完全拉格朗日SPH在冲击问题中的改进和应用

光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)在模拟固体大变形、破碎和裂纹扩展等问题中有天然的优势, 但SPH固有的拉伸不稳定缺陷是SPH在计算固体力学领域进一步应用的一大障碍. 完全拉格朗日SPH (total Lagrangian-SPH, TL-SPH)方法是一种有效的改善拉伸不稳定的措施, 但其仍面临边界区域精度低、界面条件难以施加、损伤裂纹难以模拟等缺陷. 因此, 首先将可达到二阶精度的高阶SPH方法与TL-SPH耦合, 为了节省高阶方法的计算量, 进一步简化粒子选取模式, 提出TL-SFPM (TL-simplified finite particle method)方法; 其次, 将可提高界面精度的DFPM (discontinuous finite particle method)方法与TL-SPH结合, 并提出一种基于黎曼解的界面接触算法, 通过在不同材料粒子间建立黎曼模型求解不同材料间的相互作用, 分别应用于流体?固体接触和固体?固体接触中; 再者, 为了捕捉固体受外载荷后的损伤程度及破坏模式, 提出一种完全拉格朗日框架下的粒子损伤破坏模型; 最后, 通过流?固冲击的带弹性挡板溃坝算例和固?固冲击的子弹撞击靶板算例验证提出的TL-SFPM方法、界面接触算法和损伤破坏模型的合理性和精确性, 进一步扩展TL-SPH方法在计算固体冲击问题中的应用.      

一种考虑界面不连续的改进的有限粒子法

有限粒子法（finite particle method，FPM）作为SPH（smoothed particle hydrodynamics）方法的重要改进，有效提高了边界区域粒子的近似精度，但是当FPM处理多物理场时，在不连续界面附近的计算精度会大大降低，并且FPM必须满足的矩阵非奇异性也提高了对界面处理的要求。本文中基于DSPH（discontinuous SPH）方法，提出了一种考虑界面不连续的改进FPM—DSFPM（discontinuous special FPM）法，旨在改善FPM在界面不连续处的计算精度，从而进一步提高其计算效率和稳定性。首先，分析了DSFPM的核近似精度。其次，根据不同的工程问题，给出DSFPM处理小变形和大变形问题的算法流程。利用DSFPM、DSPH和FPM等3种方法对弹性铝块小变形碰撞冲击算例进行了模拟，通过对比分析铝块的速度和应力以及计算时间验证了DSFPM算法在非连续界面处计算精度和计算效率的优势。最后，通过结合DSFPM和DFPM（discontinuous FPM）实现了对于大变形问题的模拟。     

多相流动的光滑粒子流体动力学方法研究综述

光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)具有粒子方法的无网格和全拉格朗日特征, 适用于具有界面大变形、不连续性和多物理场的多相流的高精度模拟. SPH方法模拟多相流已有大量报道, 具体的实现方式也大不相同. 本文首先阐述了采用SPH方法模拟流体的基本控制方程, 以及求解过程中需要考虑的流体压力求解、表面张力、固体边界等问题. 整理和总结了基于SPH方法进行多相流模拟的主要实现方式: (1)双流体模型的拉格朗日求解器: 两相离散为两组独立SPH粒子, 并用显式相间作用耦合两相; (2)多相SPH方法: SPH方法对多相流模拟的自然延伸, 相间作用由SPH参数隐式描述; (3) SPH与其他离散方法的耦合: 差异较大的两相各自采用不同离散方法, 发挥不同拉格朗日方法的优点; (4) SPH和基于网格方法的耦合: 网格方法处理简单的单相流动主体, 获得精度和效率间的平衡. 另外, 还在模拟参数物理化等方面论述了与SPH方法模拟多相流相关的一些改进和修正方法, 并在最后讨论和建议了提高多相流SPH模拟效率和精度的措施.      

RESEARCH DEVELOPMENTS OF SMOOTHED PARTICLE HYDRODYNAMICS METHOD AND ITS COUPLING WITH FINITE ELEMENT METHOD

拉格朗日型的有限元法和光滑粒子法在模拟材料大变形问题时各存优缺点, 而有限元与光滑粒子耦合算法实现了在小变形区域采用有限元法计算, 在局部的大变形区域采用光滑粒子法计算, 有效地综合了有限元法计算效率高和光滑粒子法能够自然地模拟材料大变形问题的特点.重点论述了有限元法、光滑粒子法以及有限元与光滑粒子耦合算法的研究现状及应用进展, 并讨论了各方法中需要进一步解决的问题.最后通过算例对3种方法的计算精度和计算效率进行了分析, 供研究人员参考.     

Numerical simulation of plunging wave breaking by the weakly compressible smoothed particle hydrodynamic method

In this paper, a numerical meshless method called the weakly compressible smoothed particle hydrodynamic (WCSPH) method, which is a two-dimensionalmodel of a weakly compressible fluid, is applied to simulate the plunging wave breaking process. This model solves the viscous fluid equations to obtain the velocity and density fields and also solves the equation of state to obtain the pressure field. The WCSPH method is demonstrated to have a higher computational efficiency than the basic SPH model. To simulate the turbulent behavior of the fluid flow in the wave breaking procedure, a sub particle scale (SPS) model is used, which is obtained from the Large eddy simulation (LES) theory. To consider the accuracy of the standard WCSPH model (WCSPH model without considering the turbulent effect), a dam break test is performed, and model results are compared with available experimental data.     

SPH粒子初始化均布方法及其均布质量评价

光滑粒子流体动力学(SPH)是一种拉格朗日型无网格粒子法，粒子均布程度是影响SPH分析精度和稳定 性的重要因素．本文基于射线法提出了一种在异形多边形区域内均布SPH粒子的方法，先在多边形的最小外包 矩形范围内均布粒子，再通过射线法和辅助筛选条件保留区域内的粒子；通过生成粒子的Voronoi多边形计算 其变异系数值(Cv)，作为SPH粒子均布质量的评价标准，其值越小，粒子均布质量越高．为验证该方法提高分 析精度的有效性，基于爆轰侵彻的经典实验，建立由经典三角形和四边形均布粒子法构建的模型甲、模型乙和 本文模型丙，用 LS-DYNA 中的 SPH 模块进行仿真分析．研究表明，模型丙的 Cv 分别比模型甲和模型乙低 4.88 %和5.22 %；模型甲、乙和丙射流头部速度分别为5 960、5 900和6 060 m/s，较经典实验的6 100 m/s分别 相差2.3 %、3.3 %和0.7 %，相对于模型甲和模型乙，模型丙计算精度提高了1.6 %和2.6 %．因此，本文方法可 快速有效地均匀布置SPH粒子，提高分析精度     

12.7 mm弹侵彻不同强度钢靶的数值模拟

针对12.7 mm弹侵彻不同强度钢靶时可能出现子弹保持完整或发生破碎的情况,过去的数值模拟仅限于模拟单一模式的子弹侵彻行为。为了克服这种数值模拟的局限性,开展了模型算法、网格尺寸对模拟结果影响的研究,并将模拟结果与实验结果进行了对比,提出了一种能够用于模拟子弹保持完整或破碎的弹靶模型。研究结果表明,为模拟子弹保持完整状态,子弹和靶板应分别采用基于Lagrange算法的有限元法和光滑粒子算法,而且子弹网格尺寸和靶板粒子间距之比应至少保持在5.3左右,否则弹头会产生与实验结果不符合的异常变形。但是,在模拟子弹发生破碎侵蚀时,该比例的网格/粒子尺寸比会引起计算中止。为了克服该问题,进一步建立了一种弹体表面采用大尺寸网格、内部采用细化小尺寸网格的有限元/光滑粒子法耦合弹靶模型。计算结果表明,改进的弹靶模型可模拟子弹保持完整或者发生破碎的情况。     

SPH方法在聚能装药射流三维数值模拟中的应用

采用有限元软件LS-DYNA中的SPH算法实现聚能装药射流形成过程的三维数值模拟.将SPH方法和FEM方法与理论计算结果相比较.研究结果表明:SPH数值模拟计算过程十分稳定,避免了有限元数值模拟过程中的网格扭曲、缠绕和物质穿透等问题,而且计算精度比有限元方法更高;采用SPH方法计算的射流速度、射流长度与有限元计算结果和...     

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.     

SPH固壁边界处理方法的改进

提出一种适用于光滑质点水动力学（SPH）方法的改进的边界处理方法。在这种方法中,边界粒子的压力可通过其周围的流体粒子的压力插值得到,从而改进了耦合边界法在边界上压力不准的问题。运用这种改进的边界处理方法模拟了二维方形水箱中的非线性晃荡问题以及二维楔形体自由入水问题。模拟结果与实验结果吻合较好,证明了此改进的边界处理方法是有效的。     

A robust shell element in meshfree SPH method

With the incorporation of total Lagrangian smoothed particle hydrodynamics(SPH) method equation and moving least square(MLS) function,the traditional SPH method is improved regarding the stability and consistency.Based on Mindlin-Ressiner plate theory,the SPH method simulating dynamic behavior via one layer of particles is applied to plate’s mid-plane,i.e.,a SPH shell model is constructed.Finally,through comparative analyses on the dynamic response of square,stiffened shells and cylindrical shells under various strong impact loads with common finite element software,the feasibility,validity and numerical accuracy of the SPH shell method are verified.Consequently,further researches on SPH shell may well pave the way towards solving problems involving dynamic plastic damage,tearing or even crushing.     

SPH-FEM接触算法在冲击动力学数值计算中的应用

为了充分发挥光滑粒子流体动力学方法(Smoothed Particle Hydrodynamics,SPH)易于处理大变形以及有限元(Finite Element Method,FEM)计算精度和效率高的优势,论文基于无网格粒子接触算法,在有限元节点处设置背景粒子,通过接触力的方式计算SPH粒子和有限单元之间的接触问题...     

Normalized SPH without boundary deficiency and its application to transient solid mechanics problems

Smoothed particle hydrodynamics (SPH) method is a powerful tool for modeling solid mechanics problems, especially for large deformation problems. However, it suffers from boundary deficiency and difficulty of boundary condition treatment. In this work, a normalized SPH method is proposed to overcome these problems. The method is based on a newly developed normalized particle approximation. To derive this particle approximation, a normalized kernel approximation which is accurate for derivatives of linear functions everywhere in a problem domain is constructed, and all integral terms of the normalized kernel approximation including boundary terms are discretized by particle summations. The normalized particle approximation is free of matrix inversion, consequently attractive in computational stability and simplicity compared with other corrective particle approximations. Its approximation accuracy is demonstrated by calculating derivatives of test functions. Based on this particle approximation, the formulation of the normalized SPH method for transient solid mechanics problems is derived. Moreover, a direct method of treating traction boundary conditions is presented by making use of the boundary term of the normalized particle approximation. The accuracy and capability of the normalized SPH method are validated by the calculation of elastic wave propagation in solids and compared with commonly used SPH method.

     

基于FE重构方法的冲击破碎仿真

提出了一种结合FE和SPH的3D冲击破碎问题仿真方法——FE重构法。通过立方体FE单元填充的方式对任意几何体进行离散,并建立粒子一形心重合模型,然后将用LS-dyna软件对粒子模型进行SPH撞击仿真;基于每一个步长的仿真结果,进行FE单元的重构,并结合失效准则进行失效分析,最终得到FE与SPH混合的仿真结果。针对超高速...     

Adaptive smoothed particle hydrodynamics for high strain hydrodynamics with material strength

This paper presents the implementation of an adaptive smoothed particle hydrodynamics (ASPH) method for high strain Lagrangian hydrodynamics with material strength. In ASPH, the isotropic kernel in the standard SPH is replaced with an anisotropic kernel whose axes evolve automatically to follow the mean particle spacing as it varies in time, space, and direction around each particle. Except for the features inherited from the standard SPH, ASPH can capture dimension-dependent features such as anisotropic deformations with a more generalized elliptical or ellipsoidal influence domain. Two numerical examples, the impact of a plate against a rigid surface and the penetration of a cylinder through a plate, are investigated using both SPH and ASPH. The comparative studies show that ASPH has better accuracy than the standard SPH when being used for high strain hydrodynamic problems with inherent anisotropic deformations. PACS 46.15.-x, 83.10.Rs, 83.50.-v     

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.      

流固耦合破坏分析的多分辨率PD-SPH方法

流固耦合破坏是一类涉及结构变形与破坏以及复杂自由表面现象的强非线性力学问题. 结合近场动力学(peridynamics, PD)与光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)各自的优势并考虑其计算效率问题, 提出一种适用于分析流?固耦合破坏问题的多分辨率PD-SPH混合方法. 分别采用SPH和PD方法以不同的空间和时间分辨率对流体和结构进行离散与求解, 利用具有与流体粒子相同光滑长度的虚粒子处理流?固界面, 以高精度满足界面边界条件. 通过两个经典算例: 液柱静压力下弹性板的变形和溃坝流体冲击弹性闸门的变形问题, 表明提出的多分辨率PD-SPH方法兼具较高的计算精度和计算效率; 对含裂缝的Koyna重力坝水力劈裂问题进行模拟计算, 所得裂缝扩展路径与文献结果吻合, 说明该方法适用于涉及结构破坏的流固耦合问题仿真. 最后尝试采用该方法进行流体冲击作用下含裂纹混凝土板崩塌过程数值仿真, 准确描述混凝土板的断裂破坏和全过程中的流体运动. 多分辨率PD-SPH混合方法或可为流?固耦合作用下的结构损伤破坏仿真提供一种新选择.      

基于修正光滑粒子流体动力学算法的低能量耗散数值波浪水池开发

目前, 无网格光滑粒子流体动力学SPH粒子法在波浪与结构物相互作用研究方面得到广泛应用, 但该方法模拟波浪远距离传播时, 常常面临严重的能量耗散问题, 导致波高非物理性降低, 给大范围海域、长时间作用下的波-物耦合作用研究带来一定困难. 对此, 本文采用一种核函数修正算法, 在确保粒子间相互作用对称性的同时, 改进压力梯度离散项的计算精度, 设法解决SPH方法中能量非物理性耗散的难题. 相较于前人减缓能量非物理性衰减的方法, 本文的修正SPH算法避免了自由液面搜索等复杂处理过程, 并能保证动量守恒特性. 数值结果中, 采用振荡液滴、规则波、不规则波等算例, 验证本修正SPH算法的准确性和有效性. 结果表明, 该修正SPH算法能准确模拟振荡液滴形态变化, 且动能保持较好守恒性. 通过数值水池与物理水池两者规则波与不规则波结果的对比分析表明, 基于本文修正SPH算法建立的数值波浪水池具有较好的抗能量衰减效果, 能实现长时间、远距离波浪传播的准确模拟. 此外, 本算法能在低光滑长度系数条件下, 实现精确模拟, 将极大缩减三维SPH模拟的时间, 从而节约计算成本.      

非等温黏弹性复杂流动的改进SPH方法模拟

非等温黏弹性流体广泛存在于自然界和工业生产中,准确预测黏弹性流体的非等温流动机理和复杂流变特性有着重要的应用价值.文章提出一种改进的光滑粒子流体动力学(smoothed particle hydrodynamics,SPH)方法对非等温黏弹性复杂流动进行了数值模拟,其中流体的黏弹特性通过eXtended Pom-Pom本构模型来表征.为了提高模拟结果的精度,采用了一种核函数梯度的修正算法;为了灵活地施加边界条件,发展了边界粒子和虚拟粒子相联合的边界处理方法;为了消除流动过程中的拉伸不稳定性,施加了粒子迁移技术.运用改进SPH方法数值模拟了液滴撞击固壁和F型腔注塑成型问题,通过与Basilisk软件得到的结果进行比较验证了改进SPH方法求解非等温黏弹性流体的有效性.通过利用不同粒子初始间距进行计算,评价了改进SPH方法的数值收敛性.研究了非等温流动相较于等温流动的不同流动特征,深入分析了不同热流变参数对流动过程的影响.数值结果表明,文章提出的改进SPH方法可稳定、准确地描述非等温黏弹性复杂流动的传热机理、复杂流变特性和自由面变化特性.     

An improved particle shifting technique for incompressible smoothed particle hydrodynamics methods

The smoothed particle hydrodynamics (SPH) method is one of the powerful Lagrangian tools for modeling free surface flows. However, it suffers from particle disorder, which leads to interpolation and numerical errors. To overcome this problem, several techniques have been introduced until now, among which the particle shifting technique (PST) based on Fick's law is an efficient one. The current form of this method needs tuning parameters to fulfill numerical stability criteria. In this study, to eliminate calibration factors, a new shifting coefficient is derived theoretically based on particle positions before and after shifting, regardless of other parameters such as velocity, pressure, time step intervals, etc. The only required input is particle positions, and the main concern is conserving particle densities in their updated positions. In addition to the proposed PST, a new distribution index (DI) is introduced for measuring the spatial uniformity of particles. Furthering the research, some novel treatments are also studied to improve particle movements near free surface boundary. The proposed idea is only assessed for ISPH method in this study, and its performance in other SPH schemes needs more investigations. Following this innovative method, it is validated by modeling different cases including dam break flow, paddle movement, and elliptical water drop. In all cases, particle arrangements have been improved by means of the modified shifting method. In that sense, good agreements between simulation results with experimental data, analytical solutions, and other numerical methods approve the ability of the developed method in simulating free surface flows.