基于SPH的动力松弛法

光滑质点流体动力学方法(SPH;Smoothed Particle Hydrodynamics)是一种新的纯Lagrangian方法,由于该方法在计算空间导数的时候不需要借助于网格,从而避免了Lagrangian网格在处理大变形问题时的缠结和扭曲问题.传统上,SPH方法主要用来模拟天体问题以及流体或固体的动力问题.动力松弛法(DR;Dynamic Relax-ation)通过采用虚拟质量和虚拟阻尼将一个静力问题转化为动力问题,最早用于解决潮汐问题.DR方法从数学的角度来说是一种求解线性方程组的方法,并不涉及连续结构的离散.所以采用网格方法离散时,DR方法同样受到网格变形导致计算精度下降的困扰.论文采用SPH离散连续体,然后用DR方法求解结构的平衡状态,并根据SPH的特点,提出一种加速收敛的新型计算方法.     

PTT黏弹性流体的光滑粒子动力学方法模拟

运用光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)方法对基于PHan-Thien-Tanner (PTT)模型的黏弹性流动进行了数值模拟. 首先, 利用SPH方法模拟了基于PTT模型的平板 Poiseuille流, 通过与文献结果的比较, 验证了SPH方法模拟黏弹性流动的准确性和有效性; 随后, 基于PTT模型对黏弹性自由表面流-液滴碰撞问题进行了SPH模拟, 研 究了PTT模型中拉伸参数对碰撞过程的影响. 为了解决张力不稳定问题, 采用简化的 人工应力公式. 数值结果表明, SPH方法可有效而灵活地模拟黏弹自由表面流问题.     

三维弹性问题Taylor展开多极边界元法的误差分析

Taylor展开多极边界元法有效的提高了边界元法的求解效率,使之可用于大规模问题的计算。然而,由于计算中对基本解进行了Taylor级数展开,与传统边界元方法相比计算精度有所下降。本文主要针对三维弹性问题Taylor展开多极边界元法的计算精度和误差进行研究。文中对两种方法的计算精度进行了比较;研究了核函数的Taylor展开性质;推导了三维弹性问题基本解的误差估计公式;给出了Taylor展开多极边界元法中远近场的划分原则。通过具体的算例,证明了该方法的正确性和误差估计公式的有效性,说明了影响Taylor展开多极边界元法求解精度的因素。     

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.      

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运用von Neumann稳定性分析方法对采用3次B-样条核函数的一维标准SPH进行了稳 定性分析,在此基础上对扰动波长的影响进行了讨论,并用一维弹性杆的SPH 计算对分析结论进行了数值验证. 理论分析和数值计算表明, von Neumann分析所得的稳定性随扰动波长变化的规律与实际计算结果完全相符, SPH稳定性与扰 动波长密切相关. 对于所分析的SPH方法,在扰动波长最小处稳定性最差,而在其它扰 动波长下,SPH的计算则可以在拉伸状态下稳定.     

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...     

球形孔洞泡沫铝力学行为的SPH分析

分别基于体心立方元胞模型和随机孔洞模型建立了泡沫铝SPH模型.采用SPH方法分析了准静态加载条件下泡沫铝的单轴压缩力学性能.最大应变达70%.SPH计算所得应力-应变曲线表现出明显的弹性、平台和压实三段.分析了泡沫铝的微观变形机理,结果表明规则模型和随机模型均呈现出明显的局部塑性变形带,其中随机泡孔模型的孔壁变形以弯曲为主,局部塑性变形带表现更为明显.本文研究结果同时还说明了采用SPH方法研究泡沫材料力学行为的可行性与适应性.     

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。     

基于表面力模型的液滴冲击弹性基底SPH模拟

采用光滑粒子动力学SPH方法建立液滴冲击弹性基底的流固耦合数值模型,给出描述粘性流体和弹性固体运动的SPH离散方程和数值处理格式,引入人工耗散项来抑制标准SPH方法的数值震荡。为模拟液滴的表面张力效应,通过精确检测边界粒子,采用拉格朗日插值方法计算表面法向量和曲率,结合界面理论中的连续表面力CSF方法,建立了适用于自由表面液滴的表面力模型,方形液滴变形的模拟结果与拉普拉斯理论解吻合较好。随后,采用SPH流固耦合模型模拟1.0 mm直径水滴以不同速度(0.2 m/s～3.0 m/s)冲击两种薄板型基底,分析了基底弹性变形对液滴铺展、收缩以及回弹行为的影响。     

高速碰撞数值计算中的SPH自适应粒子分布法

针对传统光滑粒子法在计算高速碰撞问题时会出现近邻粒子逸出核函数影响域而产生数值破坏这一缺陷,提出了一种根据粒子间距变化自动添加、合并粒子的SPH自适应粒子分布算法。采用该方法对Taylor碰撞和超高速碰撞问题进行了数值模拟,结果表明,该方法可以有效地消除计算中出现的数值破坏,提高计算精度。     

A one-dimensional meshfree particle formulation for simulating shock waves

In this paper, a one-dimensional meshfree particle formulation is proposed for simulating shock waves, which are associated with discontinuous phenomena. This new formulation is based on Taylor series expansion in the piecewise continuous regions on both sides of a discontinuity. The new formulation inherits the meshfree Lagrangian and particle nature of SPH, and is a natural extension and improvement on the traditional SPH method and the recently proposed corrective smoothed particle method (CSPM). The formulation is consistent even in the discontinuous regions. The resultant kernel and particle approximations consist of a primary part similar to that in CSPM, and a corrective part derived from the discontinuity. A numerical study is carried out to examine the performance of the formulation. The results show that the new formulation not only remedies the boundary deficiency problem but also simulates the discontinuity well. The formulation is applied to simulate the shock tube problem and a 1-D TNT slab detonation. It is found that the proposed formulation captures the shock wave at comparatively lower particle resolution. These preliminary numerical tests suggest that the new meshfree particle formulation is attractive in simulating hydrodynamic problems with discontinuities such as shocks waves.Received: 8 October 2002, Accepted: 10 May 2003, Published online: 15 August 2003     

Dynamic Model for LES Without Test Filtering: Quantifying the Accuracy of Taylor Series Approximations

The dynamic model for large-eddy simulation (LES) of turbulent flows requires test filtering the resolved velocity fields in order to determine model coefficients. However, test filtering is costly to perform in LES of complex geometry flows, especially on unstructured grids. The objective of this work is to develop and test an approximate but less costly dynamic procedure which does not require test filtering. The proposed method is based on Taylor series expansions of the resolved velocity fields. Accuracy is governed by the derivative schemes used in the calculation and the number of terms considered in the approximation to the test filtering operator. The expansion is developed up to fourth order, and results are tested a priori based on direct numerical simulation data of forced isotropic turbulence in the context of the dynamic Smagorinsky model. The tests compare the dynamic Smagorinsky coefficient obtained from filtering with those obtained from application of the Taylor series expansion. They show that the expansion up to second order provides a reasonable approximation to the true dynamic coefficient (with errors on the order of about 5% for c _s ²), but that including higher-order terms does not necessarily lead to improvements in the results due to inherent limitations in accurately evaluating high-order derivatives. A posteriori tests using the Taylor series approximation in LES of forced isotropic turbulence and channel flow confirm that the Taylor series approximation yields accurate results for the dynamic coefficient. Moreover, the simulations are stable and yield accurate resolved velocity statistics. Received 20 February 2001 and accepted 24 July 2001     

一种基于黎曼解处理大密度比多相流SPH的改进算法

多相流界面存在密度、黏性等物理场间断,直接采用传统光滑粒子水动力学(smoothedparticle hydrodynamics,SPH)方法进行数值模拟,界面附近的压力和速度存在震荡.一套基于黎曼解能够处理大密度比的多相流SPH计算模型被提出,该模型利用黎曼解在处理接触间断问题方面的优势,将黎曼解引入到SPH多相流计算模型中,为了能够准确求解多相流体物理黏性、减小黎曼耗散,对黎曼形式的SPH动量方程进行了改进,又将Adami固壁边界与黎曼单侧问题相结合来施加多相流SPH固壁边界,同时模型中考虑了表面张力对小尺度异相界面的影响,该模型没有添加任何人工黏性、人工耗散和非物理人工处理技术,能够反应多相流真实物理黏性和物理演变状态.采用该模型首先对三种不同粒子间距离散下方形液滴震荡问题进行了数值模拟,验证了该模型在处理异相界面的正确性和模型本身的收敛性;后又通过对Rayleigh--Taylor不稳定、单气泡上浮、双气泡上浮问题进行了模拟计算,结果与文献对比吻合度高,异相界面捕捉清晰,结果表明,本文改进的多相流SPH模型能够稳定、有效的模拟大密度比和黏性比的多相流问题.      

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.     

SPH computation of plunging waves using a 2‐D sub‐particle scale (SPS) turbulence model

The paper presents a 2‐D large eddy simulation (LES) modelling approach to investigate the properties of the plunging waves. The numerical model is based on the smoothed particle hydrodynamics (SPH) method. SPH is a mesh‐free Lagrangian particle approach which is capable of tracking the free surfaces of large deformation in an easy and accurate way. The Smagorinsky model is used as the turbulence model due to its simplicity and effectiveness. The proposed 2‐D SPH–LES model is applied to a cnoidal wave breaking and plunging over a mild slope. The computations are in good agreement with the documented data. Especially the computed turbulence quantities under the breaking waves agree better with the experiments as compared with the numerical results obtained by using the k–ε model. The sensitivity analyses of the SPH–LES computations indicate that both the turbulence model and the spatial resolution play an important role in the model predictions and the contributions from the sub‐particle scale (SPS) turbulence decrease with the particle size refinement. Copyright © 2006 John Wiley & Sons, Ltd.     

A corrected particle method with high-order Taylor expansion for solving the viscoelastic fluid flow

In this paper, a corrected particle method based on the smoothed particle hydrodynamics (SPH) method with high-order Taylor expansion (CSPH-HT) for solving the vis-coelastic flow is proposed and investigated. The validity and merits of the CSPH-HT method are first tested by solv-ing the nonlinear high order Kuramoto-Sivishinsky equation and simulating the drop stretching, respectively. Then the flow behaviors behind two stationary tangential cylinders of polymer melt, which have been received little attention, are investigated by the CSPH-HT method. Finally, the CSPH-HT method is extended to the simulation of the filling process of the viscoelastic fluid. The numerical results show that the CSPH-HT method possesses higher accuracy and stability than other corrected SPH methods and is more reliable than other corrected SPH methods.     

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.     

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.     

改进的泰勒公式及其数值验证

将光滑粒子法（smoothed particle hydrodynamics method, SPH）应用于金属平板爆轰驱动过程的数值模拟,得到了炸药与金属相互作用的清晰的图像和平板抛射角的变化。根据抛射角方程对泰勒公式进行了修正,得到了改进的泰勒公式。利用数值模拟得到的结果比较了平板驱动几种不同的抛射角公式,改进的泰勒公式准确反映出了抛射角下降并趋于终态的规律,其对平板抛射角的描述更为准确。