to density ratios of 1:100, artificial wave speed ratios of 1:4, and high air velocities. The fifth case is about the propagation of internal gravity waves up to density ratios of 1:100 and artificial wave speed ratios of 1:4. It is demonstrated that the quasi‐buoyancy model may be used to stabilize the interface between 2 fluids up to high density ratios, with real (low) viscosities and more realistic wave speed ratios than achieved by other weakly compressible SPH multi‐fluid models. Real wave speed ratios can be achieved as long as the fluid velocities are not very high. Although the wave speeds may be artificial in many cases, correct and realistic wave speed ratios are essential in the modelling of heat transfer between 2 fluids (eg, in engineering applications such as gas turbines).     

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 innovative open boundary treatment for incompressible SPH

An innovative inflow/outflow boundary treatment has been proposed to be used in smoothed particle hydrodynamics (SPH). Among other strategies, it involves the use of extended regions at open boundary sections and a procedure to enforce the mass continuity constraint, as well as to minimize outflow reflections. This methodology has been coupled with a modified ‘particle shifting’ algorithm, so that the robustness of the method could be ensured at high Reynolds number regimes. Confined flow around a square cylinder with an open outflow has been selected as the flow problem to analyze the performance of the new method. Detailed comparisons with data available in the literature for a variety of mesh‐based methods have been made for two different values of the blockage ratio β, namely for β = 1/4 and 1/8, and a range of supercritical Reynolds numbers. The results obtained with the present implementation of truly incompressible SPH have demonstrated numerical accuracy comparable with that of other methods, as well as the success of the open boundary treatment. A direct comparison with previously published SPH results for a distinct blockage ratio, namely for β = 1/5, has also revealed that a major improvement has been achieved by the use of the method described in this paper. Copyright © 2015 John Wiley & Sons, Ltd.     

光滑粒子动力学方法的发展与应用

光滑粒子动力学(smoothed particle hydrodynamics,SPH)是一种拉格朗日型无网格粒子方法,已经成功地应用到了工程和科学的众多领域.SPH使用粒子离散及代表所模拟的介质,并且基于粒子体系估算和近似介质运动的控制方程.本文分析和综述了SPH模拟方法的发展历程、数值方法与应用进展.介绍了SPH方法的基本思想;从连续性、边界处理、稳定性和计算效率4个方面阐述了SPH方法的研究现状;介绍了SPH方法近年来在可压缩流动、不可压缩流动以及弹塑性材料高速变形与失效方面的一些典型应用;并对SPH方法的发展与应用进行了预测与展望.      

Unified semi‐analytical wall boundary conditions for inviscid,laminar or turbulent flows in the meshless SPH method

Wall boundary conditions in smoothed particle hydrodynamics (SPH) is a key issue to perform accurate simulations. We propose here a new approach based on a renormalising factor for writing all boundary terms. This factor depends on the local shape of a wall and on the position of a particle relative to the wall, which is described by segments (in two‐dimensions), instead of the cumbersome fictitious or ghost particles used in most existing SPH models. By solving a dynamic equation for the renormalising factor, we significantly improve traditional wall treatment in SPH, for pressure forces, wall friction and turbulent conditions. The new model is demonstrated for cases including hydrostatic conditions for still water in a tank of complex geometry and a dam break over triangular bed profile with sharp angle where significant improved behaviour is obtained in comparison with the conventional boundary techniques. The latter case is also compared with a finite volume and volume‐of‐fluid scheme. The performance of the model for a two‐dimensional laminar flow in a channel is demonstrated where the profiles of velocity are in agreement with the theoretical ones, demonstrating that the derived wall shear stress balances the pressure gradient. Finally, the performance of the model is demonstrated for flow in a schematic fish pass where both the velocity field and turbulent viscosity fields are satisfactorily reproduced compared with mesh‐based codes. Copyright © 2012 John Wiley & Sons, Ltd.     

A novel method to calculate the pressure interaction between dust and fluid using SPH

Unstable behavior of smoothed particle hydrodynamics (SPH) dust particles, such as clumping or fingering under certain conditions, has been reported by several researchers who have conducted studies on dusty fluid SPH. The simulation results in this study show that this instability is numerical, and the instability is mainly attributable to the ill‐interpolated pressure gradient in the interaction term between 2 phases. In this paper, we introduce a new method to calculate the pressure force interaction term between dust and fluid particles. The key idea is to first interpolate the pressure gradient at SPH fluid particles and then use the values to calculate the pressure gradient at SPH dust particles, in a consecutive manner. To compare the new method with the existing method, we first conducted an interpolation of pressure gradient at hydrostatic equilibrium under gravity to estimate any error. The results show that the new method is more accurate. We then conducted additional numerical tests, namely, dust‐liquid counterflow, sedimentation in a confined tank, and sedimentation in the presence of turbulence. The unphysical unstable behavior of SPH dust particles such as clumping or fingering was significantly reduced in the new method. The results also show that the instability becomes more significant when using the existing method especially for the case when simulating a flow with relatively high concentration of dust or for the case in which inertia dominates the dynamics of dust particles. Especially, in those cases, the existing method should be avoided, and the newly proposed method is highly recommended.     

Time-dependent liquid metal flows with free convection and a deformable free surface

The finite element method is employed to investigate time-dependent liquid metal flows with free convection, free surfaces and Marangoni effects. The liquid circulates in a two-dimensional shallow trough with differentially heated vertical walls. The spatial formulation incorporates mixed Lagrangian approximations to the velocity, pressure, temperature and free surface position. The time integration is performed with the backward Euler and trapezoid rule methods with step size control. The Galerkin method is used to reduce the problem to a set of non-linear equations which are solved with the Newton–Raphson method. Calculations are performed for conditions relevant to the electron beam vaporization of refractory metals. The Prandtl number is 0·015 and Grashof number are in the transition range between laminar and turbulent flow. The results reveal the effects of flow intensity, surface tension gradients, mesh refinement and time integration strategy.     

The characteristic‐based split (CBS) meshfree method for free surface flow problems in ALE formulation

A semi‐implicit characteristic‐based split (CBS) meshfree algorithm in the arbitrary Lagrangian Eulerian (ALE) framework is proposed for the numerical solution of incompressible free surface flow problem in the paper. The algorithm is the extension of general CBS method which was initially introduced in finite element framework, this is due to the fact that CBS method not only can enhance the stability, but also avoid LBB condition when equal order basis function is used to approximate velocity and pressure variables. Meanwhile, a simple way for node update and node speed calculation is developed which is used to capture the free surface exactly. The numerical solutions are compared with available analytical and numerical solutions, which shows that the proposed method has better ability to simulate the free surface incompressible flow problem. Copyright © 2009 John Wiley & Sons, Ltd.     

An improved MUSCL treatment for the SPH‐ALE method: comparison with the standard SPH method for the jet impingement case

In the present work, a new implementation of the Monotone Upwind‐centered Scheme for Conservation Laws (MUSCL) ‐ Hancock scheme has been developed for the SPH‐Arbitrary Lagrangian Eulerian (ALE) method. The resulting method was tested at various benchmark cases and then it was used to simulate the jet impingement on a flat plate for several different impingement angles, in comparison with the standard SPH method and results from literature. The SPH‐ALE method proves to produce higher quality results than the standard SPH method in all cases, while the MUSCL treatment tends to remedy the issues of the numerical viscosity, inherent to the method, up to a point. Copyright © 2012 John Wiley & Sons, Ltd.