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.      

一种新型SPH-FEM耦合算法及其在冲击动力学问题中的应用

为了充分发挥光滑粒子流体动力学方法(smoothed particle hydrodynamics,SPH)在处理大变形和有限元(finite element method,FEM)问题时计算精度高的优势,提出了一种新型SPH-FEM耦合算法.该耦合算法在大变形区域使用SPH粒子离散,其余区域使用有限元离散.在耦合界面...     

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.     

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.      

一种有效的广义特征值分析方法

提出了一种适合于自适应有限元分析中求解广义特征值问题的多重网格方法.这种方法充分利用了初始网格下的结果,通过插值或最小二乘拟合技术来得到网格变化后的新的近似特征向量,然后由多重网格迭代过程实现对结构广义特征值问题的求解.在多重网格迭代的光滑步中,选择了收敛梯度法以提高其收敛率;在粗网格校正步中,则导出了一种近似求解特征向量误差的方程.这种方法将网格离散过程和数值求解过程很好地相结合,建立了一个网格细分后广义特征值问题的快速重分析方法,与传统有限元方法相比较,具有计算简便、计算量少等特点,可以作为结构动力问题自适应有限元分析的一种十分有效的工具.     

弹性动力学的双互易杂交边界点法

将双互易法同杂交边界点法相结合,提出了求解弹性动力问题的新型数值方法------双互易杂交边界点方法. 该算法在求解弹性动力问题时,将控制方程非齐次项的域内积分转化为边界积分. 该方法将问题的解分为通解和特解两部分,通解使用杂交边界点法求得,特解则使用局部径向基函数插值得到,从而实现了使用静力问题的基本解来求解动力问题. 计算时仅仅需要边界上离散点的信息,无论积分还是插值都不需要网格,域内节点仅用来插值非齐次项,因此该算法仍是一种边界类型的无网格方法. 数值算例表明,该方法后处理简单,计算精度高,适合于求解弹性动力问题.      

一种可考虑界面不连续的改进SPH方法

SPH方法模拟工程问题时通常遇到不连续的物理量,因此有必要引入不连续的SPH方法.本文基于Taylor展开公式推导了2D和3D的不连续SPH公式.针对越过材料界面不连续物理量的计算,给出了大变形计算中确定不连续位置的方法,基于Taylor展开公式,从理论上给出了确定不连续公式中x_(k)点的方法,并用数值方法验证了此方法的有效性.比较和讨论了初始SPH方法,CSPM方法与不连续SPH方法处理不连续量的效果.结果显示不连续SPH方法在计算不连续量时有较大的优势.     

近场动力学方法及其应用

近场动力学(peridynamics,PD)是一种新兴的基于非局部作用思想建立模型并通过求解空间积分方程描述物质力学行为的方法.它兼有分子动力学方法和无网格方法的优点,避免了基于连续性假设建模和求解空间微分方程的传统宏观方法在面临不连续问题时的奇异性,又突破了经典分子动力学方法在计算尺度上的局限,在宏/微观不连续力学问题分析中均表现出很高的求解精度和效率.首先概述了PD方法的理论基础、建模思路和计算体系;进而介绍了PD方法在不同尺度不连续力学问题中的应用,包括均匀与非均匀材料和结构的大变形、损伤、断裂、冲击、穿透和失稳问题,结晶相变动力学问题以及纳米材料和结构的破坏问题;最后讨论了PD方法在理论、计算和应用等方面值得进一步研究的问题.     

非结构动网格在多介质流体数值模拟中的应用

采用非结构动网格方法对含多介质的流场进行数值模拟.采用改进的弹簧方法来处理由于边界运动而产生的网格变形.采用基于格心的有限体积方法求解守恒型的ALE(Arbitrary Lagrangiall-Eulerian)方程,控制面通量的计算采用HLLC(Hartem,Lax,van Leer,Contact)方法,采用几何构造的方法使空间达到二阶精度,时间离散采用四阶Runge-Kutta方法.物质界面的处理采用虚拟流体方法.本文对含动边界的激波管、水下爆炸等流场进行数值模拟,取得较好的结果,不同时刻界面的位置和整个扩张过程被准确模拟.     

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.      

混凝土中爆炸数值仿真算法研究

用AUTODYN动力学软件对装药在混凝土介质靶中爆炸作数值仿真,研究了不同的网格描述方法,以及网格划分方法对计算结果的影响。通过实际算例比较了Lagrange算法和SPH算法以及不同的网格划分细度对靶径向、轴向不同距离的最大冲击压力、靶背过载以及损伤区、炸坑大小的模拟计算结果。分析得到了混凝土介质靶中爆炸问题数值仿真的合适算法,即拉氏算法对炸点近处的较高的最大冲击压力有较好的敏感能力,SPH算法对仿真计算爆坑形态以及抛掷体速度等具有明显的优势。对于算例问题,拉氏算法10 mm网格和SPH算法3 mm粒子即可满足一定的计算精度。     

NUMERICAL SIMULATION OF WIND-BLOWN SAND MOVEMENT BASED ON SPH

运用光滑粒子流体动力学(smoothed particles hydrodynamics, SPH)方法对沙粒和气流的相互耦合运动特性进行了分析,研究提出了风沙流的SPH数值方法并进行了数值模拟. 首先提出了风沙流的SPH建模方法和基本理论,建立了风沙流动的SPH数值模拟平台. 其次通过建立风沙流的SPH 模型并施加边界条件,对自然风作用下沙粒的运动情况进行了数值模拟,详细分析了沙粒运动轨迹及特性,最后通过与相关研究成果对比分析,验证了完善后的SPH方法有效性. 通过考虑气流场的可变性,在风沙流SPH计算模型中引入了加载(起风)和卸载(停风)方式,观察并对比分析了沙粒的运动轨迹和特性. 为进一步研究风沙流的实时动态非线性行为提供了SPH理论基础和数值分析方法.     

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。     

基于ALE,CEL和SPH方法的球形破片高速冲击充液结构对比研究

为研究ALE,CEL和SPH方法在高速冲击流固耦合动力学数值分析中的差异性,开展球形破片高速冲击充液结构数值模拟研究。建立经文献资料验证的ALE,CEL和SPH三种动力学模型,研究了流体压力变化、形成的空腔尺寸、破片速度衰减变化和充液结构变形等模拟精度,并分析相应的计算成本。结果表明,ALE,CEL和SPH三种方法均能有效模拟破片高速冲击充液结构的流固耦合动力学过程;ALE方法预测的空腔尺寸精度较高;CEL方法预测的流体压力、破片速度衰减和充液结构变形精度较高;SPH方法预测的空腔尺寸、破片速度衰减精度较高;当网格尺寸一致时,SPH方法计算时长约为ALE和CEL方法的两倍,但SPH方法前后处理更加简便。     

Efficient meshless SPH method for the numerical modeling of thick shell structures undergoing large deformations

The objective of this paper is to present an extension of the Lagrangian Smoothed Particle Hydrodynamics (SPH) method to solve three-dimensional shell-like structures undergoing large deformations. The present method is an enhancement of the classical stabilized SPH commonly used for 3D continua, by introducing a Reissner–Mindlin shell formulation, allowing the modeling of moderately thin structure using only one layer of particles in the shell mid-surface. The proposed Shell-based SPH method is efficient and very fast compared to the classical continuum SPH method. The Total Lagrangian Formulation valid for large deformations is adopted using a strong formulation of the differential equilibrium equations based on the principle of collocation. The resulting non-linear dynamic problem is solved incrementally using the explicit time integration scheme, suited to highly dynamic applications. To validate the reliability and accuracy of the proposed Shell-based SPH method in solving shell-like structure problems, several numerical applications including geometrically non-linear behavior are performed and the results are compared with analytical solutions when available and also with numerical reference solutions available in the literature or obtained using the Finite Element method by means of ABAQUS^© commercial software.     

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.     

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.     

SPH for 3D floating bodies using variable mass particle distribution

A floating body with substantial heave motion is a challenging fluid–structure interaction problem for numerical simulation. In this paper we develop SPH in three dimensions to include variable particle mass distribution using an arbitrary Lagrange–Eulerian formulation with an embedded Riemann solver. A wedge or cone in initially still water is forced to move with a displacement equal to the surface elevation of a focused wave group. A two‐dimensional wedge case is used to evaluate two forms of repulsive‐force boundary condition on the body; the force depending on the normal distance from the object surface produced closer agreement with the experiment. For a three‐dimensional heaving cone the comparison between SPH and experiment shows excellent agreement for the force and free surface for motion with low peak spectral frequencies while for a higher peak frequency the agreement is reasonable in terms of phase and magnitude, but a small discrepancy appears at the troughs in the motion. Capturing the entire three‐dimensional flow field using an initially uniform particle distribution with sufficiently fine resolution requires an extremely large number of particles and consequently large computing resource. To mitigate this issue, we employ a variable mass distribution with fine resolution around the body. Using a refined mass distribution in a preselected area avoids the need for a dynamic particle refinement scheme and leads to a computational speedup of more than 600% or much improved results for a given number of particles. SPH with variable mass distribution is then applied to a single heaving‐float wave energy converter, the ‘Manchester Bobber’, in extreme waves and compared with experiments in a wave tank. The SPH simulations are presented for two cases: a single degree‐of‐freedom system with motion restricted to the vertical direction and with general motion allowing six degrees‐of‐freedom. The motion predicted for the float with general motion is in much closer agreement with experimental data than the vertically constrained system. Using variable particle mass distribution is shown to produce close agreement with a computation time 20% of that required with a uniformly fine resolution. Copyright © 2012 John Wiley & Sons, Ltd.     

弹丸入水特性的SPH计算模拟

应用SPH方法研究弹丸入水过程中的动力学特征。利用拉格朗日形式的N-S方程自编SPH程序,建立弹丸入水的计算模型,赋予相应的材料参数及状态方程,研究弹丸外形、入水速度和角度等因素对入水过程的影响。模拟结果表明:空化泡的形态及发展规律主要由弹丸的运动姿态决定;弹道越稳定,阻力因数就越小,弹丸的存速就越大。SPH方法具有较强的自适应性,适用于研究弹丸入水的流固耦合问题。     

Simulating bubble dynamics in a buoyant system

Multiphase flows are critical components of many physical systems; however, numerical models of multiphase flows with large parameter gradients can be challenging. Here, two different numerical methods, volume of fluid (VOF) and smoothed particle hydrodynamics (SPH), are used to model the buoyant rise of isolated gas bubbles through quiescent fluids for a range of Bond and Reynolds numbers. The VOF is an Eulerian grid–based method, whereas the SPH is Lagrangian and mesh free. Each method has unique strengths and weaknesses, and a comparison of the two approaches as applied to multiphase phenomena has not previously been performed. The VOF and SPH simulations are compared, verified, and validated. Results using two-dimensional VOF and SPH simulations are similar to each other and are able to reproduce numerical benchmarks and experimental results for sufficiently large Morton and Reynolds numbers. It is also shown that at low Reynolds numbers, the two methods, SPH and VOF, diverge in the transient regime of the bubble rise. Regimes that require simulations capable of representing three-dimensional drag are identified as well as regimes in which results from VOF and SPH diverge.