强制旋转动边界的SPH算法及其在挤出中的应用
|
摘要
强制动边界问题是边界通过外力强制施加并随时间变化的问题,在诸如：搅拌、强制输送、造浪等生产生活中很多领域都会遇到。比如,聚合物加工领域中的单螺杆挤出及双螺杆挤出的数值模拟,属于典型的强制动边界问题。在采用传统数值技术,例如,有限体积法和有限元法,模拟时会遇到网格畸变,且计算过程很难追踪物料的轨迹和详细变化情况,这不利于深入研究螺杆挤出过程的机理,而掌握挤出机理对于挤出过程的分析、设计及优化又非常重要。近年来,数值方法正在经历由连续介质模型到离散粒子模型的进展过程。无网格粒子法,采用基于点的近似而不依赖网格,非常有利于计算移动边界、大变形、自由表面等问题,这给复杂加工过程的模拟注入了新的活力。光滑粒子流体动力学(Smoothed particle hydrodynamics, SPH)方法是典型的无网格粒子法,它具有良好的自适应性,因此在处理一些复杂不连续问题时较传统数值方法有很大优势,已经广泛应用到波浪力学、流-固耦合、高速碰撞等的计算。
本文从经典SPH出发,深入研究经典SPH方法的改进型——不可压缩光滑粒子流体动力学(Incompressible SPH, ISPH)方法,并初步应用于螺杆挤出的二维和三维流动模拟中。研究不同边界设置方法在ISPH和经典SPH方法中的实施和适用情况；基于螺杆挤出过程,利用静态粒子法,构建二维强制旋转边界问题模型。利用FORTRAN语言编程,分别采用ISPH和移动最小二乘(Moving least squares, MLS)修正的经典SPH两种算法进行了计算。提出一种MLS修正密度的策略；进而,提出非充满状态下的强制旋转动边界自由表面流模型,并采用两种SPH方法进行模拟。设计制造一套强制旋转动边界有机玻璃流体实验装置；最后,利用SPH模拟了螺槽横截面上的二维非牛顿流模型。进一步,研究SPH方法在单螺杆三维模型中的计算。为SPH在更加复杂的单螺杆、双螺杆挤出加工过程的模拟奠定了基础。本文的主要创新成果如下：
(1)关于边界实施的研究：静态粒子方法在ISPH和经典SPH算法中的计算精度均较镜像粒子边界高,这是由于镜像粒子法在每个时间步都需要重新生成新的镜像粒子,内部粒子的不规则分布映射到镜像粒子上。排斥力方法较适合在经典SPH中使用。
(2)关于充满状态下的强制旋转动边界模拟研究：构建强制旋转动边界问题物理模型,采用静态粒子法完成该模型的边界实施,并分别采用ISPH和MLS修正的经典SPH算法,进行计算。通过与静边界及商业计算流体动力学(Computational fluid dynamics, CFD)软件FLUENT计算结果对比验证了计算结果的可靠性；提出一种MLS修正密度策略：在每个时间步,只对流体粒子的密度进行演算,边界粒子密度保持不变,而每20个时间步对全部粒子进行MLS密度修正。通过该MLS修正经典SPH的方法,计算结果表明：它可以有效消除计算域中高压力梯度区的压力振荡,在不降低计算效率的前提下保证计算的稳定性。
(3)关于非充满状态下的强制旋转动边界模拟与实验研究：设计制造一套强制旋转动边界有机玻璃流体实验装置。利于观察和记录实验过程,实验结果能够用来检验SPH方法计算结果的正确性；提出一种静态粒子结合加密壁粒子的方案,解决了在重力场下旋转的强制动边界自由表面流问题中出现的粒子逸出边界的问题,利用ISPH算法中实施该方案,实现强制旋转动边界自由表面流模型是模拟；分别对比考察ω=0.5rad/s,1.5rad/s,2.5rad/s三种不同的角速度下的ISPH计算结果和实验结果。发现,在低速下,自由表面与水平面平行,而在较高速旋转下,自由表面在螺槽与机筒的剪切与推动下,形态呈曲线分布,它们与实验结果相吻合。当转速ω≤1.5rad/s时,离心力的作用基本可以忽略不计,随着转速的加大,离心力的作用较前者大,然而,在本文所选用的参数范围内,离心力影响并不显著。
(4)关于SPH方法在螺杆挤出领域的初步应用研究：计算二维单螺杆挤出螺槽横截面非牛顿流体流场,结果显示随着剪切逐渐变稠,旋涡中心逐渐向螺槽底部方向迁移。另外,通过分析发现,在计算非牛顿流时,采用镜像粒子边界法较采用静态粒子法更可靠；在计算螺杆挤出三维模型中,入口和出口采用周期边界较采用压力边界更适合。螺槽横截面上形成环流；剪切应力分布梯度在左上角和右上角更集中；顺螺槽方向的流动平稳,产量随反向压力梯度增加呈线性下降。
The constraint moving boundary problem is a kind of time-varying boundary problem imposed by external forces, such as, agitation, forced conveying, wave making etc. in the production and living. Numerical simulation in the field of polymer processing single-screw extruder and twin screw-extruder is a typical constraint moving boundary problem. When using traditional numerical techniques such as the finite volume method and finite element method, mesh distortion frequently encountered, and the calculation process is difficult to track, however, to understand the mechanism in the screw process is very important for design and optimization of the screw. In recent years, numerical methods are being developed from the continuum model to discrete particle model. The meshless particle method, based on the point approximation instead of relying on the grid, is better for calculating the moving boundary, large deformation, and the free surface, which bring opportunity to the simulation of the complex process. Typical meshless particle method is the smoothed particle hydrodynamics (SPH), which has a good self-adaptability than the traditional numerical methods in dealing with the discontinuity problem, and has been widely applied to the wave mechanics, fluid-solid interaction, high-speed collisions, etc.
In the beginning, the standard SPH method and its improved form——incompressible SPH (ISPH) method are analyzed. Three type of boundary treatment are investigated. One constraint moving boundary problem in screw extrusion has been investigated, and the program is written in FORTRAN. The dummy particles are used to treat the moving boundary. The moving boundary problem is separately simulated by ISPH and the moving least squares (MLS) corrected standard SPH. Furthermore, a partially filled forced revolving moving boundary with free surface flow model is constructed and simulated by two SPH methods. A set of organic glass constraint revolving moving boundary fluid experimental device is designed and manufactured; finally, a two-dimensional non-Newtonian flow model for cross-section of the groove is simulated. Furthermore, a single screw extruder three-dimensional flow is calculated using this algorithm. It laid the foundation for SPH to compute more complex single screw, twin screw extrusion process. The main innovations are as follows:
(1) On the boundary treatment: Three different wall boundary conditions treatments——repulsive boundary, mirror boundary, and static boundary are implemented to simulate lid-driven cavity flow with both SPH algorithms. The results show that simulations are more accurate with the static particles boundary. The repulsive boundary is fitter for the standard SPH than for ISPH.
(2) On the filled constraint moving boundary problem:One constraint moving boundary problem in screw extrusion has been investigated, and the dummy particles are used to treat the moving boundary. Then the model is separately computed by ISPH and the MLS corrected standard SPH. Through comparing the results separately produced by the moving boundary model, the fixed boundary model and the commercial software FLUENT, it has been shown that the boundary treatment method is simple and effective. One correcting scheme is suggested:in every time step, only the fluid particles' density is evolved, every20time steps, all particles' density is corrected by MLS. The results show that the correction approach can smooth the pressure oscillation in the high pressure gradient zone, guarantee the stability of the calculation without reducing the efficiency.
(3) On the partially filled constraint moving boundary problem:A set of constraint revolving moving boundary organic glass fluid experimental device is manufactured. It helps to observe and record the experimental process, the experimental results can be used to test the calculation accuracy of the SPH method. One static boundary particles with doubled wall particles scheme is proposed. If using ISPH algorithm, this scheme can avoid the escape of particles from the boundary when the free surface flow model revolving at a high speed in gravitational field. The results calculated by ISPH at three different angular velocities of the0.5rad/s,1.5rad/s, and2.5rad/s are compared with corresponding experimental results. It is found that, at low speeds, the free surface present a horizontal plane, but, at higher speeds (ω≥1.5rad/s), the free surface show to be a curve under the shear from the groove and barrel, both of them are consistent with the experimental results. With the increase of the speed, the effect of centrifugal force will gradually be revealed, but, when at a low speed (ω≤1.5rad/s), the effect of centrifugal force can be negligible.
(4) On the tentative application of SPH in moldling the screw extruding:A two-dimensional non-Newtonian flow model for cross-section of the groove is calculated. The results shows that the vortex center gradually migrate to the bottom of the groove with the shear thickening. In the calculating of non-Newtonian flow, the mirror boundary is the better choice. A single screw extruder three-dimensional flow is calculated using ISPH algorithm. Two types of inflow and outflow boundary implementation schemes including periodic boundary and pressure boundary are elaborated. The results show that:the periodic boundary is more feasible than pressure boundary. Circumfluence form in the cross-section of the groove; shear stress gradient is more concentrated in the top left angle and right angle; the flow along the spiral groove is stable, with the increase of the reverse pressure gradient, the yield decrease linearly.
本文从经典SPH出发,深入研究经典SPH方法的改进型——不可压缩光滑粒子流体动力学(Incompressible SPH, ISPH)方法,并初步应用于螺杆挤出的二维和三维流动模拟中。研究不同边界设置方法在ISPH和经典SPH方法中的实施和适用情况；基于螺杆挤出过程,利用静态粒子法,构建二维强制旋转边界问题模型。利用FORTRAN语言编程,分别采用ISPH和移动最小二乘(Moving least squares, MLS)修正的经典SPH两种算法进行了计算。提出一种MLS修正密度的策略；进而,提出非充满状态下的强制旋转动边界自由表面流模型,并采用两种SPH方法进行模拟。设计制造一套强制旋转动边界有机玻璃流体实验装置；最后,利用SPH模拟了螺槽横截面上的二维非牛顿流模型。进一步,研究SPH方法在单螺杆三维模型中的计算。为SPH在更加复杂的单螺杆、双螺杆挤出加工过程的模拟奠定了基础。本文的主要创新成果如下：
(1)关于边界实施的研究：静态粒子方法在ISPH和经典SPH算法中的计算精度均较镜像粒子边界高,这是由于镜像粒子法在每个时间步都需要重新生成新的镜像粒子,内部粒子的不规则分布映射到镜像粒子上。排斥力方法较适合在经典SPH中使用。
(2)关于充满状态下的强制旋转动边界模拟研究：构建强制旋转动边界问题物理模型,采用静态粒子法完成该模型的边界实施,并分别采用ISPH和MLS修正的经典SPH算法,进行计算。通过与静边界及商业计算流体动力学(Computational fluid dynamics, CFD)软件FLUENT计算结果对比验证了计算结果的可靠性；提出一种MLS修正密度策略：在每个时间步,只对流体粒子的密度进行演算,边界粒子密度保持不变,而每20个时间步对全部粒子进行MLS密度修正。通过该MLS修正经典SPH的方法,计算结果表明：它可以有效消除计算域中高压力梯度区的压力振荡,在不降低计算效率的前提下保证计算的稳定性。
(3)关于非充满状态下的强制旋转动边界模拟与实验研究：设计制造一套强制旋转动边界有机玻璃流体实验装置。利于观察和记录实验过程,实验结果能够用来检验SPH方法计算结果的正确性；提出一种静态粒子结合加密壁粒子的方案,解决了在重力场下旋转的强制动边界自由表面流问题中出现的粒子逸出边界的问题,利用ISPH算法中实施该方案,实现强制旋转动边界自由表面流模型是模拟；分别对比考察ω=0.5rad/s,1.5rad/s,2.5rad/s三种不同的角速度下的ISPH计算结果和实验结果。发现,在低速下,自由表面与水平面平行,而在较高速旋转下,自由表面在螺槽与机筒的剪切与推动下,形态呈曲线分布,它们与实验结果相吻合。当转速ω≤1.5rad/s时,离心力的作用基本可以忽略不计,随着转速的加大,离心力的作用较前者大,然而,在本文所选用的参数范围内,离心力影响并不显著。
(4)关于SPH方法在螺杆挤出领域的初步应用研究：计算二维单螺杆挤出螺槽横截面非牛顿流体流场,结果显示随着剪切逐渐变稠,旋涡中心逐渐向螺槽底部方向迁移。另外,通过分析发现,在计算非牛顿流时,采用镜像粒子边界法较采用静态粒子法更可靠；在计算螺杆挤出三维模型中,入口和出口采用周期边界较采用压力边界更适合。螺槽横截面上形成环流；剪切应力分布梯度在左上角和右上角更集中；顺螺槽方向的流动平稳,产量随反向压力梯度增加呈线性下降。
The constraint moving boundary problem is a kind of time-varying boundary problem imposed by external forces, such as, agitation, forced conveying, wave making etc. in the production and living. Numerical simulation in the field of polymer processing single-screw extruder and twin screw-extruder is a typical constraint moving boundary problem. When using traditional numerical techniques such as the finite volume method and finite element method, mesh distortion frequently encountered, and the calculation process is difficult to track, however, to understand the mechanism in the screw process is very important for design and optimization of the screw. In recent years, numerical methods are being developed from the continuum model to discrete particle model. The meshless particle method, based on the point approximation instead of relying on the grid, is better for calculating the moving boundary, large deformation, and the free surface, which bring opportunity to the simulation of the complex process. Typical meshless particle method is the smoothed particle hydrodynamics (SPH), which has a good self-adaptability than the traditional numerical methods in dealing with the discontinuity problem, and has been widely applied to the wave mechanics, fluid-solid interaction, high-speed collisions, etc.
In the beginning, the standard SPH method and its improved form——incompressible SPH (ISPH) method are analyzed. Three type of boundary treatment are investigated. One constraint moving boundary problem in screw extrusion has been investigated, and the program is written in FORTRAN. The dummy particles are used to treat the moving boundary. The moving boundary problem is separately simulated by ISPH and the moving least squares (MLS) corrected standard SPH. Furthermore, a partially filled forced revolving moving boundary with free surface flow model is constructed and simulated by two SPH methods. A set of organic glass constraint revolving moving boundary fluid experimental device is designed and manufactured; finally, a two-dimensional non-Newtonian flow model for cross-section of the groove is simulated. Furthermore, a single screw extruder three-dimensional flow is calculated using this algorithm. It laid the foundation for SPH to compute more complex single screw, twin screw extrusion process. The main innovations are as follows:
(1) On the boundary treatment: Three different wall boundary conditions treatments——repulsive boundary, mirror boundary, and static boundary are implemented to simulate lid-driven cavity flow with both SPH algorithms. The results show that simulations are more accurate with the static particles boundary. The repulsive boundary is fitter for the standard SPH than for ISPH.
(2) On the filled constraint moving boundary problem:One constraint moving boundary problem in screw extrusion has been investigated, and the dummy particles are used to treat the moving boundary. Then the model is separately computed by ISPH and the MLS corrected standard SPH. Through comparing the results separately produced by the moving boundary model, the fixed boundary model and the commercial software FLUENT, it has been shown that the boundary treatment method is simple and effective. One correcting scheme is suggested:in every time step, only the fluid particles' density is evolved, every20time steps, all particles' density is corrected by MLS. The results show that the correction approach can smooth the pressure oscillation in the high pressure gradient zone, guarantee the stability of the calculation without reducing the efficiency.
(3) On the partially filled constraint moving boundary problem:A set of constraint revolving moving boundary organic glass fluid experimental device is manufactured. It helps to observe and record the experimental process, the experimental results can be used to test the calculation accuracy of the SPH method. One static boundary particles with doubled wall particles scheme is proposed. If using ISPH algorithm, this scheme can avoid the escape of particles from the boundary when the free surface flow model revolving at a high speed in gravitational field. The results calculated by ISPH at three different angular velocities of the0.5rad/s,1.5rad/s, and2.5rad/s are compared with corresponding experimental results. It is found that, at low speeds, the free surface present a horizontal plane, but, at higher speeds (ω≥1.5rad/s), the free surface show to be a curve under the shear from the groove and barrel, both of them are consistent with the experimental results. With the increase of the speed, the effect of centrifugal force will gradually be revealed, but, when at a low speed (ω≤1.5rad/s), the effect of centrifugal force can be negligible.
(4) On the tentative application of SPH in moldling the screw extruding:A two-dimensional non-Newtonian flow model for cross-section of the groove is calculated. The results shows that the vortex center gradually migrate to the bottom of the groove with the shear thickening. In the calculating of non-Newtonian flow, the mirror boundary is the better choice. A single screw extruder three-dimensional flow is calculated using ISPH algorithm. Two types of inflow and outflow boundary implementation schemes including periodic boundary and pressure boundary are elaborated. The results show that:the periodic boundary is more feasible than pressure boundary. Circumfluence form in the cross-section of the groove; shear stress gradient is more concentrated in the top left angle and right angle; the flow along the spiral groove is stable, with the increase of the reverse pressure gradient, the yield decrease linearly.
引文
[1]刘儒勋,王志峰.数值模拟方法和运动界面的追踪[M].合肥：中国科学技术大学出版社,2001.
[2]江顺亮,朱复华.挤出过程计算机模拟[M].北京：机械工业出版社,2005.
[3]郑泓,俞炜,张洪斌等.同向啮合双螺杆挤出机挤出过程的计算机模拟[J].高分子学报,2006(5)：676-681.
[4]H. Tang, L.C. Wrobel, Z. Fan. Tracking of immiscible interfaces in multiple-material mixing processes[J]. Computational Materials Science.2004,290:103-118.
[5]任冬云.双螺杆挤出的非充满熔融理论的研究[D].北京化工大学,1997.
[6]周瑞忠,周小平,吴琛.数值方法进展：从连续介质到离散粒子模型[J].工程力学,2005,22(s1)：228-229.
[7]顾元通,丁桦.无网格法及其进展[J].力学进展,2005,35(3)：323-337.
[8]C. W. Hirt, A. A. Amsden, and J. L. Cook. An arbitrary Lagrangian-Eulerian computing method for all flow speeds[J]. Journal of Computational Physics 1997,135:203-216.
[9]F. H. Harlow, F. J. Welch. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface[J]. Phys Fluids,1965,8:2182-2189.
[10]C. W. Hirt, B. D. Nichols. Volume of fluid (VOF) method for the dynamics of free boundary[J]. Compute Phys,1981,39:201-225.
[11]C. S. Peskin. Flow patterns around hear t valves:a numerical method[J]. J Comput Phys, 1972,2:2252-2271.
[12]S. Osher, J. A. Sethain. Fronts progagating with curvature dependent speed:algorithms based on Hamilton Jacobi formulations[J]. J. Comp. Phys.,1988,79,12-49.
[13]A. A. Johnson, T. E.Tezduyar.3D simulation of fluid-particle interactions with the number of particles reaching 100[J]. Comput. Methos Appl. Mech. Engrg,1997,145(3):301-321.
[14]L. Fourment, S. Guerdoux. A 3D numerical simulation of different phases of friction stir welding[J]. International Journal of Material Forming,2009,17(7):1-32.
[15]黄志超,包忠诩,周天瑞.金属成形二维有限元网格重划技术研究[J].锻压技术,2004(5)：35-39.
[16]赵娜,刘立胜,郑剑等,网格重剖分在大变形分析中的应用[J].固体力学学报,2008,29(s1)：53-55.
[17]N. Acikgoz, C. L. Bottasso. A unified approach to t hedefo rmat ion o f simplicial and non-simplicial meshes in two and three dimensions with guaranteed validity[J]. Computers & Structures,2007.85(11-14):944-954.
[18]王海,徐国华,用于弹性旋翼流场模拟的网格变形方法[J].南京航空航天大学学报,2011,43(1)：1-6.
[19]艾辉林,陈艾荣.基于ALE格式的动网格方法数值模拟断面气动导数[J].工程力学,2009,26(7)：211-215.
[20]X. Q. Liu, Q. Ning, X. Hao. Fast dynamic grid deformation based on Delaunay graph mapping[J]. Journal of Computational Physics,2006,211(2):405-423.
[21]范锐军,周洲.基于Delaunay图映射的动弹网格技术及其应用[J].飞行力学,2010,28(2)：93-96.
[22]索奇峰,吴晴,钟易成等.振动桥梁CFD数值模拟的网格运动算法[J].计算物理,2011,28(4)：547-553.
[23]P. Matthias, Z. Thomas. Free-surface fluid dynamics on moving domains. Computer Methods in Applied Mechanics and Engineering[J].2011,200(1-4):372-382.
[24]J. A. Benek, P. G. Buning, J. L. Steger. A 3-D chimera grid embedding technique[R].1985, AIAA Paper No.85-1523.
[25]董国国,王立强.基于动态结构重叠网格的三维外挂物分离的数值模拟[J].航空兵器,2011,(2)：21-25.
[26]赵发明,高成君,夏琼.重叠网格在船舶CFD中的应用研究[J].船舶力学,2011,15(4)：332-341.
[27]姜孝海,范宝春,李鸿志.基于ALE方程的动网格膛口流场数值研究[J].计算力学学报,2008,25(4)：563-567.
[28]Y. G. Xu, D. C. Wan. Numerical simulation of fish swimming with rigid pectoral fins[J]. Journal of Hydrodynamics, Ser. B,2012, (24)2:263-272.
[29]S. Moussiere, A. Roubaud, O. Boutin.et al.2D and 3D CFD modelling of a reactive turbulent flow in a double shell supercritical water oxidation reactor[J]. The Journal of Supercritical Fluids,2012,65:25-31.
[30]E. Ferrer, R. H. J. Willden. A high order Discontinuous Galerkin-Fourier incompressible 3D Navier-Stokes solver with rotating sliding meshes[J]. Journal of Computational Physics, 2012,231(21):7037-7056.
[31]赵斌娟,袁寿其,陈汇龙.基于滑移网格研究双流道泵内非定常流动特性[J].农业工程学报,2009,25(6)：115-119.
[32]王超,黄胜,常欣等.基于滑移网格与RNG k-ε湍流模型的桨舵干扰性能研究[J].船舶力学,2011,15(7)：715-721.
[33]张小斌,项世军,曹潇丽等.用VOF方法数值计算液滴燃烧[J].化工学报,2011,62(3)：692-698.
[34]S. Osher, R. P Fedkiw. Level set methods:An overview and some recent results[J]. Journal of Computational Physics,2001,169(2):463-502.
[35]计时鸣,翁晓星,谭大鹏.基于水平集方法二维模型的软性磨粒两相流流场特性分析方法[J].物理学报,2012,61(])：1-7.
[36]H. Forrer, M. Berger. Flow simulations on cartesian grids involving complex moving geometries[C].7th Intl. Conf. on Hyperbolic Problems. Switz,1998:315-324.
[37]A. M. Roma, C. S. Peskth, M. J. Berger. An adaptive version of the immersed boundary method[J]. J Comput Phys,2000,153(2):509-534.
[38]C. S. Peskin. The immersed boundary method[J]. Acta Numer.2002,11:1-39.
[39]R. Mittal, G. Iaccarino. Immersed boundary methods[J]. Annu. Rev. Fluid Mech.2005,37: 239-261.
[40]张雄,宋康祖,陆明万.无网格法研究进展及其应用[J].计算力学学报,2003,20(6)：730-742.
[41]L. B. Lucy. A numerical approach to the testing of the fission hypothesis[J]. Astrophys. J, 1977,82(12):1013-1024.
[42]R. A. Gingold and J. J. Monaghan, Smoothed particle hydrodynamics:theory and application to non-spherical stars [J]. Mon. Not. R.Astron. Soc,1977,181(2):375-389.
[43]T. Belytschko, Y. Krongauz, D. Organ, et al. Meshless methods:An overview and recent developments[J]. Computer Methods In Applied Mechanics and Engineering,1996,139(1): 3-47.
[44]H. J. Chung, T. Belytschko. An error estimate in the EFG method[J]. Comput. Mech.1998, 21(2):91-100.
[45]T. Belytschko, M. Tabbara. Dynamic fracture using element-free Galerkin methods[J]. Int.J. Numer. Methods Engrg.1996,39(6):923-938.
[46]J. P. Ponthot, T. Belytschko. Arbitrary Lagrangian-Eulerian formulation for element-free Galerkin method[J]. Comput Methods Appl Mech. Engrg.,1998,152(1-2):19-46.
[47]P. Krysl, T. Belytschko. Analysis of thin shells by element-free Galerkin method[J]. International Journal of Solids and Structures.1996,33(20-22):3057-3080.
[48]D. Hegen. Element-free Galerkin methods in combination with finite element approaches[J]. Comput. Methods Appl. Mech. Engrg.1996,135(1-2):143-166.
[49]T. Liszka, J. Orkisz, The finite difference method at arbitrary irregular grids and its application in applied mechanics[J]. Comput. Struct.1980,11(1-2):83-95.
[50]B. Nayroles, G. Touzot, P. Villon. Generalizing the finite element method:diffuse approximation and diffuse elements [J]. Comput Mech,1992,10:307-318.
[51]E. Onate, S. Idelsohn, O. C. Zienkiewicz, et al. A finite point method in computational mechanics:Applications to convective transport and fluid flow[J]. Int J Numer Methods Engr, 1996,39:3839-3866.
[52]W. K. L iu, S Jun, Y. F Zhang. Reproducing Kernel Particle methods[J]. Int J Numer Meth Fluids,1995,20:1081-1106.
[53]C. A. Duarte, J. T. Oden. Hp clouds:a mesh less method to solve boundary value problems [R]. Technical Report 95205. Texas Institute for Computational and Applied Mathematics. University of Texas,1995.
[54]J. M. Melenk, I. Babuska. The partition of unity finite element methods:Basic theory and application[J]. Comput Methods Appl Mech Engrg,1996,139:263-288.
[55]X. Zhang, K. Z. Song, M. W. Lu. Meshless methods based on collocation with radial basis function[J]. Comput Mech,2000,26 (4):333-343.
[56]G. R. Liu. MeshFree methods:Moving beyond the finite element method[M]. CRC Press, 2003.
[57]G. R. Liu and M. B. Liu.光滑粒子流体动力学——一种无网格粒子法[M].韩旭,杨刚,强洪夫,译.长沙：湖南大学出版社,2005.
[58]张雄,刘岩.无网格法[M].北京：清华大学出版社,2004年.
[59]P. A. Moysey, M. R. Investigation of solids transport in a single-screw extruder using a 3-D discrete particle simulation[J]. Polymer Engineering & Science,2004,44(12):2203-2215.
[60]P. A. Moysey, M. R. Thompson. Modelling the solids inflow and solids conveying of single-screw extruders using the discrete element method[J]. Powder Technology,2005, 153(2):95-107.
[61]Thompson, http://chemeng.mcmaster.ca/thompson.html [OL].
[62]P. Cleary, M. Prakash, J. Ha. Novel applications of smoothed particle hydrodynamics (SPH) in metal forming[J]. Journal of Materials Processing Technology,2006,177(3):41-48.
[63]P. Cleary. Extension of SPH to predict feeding, freezing and defect creation in low pressure die casting[J]. Applied Mathematical Modelling.2010,34(11):3189-3201.
[64]曹文炅,周照耀,何毅等.压铸充型过程的SPH方法建模及数值模拟[J].华南理工大学学报(自然科学版),2011,39(1)：100-105.
[65]X. J. Fan, R. I. Tanner, R. Zheng. Smoothed particle hydrodynamics simulation of non-Newtonian moulding flow[J]. J. Non-Newtonian Fluid Mech.,2010,165(5-6):219-226.
[66]孙中国,席光,项利峰.不可压缩流动的移动粒子半隐式法数值模拟[J].应用力学学报.2007,24(3)：440-443.
[67]张驰,张雨新,万德成.SPH方法和MPS方法模拟溃坝问题的比较分析.水动力学研究与进展.2011,26(6)：736-746.
[68]M. A. Martinez, E. Cueto, M. Doblare. Natural element meshless simulation of flows involving short fiber suspensions[J]. J. Non-Newtonian Fluid Mech.2003,115(1):51-78.
[69]J.A. Garcia, LI. Gascon, E. Cueto. Meshless methods with application to Liquid Composite Molding simulation[J]. Comput. Methods Appl. Mech. Engrg.2009,198(33-36):2700-2709.
[70]F. Bernal, M. Kindelan. RBF meshless modelling of non-Newtonian Hele-Shaw flow[J]. Engineering Analysis with Boundary Elements.2007,31(10):863-874.
[71]X. K Li, Q. L. Duan, X. H. Han. Adaptive coupled arbitrary Lagrangian-Eulerian finite element and meshfree method for injection molding process[J]. Int. J. Numer. Meth. Engng. 2008,73(8):1153-1180.
[72]S. Yashiro, H. Sasaki, Y. Sakaida. Particle simulation for predicting fiber motion in injection molding of short-fiber-reinforced composites[J]. Composites:Part A.2012,43(10): 1754-1764.
[73]张响,李倩,石凡等.基于SPH方法的微注射成型数值模拟[J].2012,63(1ω：157-162.
[74]张小华,欧阳洁,张林.圆管聚合物热流中黏性耗散分析的无网格模拟[J].化工学报,2007,58(1)：15-20.
[75]杨波,欧阳洁,蒋涛,等.PTT黏弹性流体的光滑粒子动力学方法模拟[J].力学学报,2011,43(4)：667-673.
[76]J. J. Monaghan. Simulating Free Surface Flows with SPH[J]. Journal of Computational Physics,1994,110(2):399-406.
[77]J. J. Monaghan. SPH and Riemann solvers[J]. Journal of Computational Physics,1997, 136(2):298-307.
[78]M. B. Liu, G. R. Liu, K. Y. Lam. Investigations into water mitigation using a meshless particle method[J]. Shock Waves,2002,12(3):181-195。
[79]L. D. Libersky, A. G. Petschek, T. C. Carney, et al. High strain Lagrangian hydrodynamics a three-dimensional SPH code for dynamic material response[J]. J. Comput. Phys,1993, 109(1):67-75。
[80]L. D. Libersky and A. G. Petschek. Smooth particle hydrodynamics with strength of materials, In:Advances in the Free-Lagrange Method[J]. Lecture Notes in Physics,1991,395: 248-257.
[81]P. W. Randles and L. D. Libersky. Smoothed particle hydrodynamics:Some recent improvements and applications[J]. Comput. Methods Appl. Mech. Eng,1996,139(1-4): 375-408.
[82]G. R. Johnson, E. H. Petersen, and R. A. Stryk. Incorporation of an SPH option into EPIC code for a wide range of high velocity impact computations[J]. Int. J. Impact Eng,1993,14 (1-4):385-394.
[83]G. R. Johnson, R. A. Stryk, and S. R. Beissel. SPH for high velocity impact computations. Comput[J]. Methods Appl. Mech. Eng,1996,139(1-4):347-374.
[84]G. R. Johnson and S. R. Beissel.'Normalized smoothing functions for SPH impact computations[J]. Int. J. Numer. Methods Eng,1996,39(16):2725-2741.
[85]S. Potapov, B. Maurel, A. Combescure, et al. Modeling accidental-type fluid-structure interaction problems with the SPH method[J]. Computers and Structures,2009,87(11-12): 721-734.
[86]A. Colagrossi, M. Landrini. Numerical simulation of interfacial flows by smoothed particle hydrodynamic[J]. Journal of Computational Physics.2003,191(2):448-475.
[87]J. J. Monaghan. Smoothed particle hydrodynamics[J]. Annual Review Astronomics and A strophysics,1992,30:543-574.
[88]J. J. Monaghan. Smoothed particle hydrodynamics[J]. Rep. Prog. Phys.2005,68(8): 1703-1759.
[89]张锁春.光滑质点流体动力学(SPH)方法(综述)[J].计算物理,1996,13(4)：385-397
[90]张嘉钟,郑俊,于开平,等.流体力学中SPH算法张力不稳定性研究.工程力学.2010,27(2)：65-72.
[91]郑俊,于开平,魏英杰,等.SPH后处理研究[J].计算物理.2011,28(2)：213-218.
[92]刘富,童明波,陈建平,等.基于SPH方法的三维液体晃动数值模拟[J].南京航空航天大学学报.2010,42(1)：122-126.
[93]王建明,余丰,刘飞宏.SPH和FEM耦合法模拟磨料水射流中单磨粒加速过程[J].山东大学学报(工学版).2011,41(5)：114-120.
[94]任金莲,欧阳洁,蒋涛,等.修正SPH方法在自由表面模拟中的应用[J].计算力学学报.2012,29(1)：69-73.
[95]李大鸣,李晓瑜,林毅.液滴冲击自由液面的SPH法数值模拟[J].中国科学：技术科学.2011,41(8)：1055-1062.
[96]M. Yildiz, R. A. Rook, and A. Suleman. SPH with the multiple boundary tangent method. Int. J. Numer[J]. Meth. Engng 2009; 77(10):1416-1438.
[97]M. S. Shadloo, A. Zainali, Samir H. Sadek.Improved Incompressible Smoothed Particle Hydrodynamics method for simulating flow around bluff bodies[J]. Comput. Methods Appl. Mech. Engrg.2011,200(9-12):1008-1020.
[98]R. Fatehi, M. T. Manzari. A consistent and fast weakly compressible smoothed particle hydrodynamics with a new wall boundary condition[J]. Int. J. Numer. Meth. Fluids 2012; 68:905-921.
[99]C. X. Liang, C. Y. Zhang, H. Y. Liu, et al. Modeling low Reynolds number incompressible flows with curved boundaries using SPH[J]. Int. J. Numer. Meth. Fluids.2012,68(9): 1173-1188.
[100]A. Colagrossi, B. Bouscasse, M. Antuono, etal. Particle packing algorithm for SPH schemes[J]. Computer Physics Communications.2012,183(8):1641-1653.
[101]S. D. Shao. Incompressible smoothed particle hydrodynamics simulation of multifluid flows[J]. Int. J. Numer. Meth. Fluids.2012,69(11):1715-1735.
[102]M. S. Shadloo and M. Yildiz. Numerical modeling of Kelvin-Helmholtz instability using smoothed particle hydrodynamics[J]. Int. J. Numer. Meth. Engng.2011,87(10): 988-1006.
[103]Y. Z. Yan, L. Li, K. Sezer, etal. CO2 laser underwater machining of deep cavities in alumina[J]. Journal of the European Ceramic Society.2011,31(15):2793-2807.
[104]H. Takamiya, H. Okada, Y. Sakai, etal. Smoothed particle hydrodynamics analysis on semi-solid metal forming process[J]. Japan J. Indust. Appl. Math.2011,28(1):183-203.
[105]J. N. Fang, A. Parriaux, M. Rentschler, et al. Improved SPH methods for simulating free surface flows of viscous fluids[J]. Applied Numerical Mathematics,2009.59(2): 251-271
[106]J. J. Monaghan. SPH without a tensile instability[J]. Journal of Computational Physics, 2000,159(2):290-311.
[107]X. Y. Hu, N. A. Adams. A constant-density approach for incompressible multi-phase SPH[J]. Journal of Computational Physics,2009.228(6):2082-2091.
[108]J. Bonet, T-S L. Lok. Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulations[J]. Comput. Methods Appl. Mech. Engrg,1999,180(1-2): 97-115
[109]T. Belytschko, Y. Krongauz, J. Dolbow, et al. On the completeness of the meshfree particle[J]. International Journal for Numerical Methods in Engineering,1998,43(5): 785-819.
[110]W. K. Liu, S. Jun, Y. F. Zhang. Reproducing kernel particle methods[J]. Int. J. Numer. Meth. Fluids.1995,20(8-9):1081-1106.
[111]W. K. Liu, S. Jun, S. F. Li, et al. Reproducing kernel particle methods for structural dynamics[J]. Int. J. Numer. Methods Engrg.1995,38(10):1655-1679.
[112]S. H. Lee, H. J. Kim, S. Jun. Two scale meshfree method for the adaptivity of 3D stress concentration problems[J]. Comput. Mech.2000,26(4):376-387.
[113]J. S. Chen, C. Pan, C. T. Wu, et al. Reproducing kernel particle methods for large deformation analysis of non-linear structures[J]. Comput. Methods Appl. Mech. Engrg. 1996,139(1-4):195-227.
[114]S. F. Li, W. Hao, W. K. Liu. Meshfree simulations of shear banding in large deformation[J]. International Journal of Solid and Structures,2000,37(48-50): 7185-7206.
[115]J. K. Chen, J. E. Beraun. A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems[J]. Comput. Methods Appl. Mech. Engrg,2000,190(1-2): 225-239.
[116]J. K. Chen, J. E. Beraun, and C. J. Jih. An improvement for tensile instability in smoothed particle hydrodynamics[J]. Computational Mech,1999,23(4):279-287.
[117]J. K. Chen, J. E. Beraun, and C. J. Jih. A corrective smoothed particle method for boundary value problems in heat conduction[J]. International Journal for Numerical Methods in Engineering,1999,46(2):231-252.
[118]J. K. Chen, J. E. Beraun, and C. J. Jih. Completeness of corrective smoothed particle method for linear elastodynamics[J]. Computational Mechanics,1999,24(4):273-285.
[119]G. M. Zhang, R. C. Batra. Modified smoothed particle hydrodynamics method and its application to transient problems[J]. Computational Mechanics,2004,34(2):137-146.
[120]M. B. Liu, W. P. Xie, G. R. Liu. Modeling incompressible flows using a finite particle method[J]. Applied Mathematical Modelling,2005,29(12):1252-1270.
[121]P. Lancaster and K. Salkauskas. Surface generated by moving least squares methods[J]. Mathe Comp,1981,37(155):141-158.
[122]G. A. Dilts. Moving least-square particle hydrodynamics Ⅰ:Consistency and stability[J]. Int. J. Numer. Methods Eng,1999,44(8):1115-1155.
[123]G. A. Dilts. Moving least-square particle hydrodynamics Ⅱ:Conservation and boundaries[J]. Int. J. Numer. Methods Eng,2000,48(10):1503-1524.
[124]G. A. Dilts. Some recent developments for moving least squares particle methods[C]. Proceedings on Computational Fluid and Solid Mechanics, Cambridge MA,2001:1-5.
[125]S. J. Cummins, M. Rudman. An SPH projection method[J]. Journal of Computational Physics.1999,152(2):584-607.
[126]E. S. Lee, C. Moulinec, R. Xu, et al. Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method[J]. Journal of Computational Physics,2008,227(18):8417-8436.
[127]A. Khayyer, H. Gotoh, S. D. Shao. Enhanced predictions of wave impact pressure by improved incompressible SPH methods[M]. Applied Ocean Research,2009,31(2): 111-131.
[128]R. Xu, P. Stansby, D. Laurence. Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach[J]. Journal of Computational Physics, 2009,228(18):6703-6725
[129]J. P. Hughes, D. I. Graham. Comparison of incompressible and weakly-compressible SPH models for free-surface water flows[J]. Journal of Hydraulic Research.2010,48, s(1):105-117.
[130]K.Szewc, J. Pozorski and J. P. Minier. Analysis of the incompressibility constraint in the smoothed particle hydrodynamics method[J]. Int. J. Numer. Meth. Engng.2012,92(4): 343-369.
[131]A. Rafiee, S. Cummins, M. Rudman, etal. Comparative study on the accuracy and stability of SPH schemes in simulating energetic free-surface flows[J]. European Journal of Mechanics B/Fluids.2012,36:1-16.
[132]M. S. Shadloo, A. Zainali, M. Yildiz, et al. A robust weakly compressible SPH method and its comparison with an incompressible SPH[J]. Int. J. Numer. Meth. Engng.2012, 89(8):939-956.
[133]J. J Monaghan. Particle methods for hydrodynamics[J]. Computer Physics Report,1985, 3(2):71-124.
[134]J. P. Morris. A study of the stability properties of smooth particle hydrodynamics[J]. Publ.Astron.Soc.Aust,1996,13(1):97-102.
[135]D. A. Fulk. A numerical analysis of smoothed particle hydrodynamics[D]. Air Force Institute of Technology,1994.
[136]H. Takeda, S. M. Miyama, M. Sekiya. Numerical simulation of viscous flow by smoothed particle hydrodynamics[J]. Progress of Theoretical Physics,1994,92(5):939-960.
[137]L. Brookshaw. A method of calculating radiative heat diffusion in particle simulations[C]. Proceedings of the Astronomical Society of Australia,1985,6(2):207-210.
[138]O. Flebbe, S. Munzel, H. Herold, et al. Smoothed particle hydrodynamics-physical viscosity and the simulation of accretion disks[J]. The Astrophysical Journal,1994, 431(2):754-760.
[139]J. P. Morris, P. J. Fox, Y. Zhu. Modeling low reynolds number incompressible flows using SPH[J]. Journal of Computational Physics,1997,136(1):214-226.
[140]D. J. Price. Magnetic fields in astrophysics[D]. Institute of Astronomy & Churchill College University of Cambridge.2004.
[141]M. Jubelgas, V. Springel and K. Dolag. Thermal conduction in cosmological SPH simulation[J]. Mon.Not. R. Astron. Soc,2004,351(2):423-435.
[142]P. W. Cleary and J. J. Monaghan. Conduction modelling using smoothed particle hydrodynamics[J]. Journal of Computational Physics,1999,148(1):227-264.
[143]P. Espanol and M. Revenga. Smoothed dissipative particle dynamics[J]. Phys. Rev. E, 2003,67(2):026705.
[144]S. D. Shao, Y. M. Lo. Edmond. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface[J]. Advances in Water Resources,2003, 26(7):787-800.
[145]J. J. Monaghan. On the problem of penetration in particle methods[J]. Journal of Computational Physics,1989,82(1):1-15.
[146]M. B. Liu, G. R. Liu, K. Y. Lam. Constructing smoothing functions in smoothed particle hydrodynamics with applications[J]. Journal of Computational and Applied Mathematics, 2003,155(2):263-284.
[147]T. Belytschko, Y. Krongauz, D. Organ, et al. Meshless methods:An overview and recent developments[J]. Computer Methods in Applied Mechanics and Engineering,1996, 139(1-4):3-47.
[148]D. S. Balsara. Von Neumann stability analysis of smoothed particle hydrodynamics suggestions for optimal algorithms[J]. Journal of Computational Physics,1995,121(2): 357-372.
[149]J. W. Swegle, D. L. Hicks, and S. W. Attaway. Smoothed Particle Hydrodynamics stability analysis[J]. Journal of Computational Physics.1995,116(1):123-134.
[150]C. Guenther, D. L. Hicks, J.W. Swegle. Conservative smoothing versus artificial viscosity[R]. SANDIA REPORT, SAND94-1853 UC-705,1994.
[151]R. Vignjevic. Review of development of the SPH method predictive modeling of dynamic processes[M]. US:Springer,2009,367-396.
[152]C. T. Dyka. R. P. Inge. Addressing tension instability in SPH Methods[R]. Technical Report NRL/MR/6384. NRL,1994.
[153]C. T. Dyka. R. P. Inge. An approach for tension instability in smoothed particle hydrodynamics (SPH) [J]. Computers & Structures,1995.57(4):573-580.
[154]S. F. Li. W. K. Liu. Meshfree and particle methods and their applications[J]. Appl Mech Rev.2002.55(1):1-34.
[155]P. W. Randles, L. D. Libersky. Normalized SPH with stress points[J]. International Journal for Numerical Methods in Engineering,2000,48(10):1445-1462
[156]W. K. Liu, J. Adee, and S. Jun. Reproducing kernel and wavelets particle methods for elastic and plastic problems[J]. Advanced Computational Methods for Material Modeling. New Orleans:ASME,1993,175-190.
[157]W. K. Liu and O. C. Brandenburg. Reproducing kernel and wavelets particle methods[J]. Aerospace Structures:Nonlinear Dynamics and System Response,1993:39-56.
[158]W. K. Liu, S. Jun, S. Li, et al. Reproducing kernel particle methods for structural dynamics[J]. Int. J. Numer. Methods Eng,1995,38 (10):1655-1679.
[159]W. K. Liu, Y. Chen, C. T. Chang, et al. Advances in multiple scale kernel particle methods[J]. Computational Mech,1996,18(2):73-111.
[160]W. K. Liu, Y. Chen, S. Jun, et al. Overview and applications of the reproducing kernel particle methods[J]. Arch. Comput. Mech. Eng.:State of Rev,1996,3(1):3-80.
[161]W. K. Liu, S. Li, and T. Belytschko. Moving least square reproducing kernel method Part I:Methodology and convergence[J]. Comput. Methods Appl. Mech. Eng,1997,143(1-2): 422-453
[162]X. Y. Hu, N. A. Adams. An incompressible multi-phase SPH method[J]. Journal of Computational Physics,2007,227(1):264-278.
[163]A. J. Chorin. Numerical solution of the Navier-Stokes equations[J]. Math. Comp,1968, 22:745-762.
[164]H. A. Van Der Vorst. Bi-CGSTAB:A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems[J]. S.J. Sci. Stat. Comput,1992.13(2): 631-644.
[165]J. P. Hughes, D. I. Graham. Degradation and instability of incompressible SPH computations of simple viscous flows[C]. Proceedings of the Workshop "SPHERIC-Smoothed Particle Hydrodynamics European Research Interest Community" Madrid,2007.
[166]Y. Saad. Iterative methods for sparse linear system[M]. Boston:PWS Pub. Co.,2000.
[167]M. Benzi. Preconditioning techniques for large linear systems:a survey[J]. Journal of Computational Physics,2002,182(2):418-477.
[168]J. J. Monaghan, A. Kos. Solitary waves on a cretan beach[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering,1999,125(3):145-154.
[169]J. J. Monaghan, A. Kos and N. Issa. Fluid motion generated by impact[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering,2003,129(6):250-260.
[170]J. J. Monaghan, J. B. Kajtar. SPH particle boundary forces for arbitrary boundaries[J]. Computer Physics Communications,2009,180(10):1811-1820.
[171]G. Oger, M. Doring, B. Alessandrini, et al. Two-dimensional SPH simulations of wedge water entries[J]. Journal of Computational Physics,2006,213(2):803-822.
[172]S. Koshizuka, A. Nobe, Y. Oka. Numerical analysis of breaking waves using the moving particle semi-implicit method[J]. International Journal for Numerical Methods in Fluids, 1998,26(7):751-769.
[173]R. Dalrymple. and O. Knio. SPH modelling of waves[C]. In ASCE, editor, Proc. Coastal Dynamics, Lund, Sweden,2001:779-787.
[174]A. J. C. Crespo. Application of the smoothed particle hydrodynamics model SPHysics to free-surface hydrodynamics[D]. UNIVERSIDADE DE VIGO,2008.
[175]J. J. Monaghan. Smoothed particle hydrodynamic simulations of shear flow[J]. Monthly Notices of the Royal Astronomical Society,2006,365(1):199-213.
[176]D. Molteni, A. Colagrossi. A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH[J]. Computer Physics Communications,2009, 180(6):861-872.
[177]Marco Ellero, Martin Kroger, Siegfried Hess. Viscoelastic flows studied by smoothed particle dynamics[J]. J. Non-Newtonian Fluid Mech.2002,105(1):35-51.
[178]Y. P. Chui, P. A. Heng. A meshless rheological model for blood-vessel interaction in endovascular simulation[J]. Progress in Biophysics and Molecular Biology,2010, 103(2-3):252-261.
[179]H. N. Zhu, S. N. Martysa, C. Ferraris, et al. A numerical study of the flow of Bingham-like fluids in two-dimensional vane and cylinder rheometers using a smoothed particle hydrodynamics (SPH) based method[J]. J. Non-Newtonian Fluid Mech.2010, 165(7-8):362-375.
[180]孙洪全,韩纪庆.基于粒子的非牛顿流体模拟统一模型[J].哈尔滨工业大学学报,2010,42(7)：1104-1107.
[181]T. Jiang, J. Ouyang, L. Zhang, et al. The SPH approach to the process of container filling based on non-linear constitutive models[J]. Acta Mech. Sin, (2012),28(2):407-418.
[182]J. M. Buick. Lattice Boltzmann simulation of power-law fluid flow in the mixing section of a single-screw extruder[J]. Chemical Engineering Science,2009,64(1):52-58.
[183]A. R. Chell, J. M. Ottino. Fluid mechanics of mixing in a single-screw extruder[J]. Ind. Eng. Chem. Fundam.,1985,24(2):170-180.
[184]M. Vakilha, T. M. Manzari. Modelling of power-law fluid flow through porous media using smoothed particle hydrodynamics[J]. Transp Porous Med,2008,74(3):331-346.
[185]李凌丰,刘际轩,茅旭飞.螺杆加工塑料时熔体流动的数值模拟[J].机械工程学报,2011,47(24)：50-56.
[2]江顺亮,朱复华.挤出过程计算机模拟[M].北京：机械工业出版社,2005.
[3]郑泓,俞炜,张洪斌等.同向啮合双螺杆挤出机挤出过程的计算机模拟[J].高分子学报,2006(5)：676-681.
[4]H. Tang, L.C. Wrobel, Z. Fan. Tracking of immiscible interfaces in multiple-material mixing processes[J]. Computational Materials Science.2004,290:103-118.
[5]任冬云.双螺杆挤出的非充满熔融理论的研究[D].北京化工大学,1997.
[6]周瑞忠,周小平,吴琛.数值方法进展：从连续介质到离散粒子模型[J].工程力学,2005,22(s1)：228-229.
[7]顾元通,丁桦.无网格法及其进展[J].力学进展,2005,35(3)：323-337.
[8]C. W. Hirt, A. A. Amsden, and J. L. Cook. An arbitrary Lagrangian-Eulerian computing method for all flow speeds[J]. Journal of Computational Physics 1997,135:203-216.
[9]F. H. Harlow, F. J. Welch. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface[J]. Phys Fluids,1965,8:2182-2189.
[10]C. W. Hirt, B. D. Nichols. Volume of fluid (VOF) method for the dynamics of free boundary[J]. Compute Phys,1981,39:201-225.
[11]C. S. Peskin. Flow patterns around hear t valves:a numerical method[J]. J Comput Phys, 1972,2:2252-2271.
[12]S. Osher, J. A. Sethain. Fronts progagating with curvature dependent speed:algorithms based on Hamilton Jacobi formulations[J]. J. Comp. Phys.,1988,79,12-49.
[13]A. A. Johnson, T. E.Tezduyar.3D simulation of fluid-particle interactions with the number of particles reaching 100[J]. Comput. Methos Appl. Mech. Engrg,1997,145(3):301-321.
[14]L. Fourment, S. Guerdoux. A 3D numerical simulation of different phases of friction stir welding[J]. International Journal of Material Forming,2009,17(7):1-32.
[15]黄志超,包忠诩,周天瑞.金属成形二维有限元网格重划技术研究[J].锻压技术,2004(5)：35-39.
[16]赵娜,刘立胜,郑剑等,网格重剖分在大变形分析中的应用[J].固体力学学报,2008,29(s1)：53-55.
[17]N. Acikgoz, C. L. Bottasso. A unified approach to t hedefo rmat ion o f simplicial and non-simplicial meshes in two and three dimensions with guaranteed validity[J]. Computers & Structures,2007.85(11-14):944-954.
[18]王海,徐国华,用于弹性旋翼流场模拟的网格变形方法[J].南京航空航天大学学报,2011,43(1)：1-6.
[19]艾辉林,陈艾荣.基于ALE格式的动网格方法数值模拟断面气动导数[J].工程力学,2009,26(7)：211-215.
[20]X. Q. Liu, Q. Ning, X. Hao. Fast dynamic grid deformation based on Delaunay graph mapping[J]. Journal of Computational Physics,2006,211(2):405-423.
[21]范锐军,周洲.基于Delaunay图映射的动弹网格技术及其应用[J].飞行力学,2010,28(2)：93-96.
[22]索奇峰,吴晴,钟易成等.振动桥梁CFD数值模拟的网格运动算法[J].计算物理,2011,28(4)：547-553.
[23]P. Matthias, Z. Thomas. Free-surface fluid dynamics on moving domains. Computer Methods in Applied Mechanics and Engineering[J].2011,200(1-4):372-382.
[24]J. A. Benek, P. G. Buning, J. L. Steger. A 3-D chimera grid embedding technique[R].1985, AIAA Paper No.85-1523.
[25]董国国,王立强.基于动态结构重叠网格的三维外挂物分离的数值模拟[J].航空兵器,2011,(2)：21-25.
[26]赵发明,高成君,夏琼.重叠网格在船舶CFD中的应用研究[J].船舶力学,2011,15(4)：332-341.
[27]姜孝海,范宝春,李鸿志.基于ALE方程的动网格膛口流场数值研究[J].计算力学学报,2008,25(4)：563-567.
[28]Y. G. Xu, D. C. Wan. Numerical simulation of fish swimming with rigid pectoral fins[J]. Journal of Hydrodynamics, Ser. B,2012, (24)2:263-272.
[29]S. Moussiere, A. Roubaud, O. Boutin.et al.2D and 3D CFD modelling of a reactive turbulent flow in a double shell supercritical water oxidation reactor[J]. The Journal of Supercritical Fluids,2012,65:25-31.
[30]E. Ferrer, R. H. J. Willden. A high order Discontinuous Galerkin-Fourier incompressible 3D Navier-Stokes solver with rotating sliding meshes[J]. Journal of Computational Physics, 2012,231(21):7037-7056.
[31]赵斌娟,袁寿其,陈汇龙.基于滑移网格研究双流道泵内非定常流动特性[J].农业工程学报,2009,25(6)：115-119.
[32]王超,黄胜,常欣等.基于滑移网格与RNG k-ε湍流模型的桨舵干扰性能研究[J].船舶力学,2011,15(7)：715-721.
[33]张小斌,项世军,曹潇丽等.用VOF方法数值计算液滴燃烧[J].化工学报,2011,62(3)：692-698.
[34]S. Osher, R. P Fedkiw. Level set methods:An overview and some recent results[J]. Journal of Computational Physics,2001,169(2):463-502.
[35]计时鸣,翁晓星,谭大鹏.基于水平集方法二维模型的软性磨粒两相流流场特性分析方法[J].物理学报,2012,61(])：1-7.
[36]H. Forrer, M. Berger. Flow simulations on cartesian grids involving complex moving geometries[C].7th Intl. Conf. on Hyperbolic Problems. Switz,1998:315-324.
[37]A. M. Roma, C. S. Peskth, M. J. Berger. An adaptive version of the immersed boundary method[J]. J Comput Phys,2000,153(2):509-534.
[38]C. S. Peskin. The immersed boundary method[J]. Acta Numer.2002,11:1-39.
[39]R. Mittal, G. Iaccarino. Immersed boundary methods[J]. Annu. Rev. Fluid Mech.2005,37: 239-261.
[40]张雄,宋康祖,陆明万.无网格法研究进展及其应用[J].计算力学学报,2003,20(6)：730-742.
[41]L. B. Lucy. A numerical approach to the testing of the fission hypothesis[J]. Astrophys. J, 1977,82(12):1013-1024.
[42]R. A. Gingold and J. J. Monaghan, Smoothed particle hydrodynamics:theory and application to non-spherical stars [J]. Mon. Not. R.Astron. Soc,1977,181(2):375-389.
[43]T. Belytschko, Y. Krongauz, D. Organ, et al. Meshless methods:An overview and recent developments[J]. Computer Methods In Applied Mechanics and Engineering,1996,139(1): 3-47.
[44]H. J. Chung, T. Belytschko. An error estimate in the EFG method[J]. Comput. Mech.1998, 21(2):91-100.
[45]T. Belytschko, M. Tabbara. Dynamic fracture using element-free Galerkin methods[J]. Int.J. Numer. Methods Engrg.1996,39(6):923-938.
[46]J. P. Ponthot, T. Belytschko. Arbitrary Lagrangian-Eulerian formulation for element-free Galerkin method[J]. Comput Methods Appl Mech. Engrg.,1998,152(1-2):19-46.
[47]P. Krysl, T. Belytschko. Analysis of thin shells by element-free Galerkin method[J]. International Journal of Solids and Structures.1996,33(20-22):3057-3080.
[48]D. Hegen. Element-free Galerkin methods in combination with finite element approaches[J]. Comput. Methods Appl. Mech. Engrg.1996,135(1-2):143-166.
[49]T. Liszka, J. Orkisz, The finite difference method at arbitrary irregular grids and its application in applied mechanics[J]. Comput. Struct.1980,11(1-2):83-95.
[50]B. Nayroles, G. Touzot, P. Villon. Generalizing the finite element method:diffuse approximation and diffuse elements [J]. Comput Mech,1992,10:307-318.
[51]E. Onate, S. Idelsohn, O. C. Zienkiewicz, et al. A finite point method in computational mechanics:Applications to convective transport and fluid flow[J]. Int J Numer Methods Engr, 1996,39:3839-3866.
[52]W. K. L iu, S Jun, Y. F Zhang. Reproducing Kernel Particle methods[J]. Int J Numer Meth Fluids,1995,20:1081-1106.
[53]C. A. Duarte, J. T. Oden. Hp clouds:a mesh less method to solve boundary value problems [R]. Technical Report 95205. Texas Institute for Computational and Applied Mathematics. University of Texas,1995.
[54]J. M. Melenk, I. Babuska. The partition of unity finite element methods:Basic theory and application[J]. Comput Methods Appl Mech Engrg,1996,139:263-288.
[55]X. Zhang, K. Z. Song, M. W. Lu. Meshless methods based on collocation with radial basis function[J]. Comput Mech,2000,26 (4):333-343.
[56]G. R. Liu. MeshFree methods:Moving beyond the finite element method[M]. CRC Press, 2003.
[57]G. R. Liu and M. B. Liu.光滑粒子流体动力学——一种无网格粒子法[M].韩旭,杨刚,强洪夫,译.长沙：湖南大学出版社,2005.
[58]张雄,刘岩.无网格法[M].北京：清华大学出版社,2004年.
[59]P. A. Moysey, M. R. Investigation of solids transport in a single-screw extruder using a 3-D discrete particle simulation[J]. Polymer Engineering & Science,2004,44(12):2203-2215.
[60]P. A. Moysey, M. R. Thompson. Modelling the solids inflow and solids conveying of single-screw extruders using the discrete element method[J]. Powder Technology,2005, 153(2):95-107.
[61]Thompson, http://chemeng.mcmaster.ca/thompson.html [OL].
[62]P. Cleary, M. Prakash, J. Ha. Novel applications of smoothed particle hydrodynamics (SPH) in metal forming[J]. Journal of Materials Processing Technology,2006,177(3):41-48.
[63]P. Cleary. Extension of SPH to predict feeding, freezing and defect creation in low pressure die casting[J]. Applied Mathematical Modelling.2010,34(11):3189-3201.
[64]曹文炅,周照耀,何毅等.压铸充型过程的SPH方法建模及数值模拟[J].华南理工大学学报(自然科学版),2011,39(1)：100-105.
[65]X. J. Fan, R. I. Tanner, R. Zheng. Smoothed particle hydrodynamics simulation of non-Newtonian moulding flow[J]. J. Non-Newtonian Fluid Mech.,2010,165(5-6):219-226.
[66]孙中国,席光,项利峰.不可压缩流动的移动粒子半隐式法数值模拟[J].应用力学学报.2007,24(3)：440-443.
[67]张驰,张雨新,万德成.SPH方法和MPS方法模拟溃坝问题的比较分析.水动力学研究与进展.2011,26(6)：736-746.
[68]M. A. Martinez, E. Cueto, M. Doblare. Natural element meshless simulation of flows involving short fiber suspensions[J]. J. Non-Newtonian Fluid Mech.2003,115(1):51-78.
[69]J.A. Garcia, LI. Gascon, E. Cueto. Meshless methods with application to Liquid Composite Molding simulation[J]. Comput. Methods Appl. Mech. Engrg.2009,198(33-36):2700-2709.
[70]F. Bernal, M. Kindelan. RBF meshless modelling of non-Newtonian Hele-Shaw flow[J]. Engineering Analysis with Boundary Elements.2007,31(10):863-874.
[71]X. K Li, Q. L. Duan, X. H. Han. Adaptive coupled arbitrary Lagrangian-Eulerian finite element and meshfree method for injection molding process[J]. Int. J. Numer. Meth. Engng. 2008,73(8):1153-1180.
[72]S. Yashiro, H. Sasaki, Y. Sakaida. Particle simulation for predicting fiber motion in injection molding of short-fiber-reinforced composites[J]. Composites:Part A.2012,43(10): 1754-1764.
[73]张响,李倩,石凡等.基于SPH方法的微注射成型数值模拟[J].2012,63(1ω：157-162.
[74]张小华,欧阳洁,张林.圆管聚合物热流中黏性耗散分析的无网格模拟[J].化工学报,2007,58(1)：15-20.
[75]杨波,欧阳洁,蒋涛,等.PTT黏弹性流体的光滑粒子动力学方法模拟[J].力学学报,2011,43(4)：667-673.
[76]J. J. Monaghan. Simulating Free Surface Flows with SPH[J]. Journal of Computational Physics,1994,110(2):399-406.
[77]J. J. Monaghan. SPH and Riemann solvers[J]. Journal of Computational Physics,1997, 136(2):298-307.
[78]M. B. Liu, G. R. Liu, K. Y. Lam. Investigations into water mitigation using a meshless particle method[J]. Shock Waves,2002,12(3):181-195。
[79]L. D. Libersky, A. G. Petschek, T. C. Carney, et al. High strain Lagrangian hydrodynamics a three-dimensional SPH code for dynamic material response[J]. J. Comput. Phys,1993, 109(1):67-75。
[80]L. D. Libersky and A. G. Petschek. Smooth particle hydrodynamics with strength of materials, In:Advances in the Free-Lagrange Method[J]. Lecture Notes in Physics,1991,395: 248-257.
[81]P. W. Randles and L. D. Libersky. Smoothed particle hydrodynamics:Some recent improvements and applications[J]. Comput. Methods Appl. Mech. Eng,1996,139(1-4): 375-408.
[82]G. R. Johnson, E. H. Petersen, and R. A. Stryk. Incorporation of an SPH option into EPIC code for a wide range of high velocity impact computations[J]. Int. J. Impact Eng,1993,14 (1-4):385-394.
[83]G. R. Johnson, R. A. Stryk, and S. R. Beissel. SPH for high velocity impact computations. Comput[J]. Methods Appl. Mech. Eng,1996,139(1-4):347-374.
[84]G. R. Johnson and S. R. Beissel.'Normalized smoothing functions for SPH impact computations[J]. Int. J. Numer. Methods Eng,1996,39(16):2725-2741.
[85]S. Potapov, B. Maurel, A. Combescure, et al. Modeling accidental-type fluid-structure interaction problems with the SPH method[J]. Computers and Structures,2009,87(11-12): 721-734.
[86]A. Colagrossi, M. Landrini. Numerical simulation of interfacial flows by smoothed particle hydrodynamic[J]. Journal of Computational Physics.2003,191(2):448-475.
[87]J. J. Monaghan. Smoothed particle hydrodynamics[J]. Annual Review Astronomics and A strophysics,1992,30:543-574.
[88]J. J. Monaghan. Smoothed particle hydrodynamics[J]. Rep. Prog. Phys.2005,68(8): 1703-1759.
[89]张锁春.光滑质点流体动力学(SPH)方法(综述)[J].计算物理,1996,13(4)：385-397
[90]张嘉钟,郑俊,于开平,等.流体力学中SPH算法张力不稳定性研究.工程力学.2010,27(2)：65-72.
[91]郑俊,于开平,魏英杰,等.SPH后处理研究[J].计算物理.2011,28(2)：213-218.
[92]刘富,童明波,陈建平,等.基于SPH方法的三维液体晃动数值模拟[J].南京航空航天大学学报.2010,42(1)：122-126.
[93]王建明,余丰,刘飞宏.SPH和FEM耦合法模拟磨料水射流中单磨粒加速过程[J].山东大学学报(工学版).2011,41(5)：114-120.
[94]任金莲,欧阳洁,蒋涛,等.修正SPH方法在自由表面模拟中的应用[J].计算力学学报.2012,29(1)：69-73.
[95]李大鸣,李晓瑜,林毅.液滴冲击自由液面的SPH法数值模拟[J].中国科学：技术科学.2011,41(8)：1055-1062.
[96]M. Yildiz, R. A. Rook, and A. Suleman. SPH with the multiple boundary tangent method. Int. J. Numer[J]. Meth. Engng 2009; 77(10):1416-1438.
[97]M. S. Shadloo, A. Zainali, Samir H. Sadek.Improved Incompressible Smoothed Particle Hydrodynamics method for simulating flow around bluff bodies[J]. Comput. Methods Appl. Mech. Engrg.2011,200(9-12):1008-1020.
[98]R. Fatehi, M. T. Manzari. A consistent and fast weakly compressible smoothed particle hydrodynamics with a new wall boundary condition[J]. Int. J. Numer. Meth. Fluids 2012; 68:905-921.
[99]C. X. Liang, C. Y. Zhang, H. Y. Liu, et al. Modeling low Reynolds number incompressible flows with curved boundaries using SPH[J]. Int. J. Numer. Meth. Fluids.2012,68(9): 1173-1188.
[100]A. Colagrossi, B. Bouscasse, M. Antuono, etal. Particle packing algorithm for SPH schemes[J]. Computer Physics Communications.2012,183(8):1641-1653.
[101]S. D. Shao. Incompressible smoothed particle hydrodynamics simulation of multifluid flows[J]. Int. J. Numer. Meth. Fluids.2012,69(11):1715-1735.
[102]M. S. Shadloo and M. Yildiz. Numerical modeling of Kelvin-Helmholtz instability using smoothed particle hydrodynamics[J]. Int. J. Numer. Meth. Engng.2011,87(10): 988-1006.
[103]Y. Z. Yan, L. Li, K. Sezer, etal. CO2 laser underwater machining of deep cavities in alumina[J]. Journal of the European Ceramic Society.2011,31(15):2793-2807.
[104]H. Takamiya, H. Okada, Y. Sakai, etal. Smoothed particle hydrodynamics analysis on semi-solid metal forming process[J]. Japan J. Indust. Appl. Math.2011,28(1):183-203.
[105]J. N. Fang, A. Parriaux, M. Rentschler, et al. Improved SPH methods for simulating free surface flows of viscous fluids[J]. Applied Numerical Mathematics,2009.59(2): 251-271
[106]J. J. Monaghan. SPH without a tensile instability[J]. Journal of Computational Physics, 2000,159(2):290-311.
[107]X. Y. Hu, N. A. Adams. A constant-density approach for incompressible multi-phase SPH[J]. Journal of Computational Physics,2009.228(6):2082-2091.
[108]J. Bonet, T-S L. Lok. Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulations[J]. Comput. Methods Appl. Mech. Engrg,1999,180(1-2): 97-115
[109]T. Belytschko, Y. Krongauz, J. Dolbow, et al. On the completeness of the meshfree particle[J]. International Journal for Numerical Methods in Engineering,1998,43(5): 785-819.
[110]W. K. Liu, S. Jun, Y. F. Zhang. Reproducing kernel particle methods[J]. Int. J. Numer. Meth. Fluids.1995,20(8-9):1081-1106.
[111]W. K. Liu, S. Jun, S. F. Li, et al. Reproducing kernel particle methods for structural dynamics[J]. Int. J. Numer. Methods Engrg.1995,38(10):1655-1679.
[112]S. H. Lee, H. J. Kim, S. Jun. Two scale meshfree method for the adaptivity of 3D stress concentration problems[J]. Comput. Mech.2000,26(4):376-387.
[113]J. S. Chen, C. Pan, C. T. Wu, et al. Reproducing kernel particle methods for large deformation analysis of non-linear structures[J]. Comput. Methods Appl. Mech. Engrg. 1996,139(1-4):195-227.
[114]S. F. Li, W. Hao, W. K. Liu. Meshfree simulations of shear banding in large deformation[J]. International Journal of Solid and Structures,2000,37(48-50): 7185-7206.
[115]J. K. Chen, J. E. Beraun. A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems[J]. Comput. Methods Appl. Mech. Engrg,2000,190(1-2): 225-239.
[116]J. K. Chen, J. E. Beraun, and C. J. Jih. An improvement for tensile instability in smoothed particle hydrodynamics[J]. Computational Mech,1999,23(4):279-287.
[117]J. K. Chen, J. E. Beraun, and C. J. Jih. A corrective smoothed particle method for boundary value problems in heat conduction[J]. International Journal for Numerical Methods in Engineering,1999,46(2):231-252.
[118]J. K. Chen, J. E. Beraun, and C. J. Jih. Completeness of corrective smoothed particle method for linear elastodynamics[J]. Computational Mechanics,1999,24(4):273-285.
[119]G. M. Zhang, R. C. Batra. Modified smoothed particle hydrodynamics method and its application to transient problems[J]. Computational Mechanics,2004,34(2):137-146.
[120]M. B. Liu, W. P. Xie, G. R. Liu. Modeling incompressible flows using a finite particle method[J]. Applied Mathematical Modelling,2005,29(12):1252-1270.
[121]P. Lancaster and K. Salkauskas. Surface generated by moving least squares methods[J]. Mathe Comp,1981,37(155):141-158.
[122]G. A. Dilts. Moving least-square particle hydrodynamics Ⅰ:Consistency and stability[J]. Int. J. Numer. Methods Eng,1999,44(8):1115-1155.
[123]G. A. Dilts. Moving least-square particle hydrodynamics Ⅱ:Conservation and boundaries[J]. Int. J. Numer. Methods Eng,2000,48(10):1503-1524.
[124]G. A. Dilts. Some recent developments for moving least squares particle methods[C]. Proceedings on Computational Fluid and Solid Mechanics, Cambridge MA,2001:1-5.
[125]S. J. Cummins, M. Rudman. An SPH projection method[J]. Journal of Computational Physics.1999,152(2):584-607.
[126]E. S. Lee, C. Moulinec, R. Xu, et al. Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method[J]. Journal of Computational Physics,2008,227(18):8417-8436.
[127]A. Khayyer, H. Gotoh, S. D. Shao. Enhanced predictions of wave impact pressure by improved incompressible SPH methods[M]. Applied Ocean Research,2009,31(2): 111-131.
[128]R. Xu, P. Stansby, D. Laurence. Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach[J]. Journal of Computational Physics, 2009,228(18):6703-6725
[129]J. P. Hughes, D. I. Graham. Comparison of incompressible and weakly-compressible SPH models for free-surface water flows[J]. Journal of Hydraulic Research.2010,48, s(1):105-117.
[130]K.Szewc, J. Pozorski and J. P. Minier. Analysis of the incompressibility constraint in the smoothed particle hydrodynamics method[J]. Int. J. Numer. Meth. Engng.2012,92(4): 343-369.
[131]A. Rafiee, S. Cummins, M. Rudman, etal. Comparative study on the accuracy and stability of SPH schemes in simulating energetic free-surface flows[J]. European Journal of Mechanics B/Fluids.2012,36:1-16.
[132]M. S. Shadloo, A. Zainali, M. Yildiz, et al. A robust weakly compressible SPH method and its comparison with an incompressible SPH[J]. Int. J. Numer. Meth. Engng.2012, 89(8):939-956.
[133]J. J Monaghan. Particle methods for hydrodynamics[J]. Computer Physics Report,1985, 3(2):71-124.
[134]J. P. Morris. A study of the stability properties of smooth particle hydrodynamics[J]. Publ.Astron.Soc.Aust,1996,13(1):97-102.
[135]D. A. Fulk. A numerical analysis of smoothed particle hydrodynamics[D]. Air Force Institute of Technology,1994.
[136]H. Takeda, S. M. Miyama, M. Sekiya. Numerical simulation of viscous flow by smoothed particle hydrodynamics[J]. Progress of Theoretical Physics,1994,92(5):939-960.
[137]L. Brookshaw. A method of calculating radiative heat diffusion in particle simulations[C]. Proceedings of the Astronomical Society of Australia,1985,6(2):207-210.
[138]O. Flebbe, S. Munzel, H. Herold, et al. Smoothed particle hydrodynamics-physical viscosity and the simulation of accretion disks[J]. The Astrophysical Journal,1994, 431(2):754-760.
[139]J. P. Morris, P. J. Fox, Y. Zhu. Modeling low reynolds number incompressible flows using SPH[J]. Journal of Computational Physics,1997,136(1):214-226.
[140]D. J. Price. Magnetic fields in astrophysics[D]. Institute of Astronomy & Churchill College University of Cambridge.2004.
[141]M. Jubelgas, V. Springel and K. Dolag. Thermal conduction in cosmological SPH simulation[J]. Mon.Not. R. Astron. Soc,2004,351(2):423-435.
[142]P. W. Cleary and J. J. Monaghan. Conduction modelling using smoothed particle hydrodynamics[J]. Journal of Computational Physics,1999,148(1):227-264.
[143]P. Espanol and M. Revenga. Smoothed dissipative particle dynamics[J]. Phys. Rev. E, 2003,67(2):026705.
[144]S. D. Shao, Y. M. Lo. Edmond. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface[J]. Advances in Water Resources,2003, 26(7):787-800.
[145]J. J. Monaghan. On the problem of penetration in particle methods[J]. Journal of Computational Physics,1989,82(1):1-15.
[146]M. B. Liu, G. R. Liu, K. Y. Lam. Constructing smoothing functions in smoothed particle hydrodynamics with applications[J]. Journal of Computational and Applied Mathematics, 2003,155(2):263-284.
[147]T. Belytschko, Y. Krongauz, D. Organ, et al. Meshless methods:An overview and recent developments[J]. Computer Methods in Applied Mechanics and Engineering,1996, 139(1-4):3-47.
[148]D. S. Balsara. Von Neumann stability analysis of smoothed particle hydrodynamics suggestions for optimal algorithms[J]. Journal of Computational Physics,1995,121(2): 357-372.
[149]J. W. Swegle, D. L. Hicks, and S. W. Attaway. Smoothed Particle Hydrodynamics stability analysis[J]. Journal of Computational Physics.1995,116(1):123-134.
[150]C. Guenther, D. L. Hicks, J.W. Swegle. Conservative smoothing versus artificial viscosity[R]. SANDIA REPORT, SAND94-1853 UC-705,1994.
[151]R. Vignjevic. Review of development of the SPH method predictive modeling of dynamic processes[M]. US:Springer,2009,367-396.
[152]C. T. Dyka. R. P. Inge. Addressing tension instability in SPH Methods[R]. Technical Report NRL/MR/6384. NRL,1994.
[153]C. T. Dyka. R. P. Inge. An approach for tension instability in smoothed particle hydrodynamics (SPH) [J]. Computers & Structures,1995.57(4):573-580.
[154]S. F. Li. W. K. Liu. Meshfree and particle methods and their applications[J]. Appl Mech Rev.2002.55(1):1-34.
[155]P. W. Randles, L. D. Libersky. Normalized SPH with stress points[J]. International Journal for Numerical Methods in Engineering,2000,48(10):1445-1462
[156]W. K. Liu, J. Adee, and S. Jun. Reproducing kernel and wavelets particle methods for elastic and plastic problems[J]. Advanced Computational Methods for Material Modeling. New Orleans:ASME,1993,175-190.
[157]W. K. Liu and O. C. Brandenburg. Reproducing kernel and wavelets particle methods[J]. Aerospace Structures:Nonlinear Dynamics and System Response,1993:39-56.
[158]W. K. Liu, S. Jun, S. Li, et al. Reproducing kernel particle methods for structural dynamics[J]. Int. J. Numer. Methods Eng,1995,38 (10):1655-1679.
[159]W. K. Liu, Y. Chen, C. T. Chang, et al. Advances in multiple scale kernel particle methods[J]. Computational Mech,1996,18(2):73-111.
[160]W. K. Liu, Y. Chen, S. Jun, et al. Overview and applications of the reproducing kernel particle methods[J]. Arch. Comput. Mech. Eng.:State of Rev,1996,3(1):3-80.
[161]W. K. Liu, S. Li, and T. Belytschko. Moving least square reproducing kernel method Part I:Methodology and convergence[J]. Comput. Methods Appl. Mech. Eng,1997,143(1-2): 422-453
[162]X. Y. Hu, N. A. Adams. An incompressible multi-phase SPH method[J]. Journal of Computational Physics,2007,227(1):264-278.
[163]A. J. Chorin. Numerical solution of the Navier-Stokes equations[J]. Math. Comp,1968, 22:745-762.
[164]H. A. Van Der Vorst. Bi-CGSTAB:A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems[J]. S.J. Sci. Stat. Comput,1992.13(2): 631-644.
[165]J. P. Hughes, D. I. Graham. Degradation and instability of incompressible SPH computations of simple viscous flows[C]. Proceedings of the Workshop "SPHERIC-Smoothed Particle Hydrodynamics European Research Interest Community" Madrid,2007.
[166]Y. Saad. Iterative methods for sparse linear system[M]. Boston:PWS Pub. Co.,2000.
[167]M. Benzi. Preconditioning techniques for large linear systems:a survey[J]. Journal of Computational Physics,2002,182(2):418-477.
[168]J. J. Monaghan, A. Kos. Solitary waves on a cretan beach[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering,1999,125(3):145-154.
[169]J. J. Monaghan, A. Kos and N. Issa. Fluid motion generated by impact[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering,2003,129(6):250-260.
[170]J. J. Monaghan, J. B. Kajtar. SPH particle boundary forces for arbitrary boundaries[J]. Computer Physics Communications,2009,180(10):1811-1820.
[171]G. Oger, M. Doring, B. Alessandrini, et al. Two-dimensional SPH simulations of wedge water entries[J]. Journal of Computational Physics,2006,213(2):803-822.
[172]S. Koshizuka, A. Nobe, Y. Oka. Numerical analysis of breaking waves using the moving particle semi-implicit method[J]. International Journal for Numerical Methods in Fluids, 1998,26(7):751-769.
[173]R. Dalrymple. and O. Knio. SPH modelling of waves[C]. In ASCE, editor, Proc. Coastal Dynamics, Lund, Sweden,2001:779-787.
[174]A. J. C. Crespo. Application of the smoothed particle hydrodynamics model SPHysics to free-surface hydrodynamics[D]. UNIVERSIDADE DE VIGO,2008.
[175]J. J. Monaghan. Smoothed particle hydrodynamic simulations of shear flow[J]. Monthly Notices of the Royal Astronomical Society,2006,365(1):199-213.
[176]D. Molteni, A. Colagrossi. A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH[J]. Computer Physics Communications,2009, 180(6):861-872.
[177]Marco Ellero, Martin Kroger, Siegfried Hess. Viscoelastic flows studied by smoothed particle dynamics[J]. J. Non-Newtonian Fluid Mech.2002,105(1):35-51.
[178]Y. P. Chui, P. A. Heng. A meshless rheological model for blood-vessel interaction in endovascular simulation[J]. Progress in Biophysics and Molecular Biology,2010, 103(2-3):252-261.
[179]H. N. Zhu, S. N. Martysa, C. Ferraris, et al. A numerical study of the flow of Bingham-like fluids in two-dimensional vane and cylinder rheometers using a smoothed particle hydrodynamics (SPH) based method[J]. J. Non-Newtonian Fluid Mech.2010, 165(7-8):362-375.
[180]孙洪全,韩纪庆.基于粒子的非牛顿流体模拟统一模型[J].哈尔滨工业大学学报,2010,42(7)：1104-1107.
[181]T. Jiang, J. Ouyang, L. Zhang, et al. The SPH approach to the process of container filling based on non-linear constitutive models[J]. Acta Mech. Sin, (2012),28(2):407-418.
[182]J. M. Buick. Lattice Boltzmann simulation of power-law fluid flow in the mixing section of a single-screw extruder[J]. Chemical Engineering Science,2009,64(1):52-58.
[183]A. R. Chell, J. M. Ottino. Fluid mechanics of mixing in a single-screw extruder[J]. Ind. Eng. Chem. Fundam.,1985,24(2):170-180.
[184]M. Vakilha, T. M. Manzari. Modelling of power-law fluid flow through porous media using smoothed particle hydrodynamics[J]. Transp Porous Med,2008,74(3):331-346.
[185]李凌丰,刘际轩,茅旭飞.螺杆加工塑料时熔体流动的数值模拟[J].机械工程学报,2011,47(24)：50-56.