二维空间中基于黎曼解的SPH方法

应用传统的光滑粒子流体动力学(SPH)方法模拟激波问题能自主捕获波阵面,但是在接触间断界面处却不可避免地存在压力振荡。采用黎曼解修正粒子对之间的相互作用,并将基于黎曼解的SPH方法扩展到二维空间。通过对一维具有解析解的激波管问题和二维拟内爆问题的模拟,比较了基于黎曼解的SPH方法和传统的SPH方法。数值结果表明,相对于传统的SPH方法,基于黎曼解的SPH方法能够有效避免接触界面处的压力振荡,提高求解的精度。     

一种SPH应力修正算法及自由表面流中的应用

提出了一种SPH应力修正算法,即模型中的拉应力和压应力分别采用不同的插值核函数和状态方程来处理,改善应力稳定性问题。介绍了一种改进的Quintic核函数,用于改善模型中压应力的稳定性。通过增加钟型核函数的光滑长度,改善模型中拉应力的稳定性。采用该应力修正算法模拟了无重力条件下方形液滴的震荡变形过程,对比分析了不同算法的模拟结果。此外,为进一步验证算法的适用性,模拟了溃坝算例。研究表明,改进的Quintic型核函数明显改善了粒子聚集现象,该SPH应力修正方法可以使液滴具有更均匀的粒子分布以及更光滑的自由表面,有效改善了SPH方法中的压应力不稳定作用以及自由表面流的模拟精度。     

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。     

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.      

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(smoothed particle 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.     

修正SPH方法在自由表面模拟中的应用

对传统光滑粒子动力学(SPH)方法进行修正,提出了一种密度初始化方法,同时采用一种新的固壁边界处理方法,模拟溃坝问题。通过液滴旋转和无透空块体溃坝问题的模拟验证了修正SPH方法的有效性和在自由表面模拟中的准确性,分析了密度初始化对流动的影响;数值结果表明,修正SPH方法提高了数值计算的精度和稳定性。最后应用修正SPH方法模拟了有透空块体和挡板紧挨水柱的溃坝现象,比较了有无透空块体两种情况下右端直墙上压力变化情况,结果表明,透空块体可使右端直墙上的压力减小,有无挡板、挡板位置和水柱长高比对溃坝现象有重要影响。     

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.     

基于LS-DYNA的热成型钢断裂失效预测研究

固体壁面由于表面特殊结构和材料属性,时常表现出对交界面上水体的吸附作用,而这一特征对微小水体作用尤为明显。本文提出了一种湿润性固壁边界条件的计算方法,即假设壁面粒子的亲水性以及毛细吸附作用统一表现为对支持域内流体粒子的吸附力。基于光滑粒子流体动力学（SPH）方法,模拟了静态液滴在不同湿润性壁面上的变形至稳定过程。模拟了液滴撞击疏水壁面的过程,将液滴的运动过程分为碰撞、铺展、回缩和回弹四个阶段,分析各阶段壁面受力分布情况。研究表明：根据模拟液滴静态接触角的变化特点,本文湿润性固壁边界条件可以较好的反映出壁面湿润性;液滴撞击输水表面的模拟数据与试验结果趋势上吻合良好;壁面压力波伴随着液滴的铺展和回缩传播并衰减;只有在回弹后期液滴即将脱离壁面时壁面拉力起主导作用,其余各时刻壁面均以压力为主。     

基于SPH方法的湿润性固壁边界条件模拟研究

固体壁面由于表面特殊结构和材料属性,时常表现出对交界面上水体的吸附作用,而这一特征对微小水体作用尤为明显。本文提出了一种湿润性固壁边界条件的计算方法,即假设壁面粒子的亲水性以及毛细吸附作用统一表现为对支持域内流体粒子的吸附力。基于光滑粒子流体动力学（SPH）方法,模拟了静态液滴在不同湿润性壁面上的变形至稳定过程。模拟了液滴撞击疏水壁面的过程,将液滴的运动过程分为碰撞、铺展、回缩和回弹四个阶段,分析各阶段壁面受力分布情况。研究表明：根据模拟液滴静态接触角的变化特点,本文湿润性固壁边界条件可以较好的反映出壁面湿润性;液滴撞击输水表面的模拟数据与试验结果趋势上吻合良好;壁面压力波伴随着液滴的铺展和回缩传播并衰减;只有在回弹后期液滴即将脱离壁面时壁面拉力起主导作用,其余各时刻壁面均以压力为主。     

爆炸焊接界面波的数值模拟

借助动力学分析软件ANSYS/LS-DYNA 11.0,运用光滑粒子流体动力学方法(SPH方法),建立以Johnson-Cook材料模型和Grüneisen状态方程为基础的热塑性流体力学模型,对同种钢板爆炸焊接界面波进行了数值模拟.结果表明,运用SPH方法可以得到清晰的爆炸焊接界面波形貌.与实验结果的比较表明:模拟误...     

An SPH pressure correction algorithm for multiphase flows with large density ratio

In this paper, we propose an interfacial pressure correction algorithm for smoothed particle hydrodynamics (SPH) simulation of multiphase flows with large density ratios. This correction term is based on the assumption of small deformation of the interface, and derived from perturbation expansion analysis. It is also proven to be applicable in cases with complex interfaces. This correction algorithm helps to overcome the discontinuities of the pressure gradient over the interfaces, which may cause unphysical gap between different phases. This proposed correction algorithm is implemented on a recent multiphase SPH model, which is based on the assumption of pressure continuity over the interfaces. The coupled dynamic solid boundary treatment is used to simulate solid walls; and a cut‐off pressure is applied to avoid negative particle pressure, which may cause computational instabilities in SPH. Three numerical examples of air–water flows, including sloshing, dam breaking, and water entry, are presented and compared with experimental data, indicating the robustness of our pressure correction algorithm in multiphase simulations with large density ratios. Copyright © 2015 John Wiley & Sons, Ltd.     

Incompressible SPH simulation of wave breaking and overtopping with turbulence modelling

In this paper a truly incompressible version of the smoothed particle hydrodynamics (SPH) method is presented to investigate the surface wave overtopping. SPH is a pure Lagrangian approach which can handle large deformations of the free surface with high accuracy. The governing equations are solved based on the SPH particle interaction models and the incompressible algorithm of pressure projection is implemented by enforcing the constant particle density. The two‐equation k–ε model is an effective way of dealing with the turbulence and vortices during wave breaking and overtopping and it is coupled with the incompressible SPH numerical scheme. The SPH model is employed to reproduce the experiment and computations of wave overtopping of a sloping sea wall. The computations are validated against the experimental and numerical data found in the literatures and good agreement is observed. Besides, the convergence behaviour of the numerical scheme and the effects of particle spacing refinement and turbulence modelling on the simulation results are also investigated in further detail. The sensitivity of the computed wave breaking and overtopping on these issues is discussed and clarified. Copyright © 2005 John Wiley & Sons, Ltd.     

A modified SPH method to model the coalescence of colliding non-Newtonian liquid droplets

This paper develops a modified smoothed particle hydrodynamics (SPH) method to model the coalescence of colliding non-Newtonian liquid droplets. In the present SPH, a van der Waals (vdW) equation of state is particularly used to represent the gas-to-liquid phase transition similar to that of a real fluid. To remove the unphysical behavior of the particle clustering, also known as tensile instability, an optimized particle shifting technique is implemented in the simulations. To validate the numerical method, the formation of a Newtonian vdW droplet is first tested, and it clearly demonstrates that the tensile instability can be effectively removed. The method is then extended to simulate the head-on binary collision of vdW liquid droplets. Both Newtonian and non-Newtonian fluid flows are considered. The effect of Reynolds number on the coalescence process of droplets is analyzed. It is observed that the time up to the completion of the first oscillation period does not always increase as the Reynolds number increases. Results for the off-center binary collision of non-Newtonian vdW liquid droplets are lastly presented. All the results enrich the simulations of the droplet dynamics and deepen understandings of flow physics. Also, the present SPH is able to model the coalescence of colliding non-Newtonian liquid droplets without tensile instability.     

Application of particle splitting method for both hydrostatic and hydrodynamic cases in SPH

Smoothed particle hydrodynamics(SPH) method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems. However, in most simulations, uniform particle distributions are used and the multi-resolution, which can obviously improve the local accuracy and the overall computational efficiency, has seldom been applied. In this paper, a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems. The splitting algorithm is that, when a coarse(mother) particle enters the splitting region, it will be split into four daughter particles, which inherit the physical parameters of the mother particle. In the particle splitting process,conservations of mass, momentum and energy are ensured. Based on the error analysis, the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases. Finally, the scheme is validated by five basic cases, which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.Smoothed particle hydrodynamics(SPH)method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems.However,in most simulations,uniform particle distributions are used and the multi-resolution,which can obviously improve the local accuracy and the overall computational efficiency,has seldom been applied.In this paper,a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems.The splitting algorithm is that,when a coarse(mother)particle enters the splitting region,it will be split into four daughter particles,which inherit the physical parameters of the mother particle.In the particle splitting process,conservations of mass,momentum and energy are ensured.Based on the error analysis,the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases.Finally,the scheme is validated by five basic cases,which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.     

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.     

黏弹性固体中地下爆炸辐射地震波能量的演化

地下爆炸与介质的能量耦合和介质中的波传播机制是理解地下爆炸源物理的重要基础。为研究地下爆炸辐射地震波能量的传播衰减规律,分析了黏弹性介质中地下爆炸地震波能量的组成。基于无限介质中黏弹性球面波理论,给出了速度、位移、应力、应变等物理量Laplace域的理论解。利用Laplace数值逆求解方法,建立了黏弹性介质中地下爆炸辐射地震波场的计算方法。以干黄土作为典型黏弹性材料,计算给出了地震波能量的传播特征,分析了地下爆炸辐射能量的传播衰减规律。结果表明:（1）在黏弹性介质中,某球面处流入的能量随半径增加而逐渐降低。在理想弹性介质中,某球面处流入的能量在几倍弹性半径外即可稳定到某一定值;（2）在某一固定的有限观测区域内,当观测时间足够长时,势能和耗散能均趋于某一定值,辐射动能趋于零;（3）当有限的观测区域能容纳一个完整波长的地震波时,地震波辐射动能的稳态值随波传播距离的增大而减小,总体上可以用指数函数和幂函数进行分段拟合。     

Examining a modified algorithm of smoothed particle hydrodynamics for a high velocity perforation of an aluminum beam

The wide spreading of utilizing of smoothed particle hydrodynamics (SPH) for numerical studies of the complex and high rate deformations of continuums, led the current study to gain a more reliable simulation by employing a modified compressible smoothed particle hydrodynamics (MCSPH) algorithm which could be a more accurate and stable technique in high tension regions, in despite of incompressible standard SPH. The main feature of the modified compressible SPH algorithm relies on a three steps solution procedure to calculate the pressure gradient, the deviatoric stress tensor, and the body forces separately. This algorithm is free of any artificial viscosity in its formulations, as well as welcoming to compressible effects which permits the pressure shock waves in high rate plastic deformation. To examine the accuracy of the algorithm, a benchmark problem of colliding rubber cylinders was simulated first and then a high velocity perforation process of an aluminum beam struck by a rigid projectile was simulated in various projectile speeds, and the failure response of the beam in each case was accompanied by crack propagation process. The prominent capability of the utilized MCSPH can be more illustrated when it was used in simulation of thickness crack propagation a tiny crack paths and defragmentation which can be encountered as a not easy numerical case study. The adequate assurance has been more fortified when the results were compared to those reported from a Finite Element method study.