基于无滑移边界条件的SPH方法研究

在回顾了SPH无滑移边界条件施加方法的基础上,针对Ellero等人提出的无滑移边界处理方法,结合两次导数求解粘性项,分析了利用该方法求解Poiseuille流模型时遇到的不稳定问题,包括数值误差引起的不稳定问题和边界粒子场变量更新方式引起的不稳定问题,提出了相应的解决方案并对其方法进行了一定的改进,获得了更加精确的计算结果。最后尝试了一种与改进边界处理方法等效的方法,并利用Poiseuille流模型进行了验证。     

A GPU-accelerated smoothed particle hydrodynamics (SPH) model for the shallow water equations

Smoothed particle hydrodynamics (SPH) is a fully Lagrangian meshless computational method for solving the fluid dynamics equations. In recent years, it has also been employed to solve the shallow water equations (SWEs) and promising results have been obtained. However, SPH models are computationally very demanding and the SPH-SWE models considered in this work have no exception. In this paper, the Graphic Processing Units (GPUs) are explored to accelerate an SPH-SWE model for wider applications. Unlike Central Processing Units (CPUs), GPUs are highly parallelized, which makes it suitable for accelerating scientific computing algorithms like SPH. The aim is to design a GPU-based SPH model for solving the two-dimensional SWEs with variable smoothing lengths. Furthermore, a quad-tree neighbour searching method is implemented to further optimize the model performance. An idealized benchmark test and two real-world dam-break cases have been simulated to demonstrate the superior performance of the current GPU-accelerated high-performance SPH-SWE model.     

一个SPH流体实时模拟的全GPU实现框架

怎样实时地进行高度逼真的大规模流体模拟是图形学要研究的一个重要内容。流体的模拟由物理计算、碰撞检测、表面重构和渲染几个部分组成,因此有大量工作针对流体模拟中的各个部分算法进行GPU加速。提出一整套基于GPU的SPH流体模拟加速框架。在利用平滑粒子动力学(SPH)求解Navier-Stokes方程的基础上,借助基于GPU的空间划分PSS(Parallel Spatial Subdivision)来大幅度提升粒子碰撞的检测速度。同时,设计一种基于几何着色器(Geometry Shader)的流体表面信息的重建算法,并进一步地实现基于索引的优化,使得在流体表面重建过程无须遍历不包含表面的区域。实验结果表明,该方法能实时模拟出具有较好真实感的流体场景。     

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.     

一种新的有效模拟不可压缩流体的SPH方法

提出了一种基于光滑粒子流体动力学(SPH)来模拟不可压缩流体的有效方法.传统的SPH方法是针对可压缩流体设计的,而该方法是传统SPH方法的一个扩展.提出了一种新的可以满足不可压缩性的压强计算方法,讨论了压力和粘性力的新型计算方法.实验结果表明,提出的方法与以前的方法相比,能够更真实地模拟不可压缩流体.     

基于SPH与FEM的结构入水分析方法

建立基于光滑粒子动力学（smoothed particle hydrodynamics, SPH）、有限元法（finite element method, FEM）和无反射边界耦合的结构入水分析方法,将无限水域利用无反射边界条件截断成有限水域,将有限水域分为流体变形大的SPH区域、流体变形小的FEM区域和声学流体FEM区域,结构用FEM离散。采用通用接触算法模拟SPH与FEM的耦合,采用声固耦合方法处理FEM区域之间的耦合,建立流固耦合的SPH FEM分析方法。该方法结合SPH模拟大变形的优点和FEM的高效性,可实现含自由液面变形、液体飞溅和无限水域等特点的流固耦合问题的模拟,为结构入水分析缩小离散区域、降低自由度和SPH粒子数等提供一种有效的分析方法。     

Spectral properties of the SPH Laplacian operator

In order to address the question of the SPH (Smoothed Particle Hydrodynamics) Laplacian conditioning, a spectral analysis of this discrete operator is performed. In the case of periodic Cartesian particle network, the eigenfunctions and eigenvalues of the SPH Laplacian are found on theoretical grounds. The theory agrees well with numerical eigenvalues. The effects of particle disorder and non-periodicity conditions are then investigated from numerical viewpoint. It is found that the matrix condition number is proportional to the square of the particle number per unit length, irrespective of the space dimension and kernel choice.     

Towards accelerating smoothed particle hydrodynamics simulations for free-surface flows on multi-GPU clusters

Starting from the single graphics processing unit (GPU) version of the Smoothed Particle Hydrodynamics (SPH) code DualSPHysics, a multi-GPU SPH program is developed for free-surface flows. The approach is based on a spatial decomposition technique, whereby different portions (sub-domains) of the physical system under study are assigned to different GPUs. Communication between devices is achieved with the use of Message Passing Interface (MPI) application programming interface (API) routines. The use of the sorting algorithm radix sort for inter-GPU particle migration and sub-domain “halo” building (which enables interaction between SPH particles of different sub-domains) is described in detail. With the resulting scheme it is possible, on the one hand, to carry out simulations that could also be performed on a single GPU, but they can now be performed even faster than on one of these devices alone. On the other hand, accelerated simulations can be performed with up to 32 million particles on the current architecture, which is beyond the limitations of a single GPU due to memory constraints. A study of weak and strong scaling behaviour, speedups and efficiency of the resulting program is presented including an investigation to elucidate the computational bottlenecks. Last, possibilities for reduction of the effects of overhead on computational efficiency in future versions of our scheme are discussed.     

SPH truncation error in estimating a 3D function

The SPH truncation error (ε_T) can be defined as the sum of the integral kernel and the particle approximation error in Smoothed Particle Hydrodynamics modelling. Following the procedure proposed by Quinlan et al. [16] for a 1D generic derivative, we have derived an approximated 3D formulation of ε_T in reproducing a generic function. This kind of estimation is implemented in some SPH models in order to reproduce density or some transported scalars. Then a corresponding sensitivity analysis of ε_T has been performed adopting regular and irregular distributions of particles, arranged within a cube, delimited by lateral walls at each side. The evolution of ε_T has been analyzed and compared to the proposed formulation, which has been numerically estimated under some simple conditions. The SPH truncation error has then been investigated on a simple free surface test case: a supercritical flow over a channel sill. We have developed some conclusions about the dependence of ε_T on the position of the particles (inner or boundary), the shape of the function to be reproduced (f), the kernel support size (h), the particle volumes (ω), the kernel function (W), a non-dimensional distance between the volume barycentre and the particle location (δ), and a geometric anisotropy index of the particle volumes (I). We have finally underlined the difference between non-consistent simulations and estimations using Shepard’s correction.     

SPH中一种层流入口、出口边界的处理方法

提出一种替代周期边界条件的对入口、出口边界的处理方法,这种方法使用跟随虚粒子处理入口、出口边界。跟随虚粒子设置于入口、出口的外侧,这些虚粒子的速度、位置根据对应的内部粒子的速度、位置进行更新。该方法建立在对层流特性的分析的基础上,适用于具有层流入口或出口的低雷诺数流场中。利用该入、出口边界处理新方法,分别对Poiseuille流和渐扩管平面流进行数值摸拟,数值结果与理论解吻合良好。     

基于SPH算法的飞行器鸟撞数值仿真分析

应用LS-DYNA动力学仿真软件,采用SPH算法进行鸟撞平板数值仿真分析.通过与实际试验结果对比分析,仿真计算结果与试验结果吻合较好,同时得到了鸟弹撞击速度与损伤(最大应力)之间的的经验公式.鸟撞平板仿真验证了仿真方法、模型及结构属性模拟的合理性,仿真计算结论为飞行器结构抗鸟撞设计提供有价值的数据.     

Parallel‐optimizing SPH fluid simulation for realistic VR environments

In virtual environments, real‐time simulation and rendering of dynamic fluids have always been the pursuit for virtual reality research. In this paper, we present a real‐time framework for realistic fluid simulation and rendering on graphics processing unit. Because of the high demand for interactive fluids with larger particle set, the computational need is becoming higher. The proposed framework can effectively reduce the computational burden through avoiding the computation in inactive areas, where many particles with similar properties and low local pressure cluster together. While in active areas, the computation is fully carried out; thus, the fluid dynamics are largely preserved. Here, a robust particle classification technique is introduced to classify particles into either active or inactive. The test results have shown that the technique improves the time performance of fluid simulation largely. We then incorporate parallel surface reconstruction technique using marching cubes to extract the surfaces of the fluid. The introduced histogram pyramid‐based marching cubes technique is fast and memory efficiency. As a result, we are able to produce plausible and interactive fluids with the proposed framework for large‐scale virtual environments. Copyright © 2013 John Wiley & Sons, Ltd.     

SPH fluid control with self‐adaptive turbulent details

Smoothed particle hydrodynamics (SPH)‐based fluid control is often involved in fluid animation. Because most of the existing SPH fluid control methods employ the strategy of control force to control fluid particles, the artificial viscosity introduced by control force would lead to the loss of fine‐scale details. Although the introduction of the low‐pass filter can add details, it may easily destroy the target shape. To remedy the previous problems, we sample the control particles with curvature information to represent the shape complexity. Because of the shape's complexity, we suppress the generation of turbulence in the high‐curvature areas and promote turbulence in the low‐curvature regions. Our self‐adaptive way to randomly generate turbulence can effectively prevent the lack of fluid dynamics caused by the artificial viscosity. Our new method can improve the visual quality of the fluid animation, and the shape control result is consistent to the target shape. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Numerical simulation of droplet impacting liquid surface by SPH

Droplet impacting liquid surface is not only the extremely prevalent phenomenon in the nature and industrial production but also the extremely complicated problem of strong non-linear transient impact and free-surface flow. On the basis of the two-dimensional viscous incompressible N-S equations, this paper conducts a study of numerical simulation on the problem of droplet impacting liquid surface (water beads) of water container in certain initial velocity by the method of SPH (smoothed particle hydrodynam...     

基于SPH算法的钢球高速撞击肥皂数值仿真

运用光滑粒子流体动力学分析方法,对钢球高速侵彻肥皂靶标进行了数值仿真分析。建立了钢球与肥皂高速撞击数值计算模型,运用侵蚀接触算法,求解了高速钢球侵彻肥皂的动力响应时间历程,获取了钢球侵彻肥皂靶标的侵彻深度与投射物速度关系图和瞬态Von—Mises等效应力云图,分析了高速碰撞过程及碰撞过程中空腔的形成和变化情况,并与实验结果及Lagrange数值仿真结果对照,计算结果具有良好精度,表明运用SPH方法能够较好地描述高速撞击现象。文中的研究表明,SPH技术是开展创伤弹道研究的有效手段。     

一种基于自适应光滑长度的SPH液体模拟方法

传统SPH流体模拟方法通常使用固定的粒子光滑长度进行插值计算,在某些情况下会导致较大的插值误差。为提升模拟精度,建立了粒子光滑长度与邻居粒子密度调和平均数间的关系,自适应调整粒子的光滑长度,并设计和定义了相应的邻居搜索方案和核函数以解决受力不对称的问题。经实验验证,粒子邻居数方差有效降低,解决了传统SPH支持域固定导致的粒子插值误差过大的问题,使仿真结果更接近物理事实。同时由于物理计算精度的提高,模拟稳定性得到增强,可使用更大的时间步长,有效提升了模拟速度。最终,相比其他方法在视觉质量和模拟速度上均具有一定优势。     

A comparative numerical study between dissipative particle dynamics and smoothed particle hydrodynamics when applied to simple unsteady flows in microfluidics

Laminar flows through channels, pipes and between two coaxial cylinders are of significant practical interest because they often appear in a wide range of industrial, environmental, and biological processes. Discrete particle modeling has increasingly been used in recent years and in this study we examined two of these methods: dissipative particle dynamics (DPD) and smoothed particle hydrodynamics (SPH) method when applied to (a) time-dependent, plane Poiseuille flow and (b) flow between two coaxial cylinders at low Reynolds numbers. The two examples presented in this paper give insight into different features of the two discrete particle methods. It was found that both methods give results with high accuracy, but CPU time is much larger (of order 10²–10³ in the second example) for DPD than for SPH model. This difference is due to the fact that the number of time steps for the DPD model is much greater than for the SPH model (since thermal fluctuations are taken into account in the DPD model).     

基于CUDA的弱可压SPH流体建模与仿真

为了实现小尺度范围流体场景的实时、真实感模拟,采用弱可压SPH方法对水体进行建模,提出了流体计算的CPU GPU混合架构计算方法。针对邻域粒子查找算法影响流体计算效率的问题,采用三维空间网格对整个模拟区域进行均匀网格划分,利用并行前缀求和和并行计数排序实现邻域粒子的查找。最后,采用基于CUDA并行加速的Marching Cubes算法实现流体表面提取,利用环境贴图表现流体的反射和折射效果,实现流体表面着色。实验结果表明,所提出的流体建模和模拟算法能实现小尺度范围流体的实时计算和渲染,绘制出水的波动、翻卷和木块在水中晃动的动态效果,当粒子数达到1 048 576个时,GPU并行计算方法相较CPU方法的加速比为60.7。