介观尺度两相流动的数值方法与机理研究
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摘要
介观尺度通道内的多相流动涉及复杂的动力学特性，仅靠理论简化分析、实验半经验的方法以及引入许多经验关系式的数值模拟方法，很难准确描述该复杂流动中的颗粒受力、动量能量的相间传递、相间分界面的变化，影响人们对该流动真实机理的理解和掌握。
本文基于任意拉格朗日－欧拉（ALE）方法模拟惰性颗粒两相流动，采用有限元方法数值求解流场的N-S方程，并增加联立求解能量方程，应用牛顿定律追踪颗粒运动，并通过积分颗粒表面的粘性应力和压力获得颗粒的受力，从而实现了对颗粒两相流运动的真正直接数值模拟。通过Delaunay－Voronoi法生成非结构化的三角形单元网格，颗粒移动时，通过求解Laplace方程得到网格移动速度，当单元网格严重变形时网格将重新划分，以确保网格质量。控制方程通过Galerkin法离散，流体与颗粒动量方程通过推导生成一种弱解形式，这样颗粒和流体间相互作用的力和扭矩就不必专门加以计算。颗粒位置的更新将由其速度决定，时间步长由颗粒的速度和加速度来自动调整，方程的非线性部分由牛顿迭代求解，线性部分由GMRES算法来求解。用该方法模拟颗粒的沉降及颗粒溶解引起的相变及相间分界面的形状变化，在介观尺寸上阐明该复杂流动中颗粒的运动规律、相间分界面的移动变形、颗粒相相互作用形成的结构以及传热和流动的相互作用机制，得到颗粒两相流的一些新特征。通过以上方法的研究得到了以下主要结论：
（1）热对流引起了流场流动的变化和不对称，颗粒在热流体中沉降，热对流产生的力加速了冷颗粒的运动，尾部形成了涡脱落；颗粒在冷流体中沉降，热对流产生的力阻碍了冷颗粒的运动，尾部形成了羽流；颗粒溶解引起的颗粒表面形态的变化引起了颗粒的横向摆动，并使颗粒沉降速度发生了变化。
（2）双颗粒在等温流体中，经历了拖曳、亲和、翻滚后，最终分别在一侧通道壁附近稳定沉降；双颗粒在热流体中沉降，热对流引起了颗粒沉降时的水平方向的摆动，出现了周期的拖曳、亲和、翻滚现象，且颗粒趋于分散；双颗粒在冷流体中沉降，热对流使颗粒的沉降保持稳定，未出现拖曳、亲和、翻滚现象，且颗粒趋于聚集；与等温条件下颗粒沉降相比，溶解双颗粒沉降时，颗粒运动轨迹、颗粒间的相互作用除与颗粒质量相关外，还与对流引起的颗粒尾迹、涡的脱落有关。
（3）椭圆颗粒在等温流体中沉降，当椭圆长轴与x坐标轴垂直时，椭圆颗粒要发生旋转，运动行为的变化和摆动；椭圆颗粒在热流体中沉降，颗粒最终以通道中心线为平衡位置在水平方向上周期性摆动；热颗粒在冷流体中沉降，椭圆颗粒在一侧通道壁发生周期性摆动，沉降速度及角速度也出现周期性变化。
另外，基于连续力学的网格方法通常很难捕捉边界滑移、热扰动等的影响，也难以适用于含多尺度特性的各种问题，而分子动力学时间及空间尺度通常局限于纳秒和纳米级。有鉴于此，本文基于无网格粒子耗散粒子动力学方法(dissipativeparticle dynamics, DPD)，采用四次方光滑函数构造了远程排斥近距吸引的保守力势函数，对液气两相流动进行了模拟。并完善了DPD方法中的运动颗粒受力、扭矩计算方法、运动控制方程、DPD参数，对固液两相流动进行了计算，阐明DPD方法在介观尺度上研究颗粒两相流动的可行性。
对Y型通道内的流动过程，通过调整流固粒子间作用力系数比a_w/ a_f、粒子注入速率、驱动外力等因素，模拟分析了流体在表面张力、重力以及流体与固壁相互作用下的流动过程及流动模式。研究了流动过程形成的不同的多相系统界面和接触线动力学特征。对流体绕流三维球体进行了耗散粒子动力学计算，并与经典关联式进行了对比验证。研究表明，在一定雷诺数范围内，DPD方法能准确的计算出阻力系数，在较大雷诺数时，由于流体的动力学参数及流体压缩性导致计算结果出现差异。低雷诺数时的颗粒沉降计算结果与直接数值模拟结果一致，表明DPD方法对颗粒两相流动的研究具有可行性。
Multiphase flows in meso-scale channels involve complicated dynamic behaviors.Analytical theories with simplified assumptions and experimental observations withsemi-empirical empirical formula are usually difficult to portray the forces acting onparticles, the energy and momentum transfer of the fluid-solid system and the changesof interphase boundary. Therefore they significantly influence the understanding theinherent true mechanism of meso-scale multiphase flows.
Based on the study of isothermal inertial particle sedimentation, we use afinite-element method to solve the initial value problem for the sedimentation ofparticles in a vertical channel. The algorithm is based on an Arbitrary Lagrangian-Eulerian technique(ALE). The fluid motion is computed from the conservation laws.Momentum balance are governed by the Navier-Stokes(N-S) equations, while theenergy conservation is controled by a convection-diffusion equation, in which thenatural convection is taken into account through thermal expansion. Particles moveaccording to the equations of motion of a rigid body under gravity and hydrodynamicforces arising from the motion of the fluid. An unstructured mesh of triangularelements is generated by the Delaunay-Voronoi method. As a particle moves, the meshalso moves and deforms according to a mesh velocity which is determined by aLaplace equation. When the elements become severely distorted, a re-mesh procedureis carried out to restore mesh quality. The equations are discretized using Galerkinformulation. The solid and fluid momentum equations are combined into one weakform. In this way, the forces and torques acting on the particles are balanced, and thereis no need to compute the forces and torques explicitly. The positions of the particlesare updated according to their velocities, and the time step is automatically adjustedaccording to their velocities and accelerations. The nonlinear part of the governingequation is solved by Newton iteration and the linear parts are solved using thepreconditioned GMRES algorithm. This paper aims to simulate the sedimentation andthe interphase deformation by melting, to investigate forces, trajectory, and to abtainflow field of one or more particles, obtain mechanism of particle-particle interaction with different structures and flow patterns. The main conclusions are as follows:
(1) Thermal convection induces asymmetric of the flow field. For cold particles,downward thermal convection accelerates up the sedimentation, The vortex sheddingalso contributes to the movement style of the particles; During the sedimentation of hotparticle in the cold fluid, the warm wake forms a strong upward thermal plume, the hotlayer of fluid next to the particles carry upward momentum, therefore, the hot particleshave smaller vertical velocities, lateral and angular velocity; The interface deformationof melting particles makes the particle oscillate and change the sedimentation velocity.
(2) The drafting, kissing and tumbling (DKT) scenario is found during thesedimentation of two isothermal particles. The two particles will settle steadily near thewall finally. For the sedimentation of two cold particles settling, periodic DKTscenario appears and the cold particles tend to disperse; The drafting, kissing andtumbling scenario was not found in the sedimentation of two hot particles and hotparticles tend to aggregate; Compared with isothermal sedimentation, the vortexshedding, mass losing by melting and morphology change the sedimentation velocityand trajectory.
(3) The isothermal elliptical particle rotates from parallel to vertical to the x-axisduring the process, and displays weak and somewhat irregular lateral oscillations aboutthe centerline. Elliptical particle in hot fluid develops a regular lateral oscillation alongthe centerline finally. The elliptical particle in cold fluid moves away from centerline,and then develops a regular lateral oscillation about an off-center equilibrium positionwith a periodic velocity and angular velocity.
Besides, Grid-based numerical methods within the frame of continuum mechanicsare usually difficult in capturing inherent flow physics such as boundary slip andthermal disturbance. They are also not valid to problems with multiple scale physics.In contrast, molecular dynamics (MD) is practical only on extremely small time scales(nanoseconds) and length scales (nanometers) even if the most advancedhigh-performance computers are used. In this paper, a modified dissipative particledynamics is used, which employs an interaction potential with short-range repulsion and long-distance attraction, and enables the simulation of multiphase fluid flowprocesses. Further more, we studied and improved numerical techniques to calculateforce and torque on solid particles and the governing equation of motion as well as therelated parameters. The sedimentation of a particle is later investigated with DPDmethod, In this way, we demonstrated the effectiveness of the DPD method inmodeling particle-fluid two-phase systems.
The multiphase flow through a Y shape mesoscopic channel is simulated bydissipative particle dynamics with this new potential function with differenta_w/a_f afratios of interaction strength coefficients of fluid-fluid and fluid-wall particles,rate of particles injection, external force. The results show that the new method iscapable of simulating the flow process and flow pattern. The flow past athree-dimensional sphere within two parallel plates is also studied with comparisons toclassical results. The results show that the DPD method can predict drag coefficientaccurately while Re is less than 100. When Re is bigger than 100, the results deviatefrom analytical values, mainly due to the fluid compressibility. The sedimentation of asolid sphere ball is studied and compared with the result of DNS, The results show thatit is feasible to simulate particle-fluid two-phase systems using DPD method.
本文基于任意拉格朗日－欧拉（ALE）方法模拟惰性颗粒两相流动，采用有限元方法数值求解流场的N-S方程，并增加联立求解能量方程，应用牛顿定律追踪颗粒运动，并通过积分颗粒表面的粘性应力和压力获得颗粒的受力，从而实现了对颗粒两相流运动的真正直接数值模拟。通过Delaunay－Voronoi法生成非结构化的三角形单元网格，颗粒移动时，通过求解Laplace方程得到网格移动速度，当单元网格严重变形时网格将重新划分，以确保网格质量。控制方程通过Galerkin法离散，流体与颗粒动量方程通过推导生成一种弱解形式，这样颗粒和流体间相互作用的力和扭矩就不必专门加以计算。颗粒位置的更新将由其速度决定，时间步长由颗粒的速度和加速度来自动调整，方程的非线性部分由牛顿迭代求解，线性部分由GMRES算法来求解。用该方法模拟颗粒的沉降及颗粒溶解引起的相变及相间分界面的形状变化，在介观尺寸上阐明该复杂流动中颗粒的运动规律、相间分界面的移动变形、颗粒相相互作用形成的结构以及传热和流动的相互作用机制，得到颗粒两相流的一些新特征。通过以上方法的研究得到了以下主要结论：
（1）热对流引起了流场流动的变化和不对称，颗粒在热流体中沉降，热对流产生的力加速了冷颗粒的运动，尾部形成了涡脱落；颗粒在冷流体中沉降，热对流产生的力阻碍了冷颗粒的运动，尾部形成了羽流；颗粒溶解引起的颗粒表面形态的变化引起了颗粒的横向摆动，并使颗粒沉降速度发生了变化。
（2）双颗粒在等温流体中，经历了拖曳、亲和、翻滚后，最终分别在一侧通道壁附近稳定沉降；双颗粒在热流体中沉降，热对流引起了颗粒沉降时的水平方向的摆动，出现了周期的拖曳、亲和、翻滚现象，且颗粒趋于分散；双颗粒在冷流体中沉降，热对流使颗粒的沉降保持稳定，未出现拖曳、亲和、翻滚现象，且颗粒趋于聚集；与等温条件下颗粒沉降相比，溶解双颗粒沉降时，颗粒运动轨迹、颗粒间的相互作用除与颗粒质量相关外，还与对流引起的颗粒尾迹、涡的脱落有关。
（3）椭圆颗粒在等温流体中沉降，当椭圆长轴与x坐标轴垂直时，椭圆颗粒要发生旋转，运动行为的变化和摆动；椭圆颗粒在热流体中沉降，颗粒最终以通道中心线为平衡位置在水平方向上周期性摆动；热颗粒在冷流体中沉降，椭圆颗粒在一侧通道壁发生周期性摆动，沉降速度及角速度也出现周期性变化。
另外，基于连续力学的网格方法通常很难捕捉边界滑移、热扰动等的影响，也难以适用于含多尺度特性的各种问题，而分子动力学时间及空间尺度通常局限于纳秒和纳米级。有鉴于此，本文基于无网格粒子耗散粒子动力学方法(dissipativeparticle dynamics, DPD)，采用四次方光滑函数构造了远程排斥近距吸引的保守力势函数，对液气两相流动进行了模拟。并完善了DPD方法中的运动颗粒受力、扭矩计算方法、运动控制方程、DPD参数，对固液两相流动进行了计算，阐明DPD方法在介观尺度上研究颗粒两相流动的可行性。
对Y型通道内的流动过程，通过调整流固粒子间作用力系数比a_w/ a_f、粒子注入速率、驱动外力等因素，模拟分析了流体在表面张力、重力以及流体与固壁相互作用下的流动过程及流动模式。研究了流动过程形成的不同的多相系统界面和接触线动力学特征。对流体绕流三维球体进行了耗散粒子动力学计算，并与经典关联式进行了对比验证。研究表明，在一定雷诺数范围内，DPD方法能准确的计算出阻力系数，在较大雷诺数时，由于流体的动力学参数及流体压缩性导致计算结果出现差异。低雷诺数时的颗粒沉降计算结果与直接数值模拟结果一致，表明DPD方法对颗粒两相流动的研究具有可行性。
Multiphase flows in meso-scale channels involve complicated dynamic behaviors.Analytical theories with simplified assumptions and experimental observations withsemi-empirical empirical formula are usually difficult to portray the forces acting onparticles, the energy and momentum transfer of the fluid-solid system and the changesof interphase boundary. Therefore they significantly influence the understanding theinherent true mechanism of meso-scale multiphase flows.
Based on the study of isothermal inertial particle sedimentation, we use afinite-element method to solve the initial value problem for the sedimentation ofparticles in a vertical channel. The algorithm is based on an Arbitrary Lagrangian-Eulerian technique(ALE). The fluid motion is computed from the conservation laws.Momentum balance are governed by the Navier-Stokes(N-S) equations, while theenergy conservation is controled by a convection-diffusion equation, in which thenatural convection is taken into account through thermal expansion. Particles moveaccording to the equations of motion of a rigid body under gravity and hydrodynamicforces arising from the motion of the fluid. An unstructured mesh of triangularelements is generated by the Delaunay-Voronoi method. As a particle moves, the meshalso moves and deforms according to a mesh velocity which is determined by aLaplace equation. When the elements become severely distorted, a re-mesh procedureis carried out to restore mesh quality. The equations are discretized using Galerkinformulation. The solid and fluid momentum equations are combined into one weakform. In this way, the forces and torques acting on the particles are balanced, and thereis no need to compute the forces and torques explicitly. The positions of the particlesare updated according to their velocities, and the time step is automatically adjustedaccording to their velocities and accelerations. The nonlinear part of the governingequation is solved by Newton iteration and the linear parts are solved using thepreconditioned GMRES algorithm. This paper aims to simulate the sedimentation andthe interphase deformation by melting, to investigate forces, trajectory, and to abtainflow field of one or more particles, obtain mechanism of particle-particle interaction with different structures and flow patterns. The main conclusions are as follows:
(1) Thermal convection induces asymmetric of the flow field. For cold particles,downward thermal convection accelerates up the sedimentation, The vortex sheddingalso contributes to the movement style of the particles; During the sedimentation of hotparticle in the cold fluid, the warm wake forms a strong upward thermal plume, the hotlayer of fluid next to the particles carry upward momentum, therefore, the hot particleshave smaller vertical velocities, lateral and angular velocity; The interface deformationof melting particles makes the particle oscillate and change the sedimentation velocity.
(2) The drafting, kissing and tumbling (DKT) scenario is found during thesedimentation of two isothermal particles. The two particles will settle steadily near thewall finally. For the sedimentation of two cold particles settling, periodic DKTscenario appears and the cold particles tend to disperse; The drafting, kissing andtumbling scenario was not found in the sedimentation of two hot particles and hotparticles tend to aggregate; Compared with isothermal sedimentation, the vortexshedding, mass losing by melting and morphology change the sedimentation velocityand trajectory.
(3) The isothermal elliptical particle rotates from parallel to vertical to the x-axisduring the process, and displays weak and somewhat irregular lateral oscillations aboutthe centerline. Elliptical particle in hot fluid develops a regular lateral oscillation alongthe centerline finally. The elliptical particle in cold fluid moves away from centerline,and then develops a regular lateral oscillation about an off-center equilibrium positionwith a periodic velocity and angular velocity.
Besides, Grid-based numerical methods within the frame of continuum mechanicsare usually difficult in capturing inherent flow physics such as boundary slip andthermal disturbance. They are also not valid to problems with multiple scale physics.In contrast, molecular dynamics (MD) is practical only on extremely small time scales(nanoseconds) and length scales (nanometers) even if the most advancedhigh-performance computers are used. In this paper, a modified dissipative particledynamics is used, which employs an interaction potential with short-range repulsion and long-distance attraction, and enables the simulation of multiphase fluid flowprocesses. Further more, we studied and improved numerical techniques to calculateforce and torque on solid particles and the governing equation of motion as well as therelated parameters. The sedimentation of a particle is later investigated with DPDmethod, In this way, we demonstrated the effectiveness of the DPD method inmodeling particle-fluid two-phase systems.
The multiphase flow through a Y shape mesoscopic channel is simulated bydissipative particle dynamics with this new potential function with differenta_w/a_f afratios of interaction strength coefficients of fluid-fluid and fluid-wall particles,rate of particles injection, external force. The results show that the new method iscapable of simulating the flow process and flow pattern. The flow past athree-dimensional sphere within two parallel plates is also studied with comparisons toclassical results. The results show that the DPD method can predict drag coefficientaccurately while Re is less than 100. When Re is bigger than 100, the results deviatefrom analytical values, mainly due to the fluid compressibility. The sedimentation of asolid sphere ball is studied and compared with the result of DNS, The results show thatit is feasible to simulate particle-fluid two-phase systems using DPD method.
引文
[1]Gary S S.流体力学与国土安全.力学进展. 2007, 37(4):614-627
[2]Furton K G, Myers L J. The scientific foundation and efficacy of the use of canines aschemical detectors for explosives. Talanta. 2001, 54(3): 487-500
[3]Henderson D A. The threat of aerosolized biological weapons. ASHRAE J. 2004,46(12):50-53
[4]陈耀松,单肖文,陈沪东.计算流体力学的新方向及其在工业上的应用.中国科学E辑：技术科学. 2007, 37(9):1107-1116
[5]Edge B A, Paterson E G, Settles G S. Computational study of the wake and contaminanttransport of a walking human. J Fluids Eng. 2005, 127: 967-977
[6]Brook D R, Beck N V, Clem C V. Validation of the urban dispersion model. 8thInt. Conf.on harmonisation within atmospheric dispersion modeling for regulatory purposes. 2003, 8-12
[7]方震华,黄慧锋.微电子机械系统（MEMS）技术在军用设备中的应用现状.电子机械工程. 2010,26(4):1-4
[8]Laser D J, Santiago J G. A review of micropumps. J Micromech Microeng. 2004, 14(6):35-64
[9]李战华,崔海航.微尺度流动特性.机械强度. 2001, 23(4): 476-480
[10]张颖,王蔚,田丽等.微流动的尺寸效应. MEMS器件与技术. 2008, 45(1): 33-37
[11]Kampen N G van. Stochastic processes in physics and chemistry. North Holland,Amsterdam, 1981: 57-460
[12]Liu G R, Liu M B. Smoothed particle hydrodynamics–a meshfree particle method.Singapore, World Scientific,2003: 35-58
[13]Liu M B and Liu G R. Restoring particle inconsistency in smoothed particlehydrodynamics. Appl Numer Math. 2006,56:19-36
[14]Liu M B, Liu G R. Meshfree particle simulation of micro channel flows with surfacetension. Comput Mech. 2005, 35:332-341
[15]刘谋斌,常建忠.光滑粒子动力学方法中粒子分布与数值稳定性分析.物理学报.2010, 59(6): 3654-3662
[16]刘谋斌,宗智,常建忠.光滑粒子动力学方法的发展与应用.力学进展. 2011, 41(2):217-234
[17]Mcnamara G R, Zanettic G. Use of the lattice Boltzmann euqation to simulate lattice - gasautomata. Phys Rev Lett.1988, 61: 2332-2335
[18]Bhatnagar P L, Gross E P, Krook M. A model for collision processes in gases.Ⅰ: smallamplitude processes in charged and neutral one-component system. Phys Rev. 1954, 94:511-525
[19]王兴勇,索丽生,程永光,刘德有.双重网格的Lattice Boltzmann方法.河海大学学报（自然科学版）. 2003, 31(1): 5-10
[20]Bird G A. Approach to translational equilibrium in a rigid sphere gas. Phys Fluids. 1963,6(10): 1518-1519
[21]周力行.离散型湍流多相流动的研究进展和需求.力学进展.2008, 38(5):610-620
[22]Liu M B, Meakin P, Huang H. Dissipative particle dynamics simulation of fluid motionthrough an unsaturated fracture and fracture function. J Comput Phys. 2007, 222, 110-130
[23]Liu M B, Paul M, Hai H. Dissipative particle dynamics with attractive and repulsiveparticle-particle interaction. Phys Fluids. 2006, 18: 017101
[24]Nicos S M. Velocity verlet algorithm for dissipative- particle - dynamics - based modelsof suspensions. Phys Rev E. 59(3): 3733-3736
[25]Yu Z S , Shao X M, Wachs A . A fictitious domain method for particulate flows with heattransfer. J Comput Phys., 2006, 217:424-451
[26]Choi H M , Kurihara T , Monji H , Matsui G. Measurement of particle/bubble motion andturbulence around it by hyrid PIV. Flow Meas Instrum. 2002, 12: 421-428
[27]Gidaspow D. Multiphase flow and fluidization: Continuum and kinetic theory description.New York : Academic Press, 1994: 6- 100
[28]伊杰里奇克N E .水力摩阻手册.北京,航空发动机编辑部.1985, 256-300
[29]Acrivos A, Taylor T D. Heat and mass transfer from single spheres in Stokes flow. PhysFluids. 1962. 5:387-394
[30]Levich V G.. Physicochemical Hydrodynamics. New Jersey, Prentice-Hall. 1962: 16-100
[31]Shah N, Reed X B. Reaction-enhanced convective diffusion of a reacting species from asphere to a fluid in viscous axisymmetric straining flow. ASP/DFD Annual Meeting,Philadelphia, November 1998, FL.09.
[32]Sadhal S S, Ayyaswamy P S, Chung J N. Transport Phenomena with Drops and Bubbles.German, Springer. 1997: 12-200
[33]Jog M A, Ayyaswamy P S, Cohen I.M. Evaporation and combustion of a slowly movingliquid fuel drplet: high-order theory. J Fluid Mech.1996. 307:135-165
[34]Dwyer H A, Sanders B R. A detailed study of burning fuel droplets. Proc. 21stSymp.(Int’l) on Combustion. Pittsburgh, The Combustion Institute, 1986, 633-639 1986
[35]McLeod P, Riley D S, Sparks R S J. Melting of a sphere in hot fluid. J Fluid Mech. 1996,327: 303-409
[36]Shigeo A, Hideo I. Melting Characteristics of ice water slurry by warm air bubbling. Int JTherm Sci. 2001,40:724-737
[37]Mezhericher M, Levy A, Borde I. Heat and mass transfer of single droplet/wet particledrying. Chem Eng Sci. 2008,63:12-23
[38]Hao Y, Prosperetti A. Vapor bubble dynamics in non-uniform flows. APS/DFD AnnualMeeting. 1998: AA.03,
[39]Juric D, Tryggvason G. Computations of boiling flows. Int J Multiphase Flow. 1998. 24:387-410
[40]Yu Z S, Shao X M, Wachs A. A fictitious domain method for particulate flows with heattransfer. J Comput Phys.2006.217:424-452
[41]Kaoru M, Gang C. PIV measurement of particle motion in spiral gas-solid two-phaseflow. Exp Therm Fluid Sci .1999,19: 194-203
[42]石惠娴,王勤辉,骆仲泱,岑可法. PIV应用于气固多相流动的研究现状.动力工程.2002, 22(1): 1589-1593
[43]Choi H M, Kurihara T, Monji H, Matsui G. Measurement of particle/bubble motion andturbulence around it by hybrid PIV. Flow Meas Instrum. 2002, 12: 421-428
[44]由长福,祁海鹰,徐旭常,山本富士夫.采用PIV技术研究循环流化床内气固两相流动.应用力学学报. 2004, 21(4): 1-5
[45]周力行.离散型湍流多相流动的研究进展和需求.力学进展. 2008,38(5):610-622
[46]葛蔚,麻景森,张家元,唐德翔,陈飞国,王小伟,郭力,李静海.复杂流动多尺度模拟中的粒子方法.科学通报. 2005:841-853
[47]欧阳洁,李静海.模拟气固两相流动非均匀结构的颗粒运动分解轨道模型.中国科学(B辑).1999. 29:29-38
[48]亢力强,郭烈锦.风沙跃移中颗粒冲击起动的数值模拟.自然科学进展. 2005,15:252-256
[49]樊建人,胡桂林,姚军,岑可法.气固两相圆柱绕流的直接数值模拟.工程热物理学报.2003. 24:433-436
[50]王叶龙,林建忠,石兴.柱状粒子间相互作用对沉降运动的影响.自然科学进展. 2004.14:39-45
[51]郭烈锦.两相与多相流动力学.西安，西安交通大学出版社.2002, 574-600
[52]车得福,李会雄.多相流及其应用.西安，西安交通大学出版社.2007, 500-624
[53]仇铁,由长福,祁海鹰,徐旭常.多相流动的直接数值模拟进展.力学进展. 2003,33:507-517
[54]王维，李佑楚．颗粒流体两相流模型研究进展．化学进展. 2000，12：208-217
[55]金文,张鸿雁,何文博.微通道内流流场的数值模拟及Micro-PIV测量.应用基础与工程科学学报. 2011, 19(3): 389-397
[56]Drew D. Mathematical modeling of two-phase flow. Ann Rev Fluid Mech. 1983, 15:261-291
[57]Joseph D D, Lundgren T S. Ensemble averaged and mixture theory equation forincompressible fluid particle suspensions. Intl J Multiphase flow. 1990, 16: 35-42
[58]Feng J, Hu H H, Joseph D D. Direct simulation of initial value problems for the motion ofsolid bodies in a Newtonian fluid Part 1. Sedimention. J Fluid Mech. 1994, 26: 95-134
[59]纪军,刘涛,林宗虎,郭烈锦,白博峰．两相流研究的国际动向.国际学术动态，2005,6:25-26
[60]Rouson D W I, Eaton J K. Direct numerical simulation of turbulent channel flow withimmersed particels. ASMEFED. 1994, 185: 47-57
[61]Luo K, Fan J R, Chen K F. Local-focusing phenomenon and turbulence modulation inparticle-laden turbulent jets. Chin J Chem Eng. 2005, 13(2): 161-166
[62]Feng J, Joseph D D. The unsteady motion of solid particles in creeping flows. J FluidMech. 1995, 303:83-102
[63]Hu H H, Joseph D D, Crochet M J. Direct simulation of fluid particle motions. TheoretComput Fluid Dynam. 1992, 3: 285-306
[64]Gan H, Chang J Z, Feng J, Hu H H. Direct numerical simulation of the sedimentation ofsolid particles with thermal convection. J Fluid Mech. 2003. 481:385-411
[65]Joseph D D. Flow induced microstructure in Newtonian and viscoelastic fluids.Proceeding of the fifth world congress of chemical engineering, Particle technology track.California: American institute of chemical engineers. 1996, 133-155
[66]李文春,金晗辉,任安禄,樊建人,岑可法.气固两相三维圆柱绕流的直接数值模拟.工程热物理学报. 27(5): 808-810
[67]Luo K, Wang Z L, Fan J R. A modified immersed boundary method for simulations offluid-particle interactions. Comput Methods Appl Mech Engrg. 2007,197:36-46
[68]嵇峰,樊建人,任安禄,岑可法.气固两相圆柱绕流转捩两种模式的三维直接数值模拟.中国电机工程学报. 26(23): 55-60
[69]贺铸,柳朝晖,陈胜,翁磊,郑楚光.各向同性湍流中颗粒弥散的直接数值模拟.化工学报. 2006, 57(2) :301-305
[70]陈胤密,柳朝晖,郑楚光.颗粒碰撞的直接数值模拟.计算物理. 2004, 21(5): 421-426
[71]陈斌, Kawamura K, Kodama Y.静止水中单个上升气泡的直接数值模拟.工程热物理学报. 2005, 26(6): 980-982
[72]陈斌.高粘度流体中上升气泡的直接数值模拟.工程热物理学报. 2006，27(2):255-258
[73]仇佚,由长福,祁海鹰,徐旭常.用无网格伽辽金法模拟流动中的颗粒运动.化工学报. 2006, 57(6): 1323-1328
[74]刘汉涛,仝志辉,安康,马理强.溶解与热对流对固体颗粒运动影响的直接数值模拟.物理学报. 2009，58（9）：6369-6375
[75]刘汉涛,常建忠,安康,苏铁熊.热对流条件下双颗粒沉降的直接数值模拟.物理学报.2010, 59(3): 1877-1883
[76]刘汉涛,常建忠,马理强,安康.两相流动中椭圆颗粒沉降规律的数值模拟.水利水运工程学报. 2010，3: 75-78
[77]Chang J Z, Liu H T, Su T X, Liu M B. Direct Numerical Simulation of ParticleSedimentation in Two-phase Flow under Thermal Convection. Int J Comp Meth. 2011,8(4):851-861
[78]常建忠,安康,刘汉涛.固体颗粒在热对流下沉降的直接数值模拟研究.力学学报.2010 42(2): 205-211
[79]安康,常建忠,刘汉涛.通道宽度对单颗粒沉降运动影响的直接数值模拟,水运工程.2008, 418(8):6-9
[80]Paulo N. Baptista, Fernanda A.R. Oliveira, Jorge C. Oliveira, Sudhir K. Sastry.Dimensionless analysis of fluid-to-particle Heat Transfer coefficients. J Food Eng.1997,31:199-218
[81]Guardo A, Coussirat M, Recasens F, Larrayoz M A, Escaler X. CFD studies onparticle-to-fluid mass and heat transfer in packed beds: Free convection effects in supercriticalfluids. Chem Eng Sci. 2007,62:5503-5511
[82]陶文铨.计算传热学的近代进展.北京:科学出版社. 2001,383-432
[83]郭照立,郑楚光.格子Boltzman方法的原理及应用.北京:科学出版社. 2009, 1-14
[84]Frenkel D, Smit B. Understanding molecular simulation: From algorithms to applications:Academic Press. 2002, 10-200
[85]Rapaport D C.The art of molecular dynamics simulation: Cambridge University Press.2004, 20-200
[86]Hoogerbrugge P J, Koelman J M V A. Simulating microscopic hydrodynamic phenomenawith disipative particle dynamics. Europhys Lett. 1992, 19: 155
[87]Koelman J M V A, Hoogerbrugge P J. Dynamic simulation of hard-sphere suspensionsunder steady shear, Europhys Lett. 1993,21:363–368
[88]Revenga M, Zúiga I, Espa ol P. Boundary conditions in dissipative particle dynamics.Comput Phys Commun. 1999, 121:309-311
[89]Espa ol P, Warren P. Statistical mechanics of dissipative particle dynamics, EurophysLett. 1995,30: 191-196
[90]Marsh C A, Backx G, Ernst X H. Static and dynamic properties of dissipative particledynamics. Phys Rev. 1997, 56:1676-1691
[91]Marsh C A. Theoretical aspect of dissipative particle dynamics. Ph.D. Thesis Universityof Oxford, 1998, 1-20
[92]李红霞,强洪夫.耗散粒子动力学模拟方法的发展和应用.力学进展. 2009,39(2):165-175
[93]Soddemann T, Dünweg B, Kremer K. Dissipative particle dynamics: a useful thermostatfor equilibrium and nonequilibrium molecular dynamics simulations . Phys Rev E,2003,68(4):1-8
[94]陈硕,赵钧,范西俊,王丹.复杂流体流动的耗散粒子动力学研究进展,科技通报.2006,22(5)：596-602
[95]Liu M B, Meakin P, Huang H. Dissipative particle dynamics simulation of fluid motionthrough an unsaturated fracture and fracture junction, J Comput Phys. 2007, 222:110-130
[96]Sangani A S, Acrivos A. Slow flow past periodic arrays of cylinders with application toheat transfer. Int J Multiphase Flow. 1982, 8:193-206
[97]Boek E S, Coveney P V, Lekkerkerker H N W. Computer simulation of rheologicalphenomena in dense colloidal suspensions with dissipative particle dynamics, J Phys-CondensMat. 1996, 8:9509-9512
[98]Boek E S, Coveney P V, Schoot H N W P. Simulating the rheology of dense colloidalsuspensions using dissipative particle dynamics. Phys Rev. 1997, 55:3124-3133
[99]Boek E S, Schoot H N W P. Resolution Effects in Dissipative Particle DynamicsSimulations, Int J Mod Phys C. 1998, 9(8):1307-1318
[100]Kim J M, Phillips R J. Dissipative particle dynamics simulation of flow around sphereand cylinders at finite Reynolds numbers. Chem Eng Sci. 2004,59:4155-4168
[101]Chen S, Phan-Thien N, Khoo B C , Fan X J. Flow around spheres by dissipative particledynamics. Phys Fluids. 2006,18(10):103605
[102]Reddy H, Abraham J. Dissipative-particle dynamics simulation of flow over a stationarysphere in compliant channels. Phys Fluids. 2009, 21(5):053303
[103]Kong Y, Manke C W, Madden W G., Schlijper A G. Simulation of a confined polymer insolution using the dissipative particle dynamics method. Int J Thermophys.1994,15:1093–1101
[104]Malfreyt P, Tildesley D J.Dissipative particle dynamics simulations of grafted polymerchains between two walls. Langmuir. 2000, 16:4732–4740
[105]Jones J L, Lal M, Ruddock J N, Spenley N A. Dynamics of a drop at a liquid/solidinterface in simple shear fields:a mesoscopic simulation study.Faraday Discuss. 1999,112:129–142
[106]Visser D C, Hoefsloot H C J, Iedema P D. Comprehensive boundary method for solidwalls in dissipative particle dynamics, J Comput Phys. 2005,205:626-639
[107]Revenga M. Boundary models in DPD.Int J Mod Phys C. 1998, 9:1319–1328
[108]Adrian M A, Jens H W, Petros K. A stochastic boundary forcing for dissipative particledynamics. J Comput Phys. 2007,225:1125-1136
[109]Wang Y M, Jiang W H, Miller S, Eckstein E. Dissipative particle dynamics simulation ofon-chip hydrodynamic chromatography. Journal of Chronatography A, 2008,1198:140-147
[110]Patankar N A, Singh P, Joseph D D, Glowinski R, Pan T W. A new formulation of thedistributed Lagrange multiplier/fictitious domain method for particulate flows. Int JMultiphase flow. 1999: 1-24
[111]Hu H H. Direct simulation of flows of solid-liquid mixtures. Int J Multiphase flow. 1996,22(2): 335-352
[112]Hu H H. Numerical simulation of channel Poiseuille flow of solid-liquid mixtures.Proceeding of the fluids engineering division summer meeting. USA: American society ofmechanical engineers, 1996: 97-103
[113]张雄,陆明万,王建军.任意拉格朗日－欧拉描述法研究进展.计算力学学报. 1997,14(1):91-102
[114]Noh W F. Methods in computational physics.NY: Academic Press. 1964, 110-130
[115]Hughes T J R, Liu W K, Zimmerman T K. Lagrangian-Eulerian finite elementformulation for incompressible viscous flows. Comput Meth Appl Mech Engrg. 1981,29:329-349
[116]Ramaswamy B, Kawahara M. Arbitrary Lagrangian-Eulerian finite element method forunsteady, convective, incompressible viscous free surface fluid flow. Int J Num MethodsFluids, 1987,7:1053-1075
[117]Donea J, Fasoli-Stellap, et al. Lagrangian and Eulerian finite element techniques fortransient fluid-structure interaction problems, in: Trans. SMiRT-4, Paper B1/2, USA,1977,15-19
[118]Donea J. Arbitrary Lagrangian-Eulerian finite element methods, in: T. Belytschko and T.J. T. Hughes, eds. Computational Methods for Transient Analysis, North-Holland, Amsterdam,1983:473-516
[119]Nitikitpaiboon C. An arbitrary Lagrangian-Eulerian velocity potential formulation forfluid-structure interaction. Computers and Structures, 1993,47(4):871-891
[120]Hughes T J R, Liu W K, Zimmerman T K. Lagrangian–Eulerian finite elementformulation for incompressible viscous flows. Comput Meth Appl Mech Eng. 1981, 29:329-335
[121]Hu H H, Patankar N A, Zhu M Y. Direct numerical simulations of Fluid–Solidsystems using the arbitrary Lagrangian–Eulerian technique. J Comput Phys. 2001, 169:427-462
[122]Nomura T, Hughes T J R. An arbitrary Lagrangian-Eulerian finite element method forinteraction of fluid and a rigid body. Comp Meth Appl Mech Eng. 1992, 95(1) : 115-138
[123]Kuhl E, Hulshoff S, Borst R. An arbitrary Lagrangian Eulerian finite-element approachfor fluid-structure interaction phenomena. Int J Numer Meth Engng. 2003, 57: 117-142
[124]Jose D D, Fortes A, Lundgren T S, Singh P. Nonlinear mechanics of fluidization of bedsof spheres, cylinders and disks in water. Panpanicolau G, ed. Advances in multiphase flow andrelated problems. USA, SIAM, 1987: 101-122
[125]George P L. Automatic Mesh Generation, Application to Finite Element Methods. NewYork: Wiley. 1991: 1-200
[126]谢德馨,姚缨英,白保东,李绵彪.三维涡流场的有限元分析.北京：机械工业出版社.2001: 153-182
[127]蔡庆东.结构和非结构网格上统一的数值离散方法.庄逢甘,郑哲敏.钱学森技术科学思想与力学.北京：国防工业出版社. 2001: 232-236
[128]李万平.计算流体力学.武汉：华中科技大学出版社.2004:160-180
[129]Glowinski R, Pan, T W, Hesla T I, Joseph D D. A distributed Lagrangemultiplier/fictitious domain method for particulate flows. Int J Multiphase Flow. 1999, 25:755-794
[130]Chang, Finlayson. Heat transfer in flow past cylinders at Re<150 Part 1. Calculations forconstant fluid properties. Numer Heat Tr. 1987, 12:179-195
[131]Dennis, Chang G Z. Numerical solutions for steady flow past a circular cylinder atReynolds numbers up to 100. J Fluid Mech. 1970, 42(3):471-489
[132]Kuehn, Goldstein. An experimental and theoretical study of natural convection in theannulus between horizontal concentric cylinders. J Fluid Mech. 1976,74 (4): 695 -719
[133]McLeod P, Riley D S, Sparks R S J. Melting of a sphere in hot fluid. J Fluid Mech.1996,327, 393-409
[134]Kerr R C. Melting driven by vigorous compositional convection. J. Fluid Mech.1994,280, 255-295
[135]You C F, Qi H Y, Xu X C. Numerical simulation of drag force on non-spherical particlein gas-particle two-phase flow. J Chem Ind Eng. 2003,54(2):188-191
[136]Weinberg S. The discovery of subatomic particles. Cambridge: Cambridge universitypress. 2003: 1-50
[137]Marx D, Hutter J. Ab initio molecular dynamics: theory and implementation. Int JGrotendorst. 2000, 1: 301-449
[138]Groot R D, Warren P B. Dissipative particle dynamics: Bridging the gap betweenatomistic and mesoscopic simulation. J Chem Phys. 1997,107: 4423
[139]Marsh C. Theoretical Aspect of Dissipative Particle Dynamics, Ph D thesis, Universityof Oxford, 1998: 16-100
[140]Http://ocw.mit.edu/QcwWeb/Nuclear-Engineering/22-00JSpring2006/LectureNotes/index.htm
[141]Baydin A G. Dissipative particle dynamics and coarse-graining- Review of existingtechniques , trails with evolutionary algorithms. Master Dissertation. Sweden: Chalmersuniversity of technology, 2008
[142]刘谋斌,常建忠.耗散粒子动力学处理复杂固体壁面的一种有效方法.物理学报.2010, 59(11):7556-7563
[143]李振,胡国辉,周哲玮.耗散粒子动力学中实现滑移边界条件的数值方法.上海大学学报（自然科学版）. 2009, 15(6):628-633
[144]Revenga M, Zuniga I, Espanol P. Boundary model in DPD. Int J of modem phys C. 1998,9(8): 1319- 1328
[145]Revenga M, Zuniga I, Espanol P. Boundary conditions in dissipative particle dynamics.Comput Phys Commun. 1999: 309-311
[146]Rapaport D C. The Art of Molecular Dynamics Simulation. Cambridge: CambridgeUniversity Press. 1995: 44-82
[147]Irving J H，Kirkwood J G. The statistical mechanics of transport processes IV. Theequation of hydrodynamics. J Chem Phys.1950, 18: 817-829
[148]Pivkin I V, George E K. A new method to impose no-slip boundary conditions indissipative dynamics . J Comput Phys. 2005, 207: 114-128
[149]Fodi B, Hentschke R. Simulated phase behavior of model surfactant solutions,LANGMUIR.2000, 16 : 1626-1631
[150]Liu M B, Meakin P, Huang H. Dissipative particle dynamics simulation of pore-scalemultiphase fluid flow. Water Resour Res. 2007,43, W04411: 1-14
[151]Liu M B, Meakin P, Huang H. Dissipative particle dynamics simulation of multiphasefluid flow in microchannels and microchannel networks. Phys Fluid. 2007,19, 033302: 1-11
[152]Batchelor G K. An introduction to fluid dynamics. Cambridge,Cambridge UniversityPress. 1967: 174-260
[153]Brown P P, Lawler D F. Sphere drag and settling velocity revisited . J Environ Eng. 2003,129: 222-228
[154]Buss S R. Accurated and efficient simulation of rigid-body rotations. J Comput Phys.2000, 164: 377-406
[2]Furton K G, Myers L J. The scientific foundation and efficacy of the use of canines aschemical detectors for explosives. Talanta. 2001, 54(3): 487-500
[3]Henderson D A. The threat of aerosolized biological weapons. ASHRAE J. 2004,46(12):50-53
[4]陈耀松,单肖文,陈沪东.计算流体力学的新方向及其在工业上的应用.中国科学E辑：技术科学. 2007, 37(9):1107-1116
[5]Edge B A, Paterson E G, Settles G S. Computational study of the wake and contaminanttransport of a walking human. J Fluids Eng. 2005, 127: 967-977
[6]Brook D R, Beck N V, Clem C V. Validation of the urban dispersion model. 8thInt. Conf.on harmonisation within atmospheric dispersion modeling for regulatory purposes. 2003, 8-12
[7]方震华,黄慧锋.微电子机械系统（MEMS）技术在军用设备中的应用现状.电子机械工程. 2010,26(4):1-4
[8]Laser D J, Santiago J G. A review of micropumps. J Micromech Microeng. 2004, 14(6):35-64
[9]李战华,崔海航.微尺度流动特性.机械强度. 2001, 23(4): 476-480
[10]张颖,王蔚,田丽等.微流动的尺寸效应. MEMS器件与技术. 2008, 45(1): 33-37
[11]Kampen N G van. Stochastic processes in physics and chemistry. North Holland,Amsterdam, 1981: 57-460
[12]Liu G R, Liu M B. Smoothed particle hydrodynamics–a meshfree particle method.Singapore, World Scientific,2003: 35-58
[13]Liu M B and Liu G R. Restoring particle inconsistency in smoothed particlehydrodynamics. Appl Numer Math. 2006,56:19-36
[14]Liu M B, Liu G R. Meshfree particle simulation of micro channel flows with surfacetension. Comput Mech. 2005, 35:332-341
[15]刘谋斌,常建忠.光滑粒子动力学方法中粒子分布与数值稳定性分析.物理学报.2010, 59(6): 3654-3662
[16]刘谋斌,宗智,常建忠.光滑粒子动力学方法的发展与应用.力学进展. 2011, 41(2):217-234
[17]Mcnamara G R, Zanettic G. Use of the lattice Boltzmann euqation to simulate lattice - gasautomata. Phys Rev Lett.1988, 61: 2332-2335
[18]Bhatnagar P L, Gross E P, Krook M. A model for collision processes in gases.Ⅰ: smallamplitude processes in charged and neutral one-component system. Phys Rev. 1954, 94:511-525
[19]王兴勇,索丽生,程永光,刘德有.双重网格的Lattice Boltzmann方法.河海大学学报（自然科学版）. 2003, 31(1): 5-10
[20]Bird G A. Approach to translational equilibrium in a rigid sphere gas. Phys Fluids. 1963,6(10): 1518-1519
[21]周力行.离散型湍流多相流动的研究进展和需求.力学进展.2008, 38(5):610-620
[22]Liu M B, Meakin P, Huang H. Dissipative particle dynamics simulation of fluid motionthrough an unsaturated fracture and fracture function. J Comput Phys. 2007, 222, 110-130
[23]Liu M B, Paul M, Hai H. Dissipative particle dynamics with attractive and repulsiveparticle-particle interaction. Phys Fluids. 2006, 18: 017101
[24]Nicos S M. Velocity verlet algorithm for dissipative- particle - dynamics - based modelsof suspensions. Phys Rev E. 59(3): 3733-3736
[25]Yu Z S , Shao X M, Wachs A . A fictitious domain method for particulate flows with heattransfer. J Comput Phys., 2006, 217:424-451
[26]Choi H M , Kurihara T , Monji H , Matsui G. Measurement of particle/bubble motion andturbulence around it by hyrid PIV. Flow Meas Instrum. 2002, 12: 421-428
[27]Gidaspow D. Multiphase flow and fluidization: Continuum and kinetic theory description.New York : Academic Press, 1994: 6- 100
[28]伊杰里奇克N E .水力摩阻手册.北京,航空发动机编辑部.1985, 256-300
[29]Acrivos A, Taylor T D. Heat and mass transfer from single spheres in Stokes flow. PhysFluids. 1962. 5:387-394
[30]Levich V G.. Physicochemical Hydrodynamics. New Jersey, Prentice-Hall. 1962: 16-100
[31]Shah N, Reed X B. Reaction-enhanced convective diffusion of a reacting species from asphere to a fluid in viscous axisymmetric straining flow. ASP/DFD Annual Meeting,Philadelphia, November 1998, FL.09.
[32]Sadhal S S, Ayyaswamy P S, Chung J N. Transport Phenomena with Drops and Bubbles.German, Springer. 1997: 12-200
[33]Jog M A, Ayyaswamy P S, Cohen I.M. Evaporation and combustion of a slowly movingliquid fuel drplet: high-order theory. J Fluid Mech.1996. 307:135-165
[34]Dwyer H A, Sanders B R. A detailed study of burning fuel droplets. Proc. 21stSymp.(Int’l) on Combustion. Pittsburgh, The Combustion Institute, 1986, 633-639 1986
[35]McLeod P, Riley D S, Sparks R S J. Melting of a sphere in hot fluid. J Fluid Mech. 1996,327: 303-409
[36]Shigeo A, Hideo I. Melting Characteristics of ice water slurry by warm air bubbling. Int JTherm Sci. 2001,40:724-737
[37]Mezhericher M, Levy A, Borde I. Heat and mass transfer of single droplet/wet particledrying. Chem Eng Sci. 2008,63:12-23
[38]Hao Y, Prosperetti A. Vapor bubble dynamics in non-uniform flows. APS/DFD AnnualMeeting. 1998: AA.03,
[39]Juric D, Tryggvason G. Computations of boiling flows. Int J Multiphase Flow. 1998. 24:387-410
[40]Yu Z S, Shao X M, Wachs A. A fictitious domain method for particulate flows with heattransfer. J Comput Phys.2006.217:424-452
[41]Kaoru M, Gang C. PIV measurement of particle motion in spiral gas-solid two-phaseflow. Exp Therm Fluid Sci .1999,19: 194-203
[42]石惠娴,王勤辉,骆仲泱,岑可法. PIV应用于气固多相流动的研究现状.动力工程.2002, 22(1): 1589-1593
[43]Choi H M, Kurihara T, Monji H, Matsui G. Measurement of particle/bubble motion andturbulence around it by hybrid PIV. Flow Meas Instrum. 2002, 12: 421-428
[44]由长福,祁海鹰,徐旭常,山本富士夫.采用PIV技术研究循环流化床内气固两相流动.应用力学学报. 2004, 21(4): 1-5
[45]周力行.离散型湍流多相流动的研究进展和需求.力学进展. 2008,38(5):610-622
[46]葛蔚,麻景森,张家元,唐德翔,陈飞国,王小伟,郭力,李静海.复杂流动多尺度模拟中的粒子方法.科学通报. 2005:841-853
[47]欧阳洁,李静海.模拟气固两相流动非均匀结构的颗粒运动分解轨道模型.中国科学(B辑).1999. 29:29-38
[48]亢力强,郭烈锦.风沙跃移中颗粒冲击起动的数值模拟.自然科学进展. 2005,15:252-256
[49]樊建人,胡桂林,姚军,岑可法.气固两相圆柱绕流的直接数值模拟.工程热物理学报.2003. 24:433-436
[50]王叶龙,林建忠,石兴.柱状粒子间相互作用对沉降运动的影响.自然科学进展. 2004.14:39-45
[51]郭烈锦.两相与多相流动力学.西安，西安交通大学出版社.2002, 574-600
[52]车得福,李会雄.多相流及其应用.西安，西安交通大学出版社.2007, 500-624
[53]仇铁,由长福,祁海鹰,徐旭常.多相流动的直接数值模拟进展.力学进展. 2003,33:507-517
[54]王维，李佑楚．颗粒流体两相流模型研究进展．化学进展. 2000，12：208-217
[55]金文,张鸿雁,何文博.微通道内流流场的数值模拟及Micro-PIV测量.应用基础与工程科学学报. 2011, 19(3): 389-397
[56]Drew D. Mathematical modeling of two-phase flow. Ann Rev Fluid Mech. 1983, 15:261-291
[57]Joseph D D, Lundgren T S. Ensemble averaged and mixture theory equation forincompressible fluid particle suspensions. Intl J Multiphase flow. 1990, 16: 35-42
[58]Feng J, Hu H H, Joseph D D. Direct simulation of initial value problems for the motion ofsolid bodies in a Newtonian fluid Part 1. Sedimention. J Fluid Mech. 1994, 26: 95-134
[59]纪军,刘涛,林宗虎,郭烈锦,白博峰．两相流研究的国际动向.国际学术动态，2005,6:25-26
[60]Rouson D W I, Eaton J K. Direct numerical simulation of turbulent channel flow withimmersed particels. ASMEFED. 1994, 185: 47-57
[61]Luo K, Fan J R, Chen K F. Local-focusing phenomenon and turbulence modulation inparticle-laden turbulent jets. Chin J Chem Eng. 2005, 13(2): 161-166
[62]Feng J, Joseph D D. The unsteady motion of solid particles in creeping flows. J FluidMech. 1995, 303:83-102
[63]Hu H H, Joseph D D, Crochet M J. Direct simulation of fluid particle motions. TheoretComput Fluid Dynam. 1992, 3: 285-306
[64]Gan H, Chang J Z, Feng J, Hu H H. Direct numerical simulation of the sedimentation ofsolid particles with thermal convection. J Fluid Mech. 2003. 481:385-411
[65]Joseph D D. Flow induced microstructure in Newtonian and viscoelastic fluids.Proceeding of the fifth world congress of chemical engineering, Particle technology track.California: American institute of chemical engineers. 1996, 133-155
[66]李文春,金晗辉,任安禄,樊建人,岑可法.气固两相三维圆柱绕流的直接数值模拟.工程热物理学报. 27(5): 808-810
[67]Luo K, Wang Z L, Fan J R. A modified immersed boundary method for simulations offluid-particle interactions. Comput Methods Appl Mech Engrg. 2007,197:36-46
[68]嵇峰,樊建人,任安禄,岑可法.气固两相圆柱绕流转捩两种模式的三维直接数值模拟.中国电机工程学报. 26(23): 55-60
[69]贺铸,柳朝晖,陈胜,翁磊,郑楚光.各向同性湍流中颗粒弥散的直接数值模拟.化工学报. 2006, 57(2) :301-305
[70]陈胤密,柳朝晖,郑楚光.颗粒碰撞的直接数值模拟.计算物理. 2004, 21(5): 421-426
[71]陈斌, Kawamura K, Kodama Y.静止水中单个上升气泡的直接数值模拟.工程热物理学报. 2005, 26(6): 980-982
[72]陈斌.高粘度流体中上升气泡的直接数值模拟.工程热物理学报. 2006，27(2):255-258
[73]仇佚,由长福,祁海鹰,徐旭常.用无网格伽辽金法模拟流动中的颗粒运动.化工学报. 2006, 57(6): 1323-1328
[74]刘汉涛,仝志辉,安康,马理强.溶解与热对流对固体颗粒运动影响的直接数值模拟.物理学报. 2009，58（9）：6369-6375
[75]刘汉涛,常建忠,安康,苏铁熊.热对流条件下双颗粒沉降的直接数值模拟.物理学报.2010, 59(3): 1877-1883
[76]刘汉涛,常建忠,马理强,安康.两相流动中椭圆颗粒沉降规律的数值模拟.水利水运工程学报. 2010，3: 75-78
[77]Chang J Z, Liu H T, Su T X, Liu M B. Direct Numerical Simulation of ParticleSedimentation in Two-phase Flow under Thermal Convection. Int J Comp Meth. 2011,8(4):851-861
[78]常建忠,安康,刘汉涛.固体颗粒在热对流下沉降的直接数值模拟研究.力学学报.2010 42(2): 205-211
[79]安康,常建忠,刘汉涛.通道宽度对单颗粒沉降运动影响的直接数值模拟,水运工程.2008, 418(8):6-9
[80]Paulo N. Baptista, Fernanda A.R. Oliveira, Jorge C. Oliveira, Sudhir K. Sastry.Dimensionless analysis of fluid-to-particle Heat Transfer coefficients. J Food Eng.1997,31:199-218
[81]Guardo A, Coussirat M, Recasens F, Larrayoz M A, Escaler X. CFD studies onparticle-to-fluid mass and heat transfer in packed beds: Free convection effects in supercriticalfluids. Chem Eng Sci. 2007,62:5503-5511
[82]陶文铨.计算传热学的近代进展.北京:科学出版社. 2001,383-432
[83]郭照立,郑楚光.格子Boltzman方法的原理及应用.北京:科学出版社. 2009, 1-14
[84]Frenkel D, Smit B. Understanding molecular simulation: From algorithms to applications:Academic Press. 2002, 10-200
[85]Rapaport D C.The art of molecular dynamics simulation: Cambridge University Press.2004, 20-200
[86]Hoogerbrugge P J, Koelman J M V A. Simulating microscopic hydrodynamic phenomenawith disipative particle dynamics. Europhys Lett. 1992, 19: 155
[87]Koelman J M V A, Hoogerbrugge P J. Dynamic simulation of hard-sphere suspensionsunder steady shear, Europhys Lett. 1993,21:363–368
[88]Revenga M, Zúiga I, Espa ol P. Boundary conditions in dissipative particle dynamics.Comput Phys Commun. 1999, 121:309-311
[89]Espa ol P, Warren P. Statistical mechanics of dissipative particle dynamics, EurophysLett. 1995,30: 191-196
[90]Marsh C A, Backx G, Ernst X H. Static and dynamic properties of dissipative particledynamics. Phys Rev. 1997, 56:1676-1691
[91]Marsh C A. Theoretical aspect of dissipative particle dynamics. Ph.D. Thesis Universityof Oxford, 1998, 1-20
[92]李红霞,强洪夫.耗散粒子动力学模拟方法的发展和应用.力学进展. 2009,39(2):165-175
[93]Soddemann T, Dünweg B, Kremer K. Dissipative particle dynamics: a useful thermostatfor equilibrium and nonequilibrium molecular dynamics simulations . Phys Rev E,2003,68(4):1-8
[94]陈硕,赵钧,范西俊,王丹.复杂流体流动的耗散粒子动力学研究进展,科技通报.2006,22(5)：596-602
[95]Liu M B, Meakin P, Huang H. Dissipative particle dynamics simulation of fluid motionthrough an unsaturated fracture and fracture junction, J Comput Phys. 2007, 222:110-130
[96]Sangani A S, Acrivos A. Slow flow past periodic arrays of cylinders with application toheat transfer. Int J Multiphase Flow. 1982, 8:193-206
[97]Boek E S, Coveney P V, Lekkerkerker H N W. Computer simulation of rheologicalphenomena in dense colloidal suspensions with dissipative particle dynamics, J Phys-CondensMat. 1996, 8:9509-9512
[98]Boek E S, Coveney P V, Schoot H N W P. Simulating the rheology of dense colloidalsuspensions using dissipative particle dynamics. Phys Rev. 1997, 55:3124-3133
[99]Boek E S, Schoot H N W P. Resolution Effects in Dissipative Particle DynamicsSimulations, Int J Mod Phys C. 1998, 9(8):1307-1318
[100]Kim J M, Phillips R J. Dissipative particle dynamics simulation of flow around sphereand cylinders at finite Reynolds numbers. Chem Eng Sci. 2004,59:4155-4168
[101]Chen S, Phan-Thien N, Khoo B C , Fan X J. Flow around spheres by dissipative particledynamics. Phys Fluids. 2006,18(10):103605
[102]Reddy H, Abraham J. Dissipative-particle dynamics simulation of flow over a stationarysphere in compliant channels. Phys Fluids. 2009, 21(5):053303
[103]Kong Y, Manke C W, Madden W G., Schlijper A G. Simulation of a confined polymer insolution using the dissipative particle dynamics method. Int J Thermophys.1994,15:1093–1101
[104]Malfreyt P, Tildesley D J.Dissipative particle dynamics simulations of grafted polymerchains between two walls. Langmuir. 2000, 16:4732–4740
[105]Jones J L, Lal M, Ruddock J N, Spenley N A. Dynamics of a drop at a liquid/solidinterface in simple shear fields:a mesoscopic simulation study.Faraday Discuss. 1999,112:129–142
[106]Visser D C, Hoefsloot H C J, Iedema P D. Comprehensive boundary method for solidwalls in dissipative particle dynamics, J Comput Phys. 2005,205:626-639
[107]Revenga M. Boundary models in DPD.Int J Mod Phys C. 1998, 9:1319–1328
[108]Adrian M A, Jens H W, Petros K. A stochastic boundary forcing for dissipative particledynamics. J Comput Phys. 2007,225:1125-1136
[109]Wang Y M, Jiang W H, Miller S, Eckstein E. Dissipative particle dynamics simulation ofon-chip hydrodynamic chromatography. Journal of Chronatography A, 2008,1198:140-147
[110]Patankar N A, Singh P, Joseph D D, Glowinski R, Pan T W. A new formulation of thedistributed Lagrange multiplier/fictitious domain method for particulate flows. Int JMultiphase flow. 1999: 1-24
[111]Hu H H. Direct simulation of flows of solid-liquid mixtures. Int J Multiphase flow. 1996,22(2): 335-352
[112]Hu H H. Numerical simulation of channel Poiseuille flow of solid-liquid mixtures.Proceeding of the fluids engineering division summer meeting. USA: American society ofmechanical engineers, 1996: 97-103
[113]张雄,陆明万,王建军.任意拉格朗日－欧拉描述法研究进展.计算力学学报. 1997,14(1):91-102
[114]Noh W F. Methods in computational physics.NY: Academic Press. 1964, 110-130
[115]Hughes T J R, Liu W K, Zimmerman T K. Lagrangian-Eulerian finite elementformulation for incompressible viscous flows. Comput Meth Appl Mech Engrg. 1981,29:329-349
[116]Ramaswamy B, Kawahara M. Arbitrary Lagrangian-Eulerian finite element method forunsteady, convective, incompressible viscous free surface fluid flow. Int J Num MethodsFluids, 1987,7:1053-1075
[117]Donea J, Fasoli-Stellap, et al. Lagrangian and Eulerian finite element techniques fortransient fluid-structure interaction problems, in: Trans. SMiRT-4, Paper B1/2, USA,1977,15-19
[118]Donea J. Arbitrary Lagrangian-Eulerian finite element methods, in: T. Belytschko and T.J. T. Hughes, eds. Computational Methods for Transient Analysis, North-Holland, Amsterdam,1983:473-516
[119]Nitikitpaiboon C. An arbitrary Lagrangian-Eulerian velocity potential formulation forfluid-structure interaction. Computers and Structures, 1993,47(4):871-891
[120]Hughes T J R, Liu W K, Zimmerman T K. Lagrangian–Eulerian finite elementformulation for incompressible viscous flows. Comput Meth Appl Mech Eng. 1981, 29:329-335
[121]Hu H H, Patankar N A, Zhu M Y. Direct numerical simulations of Fluid–Solidsystems using the arbitrary Lagrangian–Eulerian technique. J Comput Phys. 2001, 169:427-462
[122]Nomura T, Hughes T J R. An arbitrary Lagrangian-Eulerian finite element method forinteraction of fluid and a rigid body. Comp Meth Appl Mech Eng. 1992, 95(1) : 115-138
[123]Kuhl E, Hulshoff S, Borst R. An arbitrary Lagrangian Eulerian finite-element approachfor fluid-structure interaction phenomena. Int J Numer Meth Engng. 2003, 57: 117-142
[124]Jose D D, Fortes A, Lundgren T S, Singh P. Nonlinear mechanics of fluidization of bedsof spheres, cylinders and disks in water. Panpanicolau G, ed. Advances in multiphase flow andrelated problems. USA, SIAM, 1987: 101-122
[125]George P L. Automatic Mesh Generation, Application to Finite Element Methods. NewYork: Wiley. 1991: 1-200
[126]谢德馨,姚缨英,白保东,李绵彪.三维涡流场的有限元分析.北京：机械工业出版社.2001: 153-182
[127]蔡庆东.结构和非结构网格上统一的数值离散方法.庄逢甘,郑哲敏.钱学森技术科学思想与力学.北京：国防工业出版社. 2001: 232-236
[128]李万平.计算流体力学.武汉：华中科技大学出版社.2004:160-180
[129]Glowinski R, Pan, T W, Hesla T I, Joseph D D. A distributed Lagrangemultiplier/fictitious domain method for particulate flows. Int J Multiphase Flow. 1999, 25:755-794
[130]Chang, Finlayson. Heat transfer in flow past cylinders at Re<150 Part 1. Calculations forconstant fluid properties. Numer Heat Tr. 1987, 12:179-195
[131]Dennis, Chang G Z. Numerical solutions for steady flow past a circular cylinder atReynolds numbers up to 100. J Fluid Mech. 1970, 42(3):471-489
[132]Kuehn, Goldstein. An experimental and theoretical study of natural convection in theannulus between horizontal concentric cylinders. J Fluid Mech. 1976,74 (4): 695 -719
[133]McLeod P, Riley D S, Sparks R S J. Melting of a sphere in hot fluid. J Fluid Mech.1996,327, 393-409
[134]Kerr R C. Melting driven by vigorous compositional convection. J. Fluid Mech.1994,280, 255-295
[135]You C F, Qi H Y, Xu X C. Numerical simulation of drag force on non-spherical particlein gas-particle two-phase flow. J Chem Ind Eng. 2003,54(2):188-191
[136]Weinberg S. The discovery of subatomic particles. Cambridge: Cambridge universitypress. 2003: 1-50
[137]Marx D, Hutter J. Ab initio molecular dynamics: theory and implementation. Int JGrotendorst. 2000, 1: 301-449
[138]Groot R D, Warren P B. Dissipative particle dynamics: Bridging the gap betweenatomistic and mesoscopic simulation. J Chem Phys. 1997,107: 4423
[139]Marsh C. Theoretical Aspect of Dissipative Particle Dynamics, Ph D thesis, Universityof Oxford, 1998: 16-100
[140]Http://ocw.mit.edu/QcwWeb/Nuclear-Engineering/22-00JSpring2006/LectureNotes/index.htm
[141]Baydin A G. Dissipative particle dynamics and coarse-graining- Review of existingtechniques , trails with evolutionary algorithms. Master Dissertation. Sweden: Chalmersuniversity of technology, 2008
[142]刘谋斌,常建忠.耗散粒子动力学处理复杂固体壁面的一种有效方法.物理学报.2010, 59(11):7556-7563
[143]李振,胡国辉,周哲玮.耗散粒子动力学中实现滑移边界条件的数值方法.上海大学学报（自然科学版）. 2009, 15(6):628-633
[144]Revenga M, Zuniga I, Espanol P. Boundary model in DPD. Int J of modem phys C. 1998,9(8): 1319- 1328
[145]Revenga M, Zuniga I, Espanol P. Boundary conditions in dissipative particle dynamics.Comput Phys Commun. 1999: 309-311
[146]Rapaport D C. The Art of Molecular Dynamics Simulation. Cambridge: CambridgeUniversity Press. 1995: 44-82
[147]Irving J H，Kirkwood J G. The statistical mechanics of transport processes IV. Theequation of hydrodynamics. J Chem Phys.1950, 18: 817-829
[148]Pivkin I V, George E K. A new method to impose no-slip boundary conditions indissipative dynamics . J Comput Phys. 2005, 207: 114-128
[149]Fodi B, Hentschke R. Simulated phase behavior of model surfactant solutions,LANGMUIR.2000, 16 : 1626-1631
[150]Liu M B, Meakin P, Huang H. Dissipative particle dynamics simulation of pore-scalemultiphase fluid flow. Water Resour Res. 2007,43, W04411: 1-14
[151]Liu M B, Meakin P, Huang H. Dissipative particle dynamics simulation of multiphasefluid flow in microchannels and microchannel networks. Phys Fluid. 2007,19, 033302: 1-11
[152]Batchelor G K. An introduction to fluid dynamics. Cambridge,Cambridge UniversityPress. 1967: 174-260
[153]Brown P P, Lawler D F. Sphere drag and settling velocity revisited . J Environ Eng. 2003,129: 222-228
[154]Buss S R. Accurated and efficient simulation of rigid-body rotations. J Comput Phys.2000, 164: 377-406