光滑粒子流体动力学有限元法接触算法研究

 耦合光滑粒子流体动力学（SPH）方法和有限元法（FEM）,是研究冲击动力学问题的一种有效途径。为解决SPH粒子和有限单元间的接触问题,提出了SPH-FEM接触算法。该算法是在有限元节点处设置背景粒子,采用SPH接触算法的思想,计算施加在SPH粒子和有限元节点上的接触力,并且以外力的形式分别加入到SPH动量方程和有限元动力学方程中。利用SPH-FEM接触算法,对两杆撞击以及圆柱形钢弹正冲击钢板发生的冲塞破坏过程进行了三维数值模拟,靶板采用含损伤的Johnson-Cook模型和Grüneisen状态方程,模拟结果与实验结果吻合较好。     

基于Lagrange及SPH算法的花岗岩侵彻数值模拟

为研究不同算法对弹体侵彻花岗岩模拟的影响,基于仿真分析软件LS-DYNA中的Lagrange算法及SPH(Smooth particle hydrodynamics)算法,采用Lagrange、SPH-Lagrange耦合及SPH算法分别对弹体侵彻、贯穿花岗岩靶体进行数值模拟,并从计算效率、侵彻深度、速度衰减、靶体损伤、Mises应力分布多方面对比模拟结果,分析3种算法用于研究岩石侵彻问题的优势和不足。研究表明:Lagrange算法的计算效率最高,计算精度高,但存在单元畸变、无撞击溅射、无后坑区等问题;SPH算法的计算效率最低,但模拟效果良好;SPH-Lagrange耦合算法兼具二者优势,但会导致应力滞后和应力波不稳定衰减。在大型模拟中应优先选用Lagrange算法和SPH-Lagrange耦合算法。     

基于SPH-FEM转换算法的7.62mm步枪弹冲击30CrMnSiA钢板的数值计算

从转换判据和时间步长控制两个方面对光滑粒子流体动力学-有限元(SPH-FEM)转换算法进行改进,采用改进的SPH-FEM转换算法对7.62 mm步枪弹冲击特殊热处理的30CrMnSiA钢板进行全尺寸三维数值计算,将子弹在冲击过程中发生严重畸变的有限单元转换为SPH粒子继续参与计算.子弹采用弹塑性模型,靶板采用修正的Johnson-Cook强度模型和Gruneisen状态方程.针对不同的子弹初速,计算靶板盘形凹陷和冲塞两种破坏模式,计算结果与实验结果吻合较好.表明改进的SPH-FEM转换算法能够合理高效地利用有限单元和SPH粒子,为低强度子弹冲击高强度靶板的计算提供一种有效途径.     

水射流对煤体冲击的有限元与光滑粒子耦合法数值模拟

采用光滑粒子与有限元耦合算法对高压水射流冲击煤体进行了数值模拟,建立了长为5mm、半径为2mm的圆柱形水体以不同速度冲击煤体的计算模型。根据计算结果,分析了煤体在高压水射流冲击下的损伤模式、煤体中的应力波传播形式、煤体在高压水射流作用下的临界破煤压力。     

光滑粒子动力学方法中粒子分布与数值稳定性分析

光滑粒子动力学(SPH)作为一种拉格朗日型无网格粒子方法,已经成功地应用于包括含多相流动界面以及移动边界的可压缩和不可压缩流体运动的研究中.通过对Poiseuille流动的深入研究,探索了SPH方法中粒子分布对计算精度的影响,揭示了一种因为粒子不规则分布而导致的数值不稳定现象.研究显示,这种数值不稳定性起源于SPH方法粒子近似过程中的不连续性.使用了一种新的粒子近似格式以确保SPH方法中粒子近似的连续性.计算结果表明,这种新的粒子近似格式对于规则和不规则的粒子分布都能得到稳定精度的结果.     

耦合方法在超高速碰撞数值模拟中的应用

 相比于传统的数值方法，无网格光滑粒子法（Smoothed Particle Hydrodynamics，SPH）更适合模拟超高速碰撞问题，它能够清晰地模拟材料界面，并且能够克服中网格大变形导致的数值不稳定。然而在SPH方法中，为了得到t时刻一个节点上的物理量，需要先找出与它相互作用的临近节点，导致计算速度很慢，计算所需的时间远远大于有限元方法所需的时间。采用SPH与Lagrange法相耦合的方法对3D超高速碰撞过程进行了模拟研究。计算结果表明：SPH与Lagrange法耦合方法的计算结果与SPH计算结果精度接近，并且能够大大地节省计算时间。     

非线性薛定谔方程的高阶分裂改进光滑粒子动力学算法

为提高传统光滑粒子动力学(SPH)方法求解高维非线性薛定谔(nonlinear Schr?dinger/Gross-Pitaevskii equation, NLS/GP)方程的数值精度和计算效率,本文首先基于高阶时间分裂思想将非线性薛定谔方程分解成线性导数项和非线性项,其次拓展一阶对称SPH方法对复数域上线性导数部分进行显式求解,最后引入MPI并行技术,结合边界施加虚粒子方法给出一种能够准确、高效地求解高维NLS/GP方程的高阶分裂修正并行SPH方法.数值模拟中,首先对带有周期性和Dirichlet边界条件的NLS方程进行求解,并与解析解做对比,准确地得到了周期边界下孤立波的奇异性,且对提出方法的数值精度、收敛速度和计算效率进行了分析;随后,运用给出的高阶分裂粒子方法对复杂二维和三维NLS/GP问题进行了数值预测,并与其他数值结果进行比较,准确地展现了非线性孤立波传播中的奇异现象和玻色-爱因斯坦凝聚态中带外旋转项的量子涡旋变化过程.     

基于黎曼解的粒子间接触算法在SPH中的应用

 采用光滑粒子流体动力学（SPH）方法模拟大变形问题具有明显的优点，但传统的SPH方法在模拟冲击波与接触界面的作用时，往往会出现压力的反常跳动。采用黎曼解描述粒子间相互作用的接触算法对传统SPH方法进行修正，计算了激波管和飞片碰撞（包含接触界面）问题中波的传播，并将计算结果与解析解作比较。结果表明，与传统的光滑粒子法相比，该改进的光滑粒子法无需引入人工粘性项和人工热流项，程序结构简洁，且能较好地处理接触界面问题，从而能有效提高计算精度。     

典型自由面流动问题的SPH-ALE数值模拟

应用基于黎曼解的SPH-ALE方法对两种典型自由面流动问题进行数值模拟,并提出一种一阶核函数修正压力计算方法,通过对临近边界的水粒子压力进行核积分,近似估算固壁边界压力.给出不同时刻的流场压力分布及自由液面演化过程,将计算结果与相关的试验值及数值解进行对比,分析结果表明：SPH-ALE方法较传统SPH方法在流场压力计算精度上有较大的改进,在处理强非线性自由面流动问题时能够达到较高的精度.     

粉末高速压制成形过程中的应力波分析

应用离散单元法,模拟了粉末高速压制成形过程中的压力传播过程.根据粉末高速压制成形的工艺特性,把一次压制过程分为弹性加载、塑性变形、弹性卸载三个阶段;基于离散单元法的基本理论,分别建立了三个阶段的控制方程;应用PFC2D软件对粉末高速压制过程模腔内部颗粒的运动状态进行了数值模拟,给出了压坯内部的压力分布,得出了实验中无法测量的压坯内部应力传播波形.数值模拟结果显示,压力作用曲线表现出明显的弛豫现象,形成了倾斜度不同的锯齿状加载波形和卸载波形,压坯底层的应力波与实验得到的应力波相符. 关键词： 高速压制成形 离散单元法 接触模型 应力波     

使用AMR型背景网格的并行SPH方法

在分布式并行SPH方法中根据网格范围内粒子最大光滑长度调整网格尺度的AMR（Adaptive Mesh Refinement）背景网格,确保网格内粒子的相邻粒子位于同一个网格或者相邻的同尺寸网格范围内.与统一尺寸的背景网格相比,在光滑长度空间分布不均匀和随时间变化的情况下能够应用并减小搜索量,提高计算效率.数值结果表明,基于AMR型背景网格的并行SPH方法应用到粒子光滑长度变化很大的数值计算时能有效地降低搜索复杂度.     

Multi-resolution technique integrated with smoothed particle element method (SPEM) for modeling fluid-structure interaction problems with free surfaces

Free-surface flows, especially those associated with fluid-structure interactions(FSIs), pose challenging problems in numerical simulations. The authors of this work recently developed a smoothed particle element method(SPEM) to simulate FSIs. In this method, both the fluid and solid regions are initially modeled using a smoothed finite element method(S-FEM) in a Lagrangian frame, whereas the fluid regions undergoing large deformations are adaptively converted into particles and modeled with an improved smoothed particle hydrodynamics(SPH) method. This approach greatly improves computational accuracy and efficiency because of the advantages of the S-FEM in efficiently treating solid/fluid regions showing small deformations and the SPH method in effectively modeling moving interfaces. In this work, we further enhance the efficiency of the SPEM while effectively capturing local fluid information by introducing a multi-resolution technique to the SPEM and developing an effective approach to treat multi-resolution element-particle interfaces. Various numerical examples demonstrate that the multiresolution SPEM can significantly reduce the computational cost relative to the original version with a constant resolution.Moreover, the novel approach is effective in modeling various incompressible flow problems involving FSIs.     

Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid

As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics (SPH) method is used to model the compressible fluid, the natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit (GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.     

Smoothed particle hydrodynamics(SPH) for modeling fluid-structure interactions

Fluid-structure interaction(FSI) is a class of mechanics-related problems with mutual dependence between the fluid and structure parts and it is observable nearly everywhere, in natural phenomena to many engineering systems. The primary challenges in developing numerical models with conventional grid-based methods are the inherent nonlinearity and timedependent nature of FSI, together with possible large deformations and moving interfaces. Smoothed particle hydrodynamics(SPH) method is a truly Lagrangian and meshfree particle method that conveniently treats large deformations and naturally captures rapidly moving interfaces and free surfaces. Since its invention, the SPH method has been widely applied to study different problems in engineering and sciences, including FSI problems. This article presents a review of the recent developments in SPH based modeling techniques for solving FSI-related problems. The basic concepts of SPH along with conventional and higher order particle approximation schemes are first introduced. Then, the implementation of FSI in a pure SPH framework and the hybrid approaches of SPH with other grid-based or particle-based methods are discussed. The SPH models of FSI problems with rigid, elastic and flexible structures, with granular materials, and with extremely intensive loadings are demonstrated. Some discussions on several key techniques in SPH including the balance of accuracy, stability and efficiency, the treatment of material interface, the coupling of SPH with other methods, and the particle regularization and adaptive particle resolution are provided as concluding marks.     

Calculating the forced response of cylinders and cylindrical shells using the wave and finite element method

The dynamic response of circular cylinders can be obtained analytically in very few (and simple) cases. For complicated (thick or anisotropic) circular cylinders, researchers often resort to the finite element (FE) method. This can lead to large models, especially at higher frequencies, which translates into high computational costs and memory requirements. In this paper, the response of axially homogenous circular cylinders (that can be arbitrarily complex through the thickness) is obtained using the wave and finite element (WFE) method. Here, the homogeneity of the cylinder around the circumference and along the axis are exploited to post-process the FE model of a small rectangular segment of the cylinder using periodic structure theory and obtain the wave characteristics of the cylinder. The full power of FE methods can be utilised to obtain the FE model of the small segment. Then, the forced response of the cylinder is posed as an inverse Fourier transform. However, since there are an integer number of wavelengths around the circumference of a closed circular cylinder, one of the integrals in the inverse Fourier transform becomes a simple summation, whereas the other can be resolved analytically using contour integration and the residue theorem. The result is a computationally efficient technique for obtaining the response to time harmonic, arbitrarily distributed loads of axially homogenous, circular cylinders with arbitrary complexity across the thickness.     

Fast free-surface detection and level-set function definition in SPH solvers

The present paper proposes a novel algorithm to detect the free-surface in particle simulations, both in two and three dimensions. Since the proposed algorithms are based on SPH interpolations their implementation does not require complex geometrical procedures. Thus the free-surface detection can be easily embedded in SPH solvers, without a significant increase of the CPU time. Throughout this procedure accurate normal vectors to the free-surface are made available. Then it is possible to define a level-set function algorithm which is presented in detail. The latter allows in-depth analyses of three-dimensional free-surface simulations by using standard visualization tools, including internal features of the flow. The algorithms proposed for detecting free-surface particles and defining the level-set function are validated on simple and complex two- and three-dimensional flow simulations. The usefulness of the proposed procedures to post-process and analyze complex flows are illustrated on realistic examples.