应用格子Boltzmann模型模拟一类二维偏微分方程

针对一类含源的二维非线性偏微分方程, 通过Chapman-Enskog展开技术和多尺度分析提出了带修正项的简单格子Boltzmann模型. 用模型模拟了几类二维偏微分方程, 数值模拟结果与精确解相符合. 成功将格子Boltzmann方法应用到二维偏微分方程的数值求解中. 关键词： 二维非线性偏微分方程 格子Boltzmann模型 Chapman-Enskog多尺度展开     

一种新的模拟渗流运动的数值方法

根据格子Boltzmann方法及相关理论，建立了一个新的模拟渗流运动的数值模型，所得模型没有在边界上采取相应平均措施，同时还避免了一些非物理副产品的出现-实例计算数值结果与精确解符合较好，证明模型可靠- 关键词： 渗流 格子Boltzmann方法 数值模型     

三维方腔温盐双扩散的格子Boltzmann方法数值模拟

研究了温盐双扩散系统的多组分格子Boltzmann方法.通过对二维方腔的温盐双扩散系统的数值模拟，检验了方法的可行性及有效性，所得到的结果与差分法结果符合良好，继而将此方法推广到三维，建立了三维温盐双扩散系统的格子Boltzmann方法，对三维方腔双扩散问题进行了模拟和分析，并与差分法模拟的结果进行了比较，结果令人满意.最后，分析了格子Boltzmann方法在模拟双扩散对流问题时存在的局限性. 关键词： 格子Boltzmann方法 温盐双扩散 Boussinesq近似 数值模拟     

多相非牛顿流体驱替过程的格子Boltzmann模拟

将非牛顿流体模型引入多相格子Boltzmann方法（LBM）,研究多相非牛顿流体的驱替过程.首先以牛顿流体驱替过程作对照,比较非牛顿流体的驱替特性.然后基于简单结构模型,分析不同界面张力下,非牛顿流体的驱替能力和驱替过程中被驱替相的形态变化规律,揭示界面张力的影响机理.结果表明：界面张力在驱替过程中起阻碍作用,其它参数相同情况下,界面张力越低,流体的驱替能力越强.最后,结合四参数随机生长（QSGS）结构生成方法,模拟不同压差、不同界面张力以及不同润湿性条件下多孔复杂结构内的非牛顿多相驱替过程,分析这些参数对过程的影响.     

微多孔介质非牛顿流体格子Boltzmann模拟

根据修正Blake-Kozeny方程对Herschel-Bulkley模型的非牛顿流体在微多孔介质中流动的定量描述,通过增加外力项建立了非牛顿流体在宏观多孔介质中的格子Boltzmann模型,并将该模型应用到平板多孔介质中非牛顿流体的电渗驱动流模拟。对多孔介质渗透性参数和非牛顿流体流变性参数的影响进行模拟和分析,获得了各种参数对多孔介质中非牛顿流体流动速度的影响规律。     

耦合不可压流场输运方程的格子Boltzmann方法研究

基于格子Boltzmann方法,提出了求解耦合不可压缩流场输运方程的一种改进数值方法. 该方法使用格子Boltzmann方法求解流场方程,并根据流场格子模型的密度分布函数构建了输运方程的二阶离散格式. 通过二维平板通道流场输运系统验证了该方法的有效性.数值结果表明,该方法可以有效地减少计算过程中出现的非物理耗散, 并克服了传统模型所需巨大存储量的缺点.     

基于格子Boltzmann方法的幂律流体二维顶盖驱动流转捩研究

研究非牛顿流体转捩问题,可为调控非牛顿流体动力特性提供理论基础.相对于牛顿流体转捩问题,非牛顿流体转捩研究较少,缺乏转捩雷诺数精细预报方法.论文以格子Boltzmann方法为核心求解器,以典型非牛顿流体幂律模型为例,开展了幂律流体二维顶盖驱动流转捩模拟,给出剪切变稀和剪切增稠流体的第一转捩雷诺数,并分析了转捩雷诺数附近流场时频域特性及模态分布.结果表明,剪切变稀流体和剪切增稠流体的第一转捩雷诺数与牛顿流体差异显著,且在转捩临界雷诺数附近监控点处速度分量均呈现周期性变化趋势.通过对流场速度和涡量的本征正交分解发现,不同类型的流体在转捩临界雷诺数附近,前两阶模态均为流场的主模态,能量占比超过95%,且同类型流体不同雷诺数的主模态间具有相似的结构.     

相同尺度下气泡与复杂壁面的耦合特性研究

采用格子Boltzmann方法(LBM)建立了气液固三相耦合的动力学模型,研究了相同尺度下上浮气泡与复杂壁面的相互耦合作用.首先,基于黏性流体理论,通过构建一组格子Boltzmann(LB)方程来描述气液两相的运动,并以LB离散体积力的形式计入了黏性力、表面张力和重力.同时,采用LBM中的Half-way反弹模型与有限差分格式相结合的方式进行固壁边界的处理.然后,利用本文建立的模型,对不同特征尺寸比条件下,气泡与考虑边缘效应的平面固壁和曲面固壁的耦合特性进行了研究.研究发现固壁边界条件以及特征尺寸比对气泡的运动和拓扑结构的变化都具有明显的非线性影响.最后,研究了流体属性对气泡与复杂壁面耦合规律的影响.     

一个完全守恒的格子Boltzmann模型

利用六角形格子离散的方法,使得每个六角形Cell里含有 3种不同运动速度的粒子微团,宏观物理量用这些粒子微团的矩来定义.根据微观和宏观之间的质量、动量、能量守恒准则,建立了一个二维的D2Q19格子Boltzmann模型,从该D2Q19模型出发可推导出宏观的流体力学方程组.用该模型对冲击波在障碍物组表面上的折射现象进行数值模拟,并将计算结果与实验进行了比较.     

等离子弧焊接熔池演变过程的格子Boltzmann模拟与验证

本文应用基于分子动理论的格子Boltzmann方法,建立了描述定点等离子弧焊接熔池动态演变过程的二维数理模型,对相变过程的传热与流动现象开展模拟;根据焊接过程能量分布特点改进等离子弧的组合式热源模型,采用total-enthalpy模型求解温度、速度分布及追踪相界面。研究结果表明,模拟的熔合线形状与实验焊缝吻合,格子Boltzmann模拟得到的计算精度及计算效率均优于基于连续流体假设的有限容积法,验证了格子Boltzmann方法用于等离子弧焊接模拟的可行性和优越性;熔池中出现两个方向相反的环流,流动对焊缝形状的作用不容忽略;熔池的流动方式影响了温度场、速度场及二者协同度,直接影响固相线上的热量传递,促进了焊缝中部凸起的形成。     

Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

This paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress is also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.     

Lattice Boltzmann Simulation of Sedimentation of a Single Elastic Dumbbell in a Newtonian Fluid

Based on the lattice Boltzmann method (LBM), the sedimentations of a single elastic dumbbell in a Newtonian fluid under different initial positions and orientations, and also that of the elastic dumbbells with different free lengths of the spring under the same initial conditions have been simulated. All of the numerical results show that the final orientations of the elastic dumbbells are in the same horizontal direction, and the final positions of their centroids are all on the centerline of the tube no matter what the initial positions and orientations of the elastic dumbbell or the free lengths of the spring are. When the elastic dumbbell finally falls down vertically, the two circular cylinders of the elastic dumbbell rotate around their own symmetry-axis respectively, and their angular velocities are equal but opposite to each other. For the sedimentations of the elastic dumbbells with different free lengths of the spring, the shorter of the free length is, the faster the final angular velocity and vertical velocity of the circular cylinder will be.     

Lattice Boltzmann Simulation of Sedimentation of a Single Elastic Dumbbell in a Newtonian Fluid

Based on the lattice Boltzmann method (LBM), the sedimentations of a single elastic dumbbell in a Newtonian fluid under different initial positions and orientations, and also that of the elastic dumbbells with different free lengths of the spring under the same initial conditions have been simulated. All of the numerical results show that the final orientations of the elastic dumbbells are in the same horizontal direction, and the final positions of their centroids are all on the centerline of the tube no matter what the initial positions and orientations of the elastic dumbbell or the free lengths of the spring are. When the elastic dumbbell finally falls down vertically, the two circular cylinders of the elastic dumbbell rotate around their own symmetry-axis respectively, and their angular velocities are equal but opposite to each other. For the sedimentations of the elastic dumbbells with different free lengths of the spring, the shorter of the free length is, the faster the final angular velocity and vertical velocity of the circular cylinder will be.     

微扩张管道内幂律流体非定常电渗流动

研究了电渗驱动下幂律流体在有限长微扩张管道内非稳态流动特性.基于Ostwald-de Wael幂律模型,采用高精度紧致差分离散二维Poisson-Nernst-Planck方程及修正的Cauchy动量方程,数值模拟了初始及稳态时刻微扩张管道内幂律流体电渗流流场分布情况,研究了管道截面改变对幂律流体无量纲剪切应变率及无量纲表观黏度的影响,以及无量纲表观黏度对拟塑性流体与胀流型流体流速分布的影响.数值模拟结果显示,当扩张角和无量纲电动宽度一定时,电场驱动下的幂律流体在近壁区域速度响应都很快;初始时刻,近壁处表观黏度的变化受到剪切应变率变化的影响,从而影响了三种幂律流体速度峰值的分布,出现拟塑性流体流速在扩张段上游及扩张段近壁处速度峰值均为幂律流体中最大、而在扩张段下游三种幂律流体速度峰值相近的现象;稳态时刻,幂律流体速度剖面呈现塞型分布,且满足连续性条件下,幂律流体流速随扩张管半径增大而减小,牛顿流体流动规律与宏观尺度下流动规律相同;初始时刻,在相同电动宽度、不同壁面电势作用下,幂律流体在扩张管近壁处剪切应变率分布的差异导致表观黏度分布的差异,并最终导致拟塑性流体与胀流型流体流速分布的差异.     

Dynamics of arrays of cylinders with internal and external axial flow

Various aspects of the dynamics and stability of clusters of tubular cylinders containing internally flowing fluid and surrounded by a bounded external axial flow are examined. The general character of free motions is established by obtaining the eigenfrequencies of the system and studying their evolution with increasing flow, internal or external. Stability diagrams have been obtained for the critical flow velocities, beyond which the system would lose stability by buckling (divergence), under the combined effect of internal and external flow. Free vibration, following an initial disturbance of one of the cylinders, is studied, in order further to examine the effect of hydrodynamic coupling. It is found that beating phenomena may arise, implying energy transfer between cylinders and the possibility of transient amplitudes much larger than the initial disturbances. Also, the vibration of the system (in still fluid) when one cylinder is constrained to oscillate in a prescribed manner is examined, establishing that transmission of vibration from cylinder to cylinder can be very rapid; indeed, such constrained motion of one cylinder at certain frequencies may induce large amplified motions of others.     

Elliptic flow in an integrated (3+1)d microscopic + macroscopic approach with fluctuating initial conditions

The elliptic flow excitation function calculated in a Boltzmann approach with an intermediate hydrodynamic stage for heavy-ion reactions from GSI-SIS to the highest CERN-SPS energies is discussed in the context of the experimental data. The specific setup with initial conditions and freeze-out from a non-equilibrium transport model allows for a direct comparison between ideal fluid dynamics and hadronic transport simulations. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to higher elliptic flow values. The lower mean free path leads to higher pressure gradients in the early stage and as a consequence to higher elliptic flow values even without a phase transition. Special emphasis is put on the influence of the initial conditions on the results of the hybrid model calculation. Event-by-event fluctuations are directly taken into account via event-wise non-equilibrium initial conditions generated by the primary collisions and string fragmentations in the microscopic UrQMD model. This leads to non-trivial velocity and energy density distributions for the hydrodynamical initial conditions. Due to the more realistic initial conditions and the incorporated hadronic rescattering the results are in line with the experimental data almost over the whole energy range from E _lab=2–160A GeV.     

Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel

The effects of both magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel are studied analytically and numerically. The channel asymmetry is generated by propagation of waves on the channel walls travelling with different amplitudes, phases but with the same speed. The long wavelength and low Reynolds number assumptions are considered in obtaining solution for the flow. The flow is investigated in a wave frame of reference moving with velocity of the wave. Closed form expressions have been obtained for the stream function and the axial velocity component in fixed frame. The effects of phase difference, Knudsen number and magnetic field on the pumping characteristics and velocity field are discussed. Several known results of interest are found to follow as particular cases of the solution of the problem considered.     

Experimental study and CFD simulation of rotational eccentric cylinder in a magnetorheological fluid

In this study, a magnetorheological (MR) fluid is prepared using carbonyl iron filings and low viscosity lubricating oil. The effects of magnetic field and weight percentage of particles on the viscosity of the MR fluid have been measured using a rotational viscometer. The yield stress under an applied magnetic field was also obtained experimentally. In the absence of an applied magnetic field, the MR fluid behaves as a Newtonian fluid. When the magnetic field is applied, the MR fluid behaves like Bingham plastics with a magnetic field dependent yield stress. Afterward, the results compared with those of CFD simulation of two eccentric cylinders in the MR fluid. Results show that the influences of MR effects, caused by the applied magnetic field, on the model characteristics are significant and not negligible. The viscosity is enhanced by increasing of the magnetic field, eccentricity ratio and weight percentage of suspensions. The MR effects and increasing of weight percentage and eccentricity ratio also provide an enhancement in the yield stresses and required total torque for rotation of inner cylinder. Also the simulation results indicate a good representation of the experiment by the model.     

Magnetohydrodynamic flows as Newtonian-type gravitational motions

We study the motion of a magnetised, highly conductive fluid within the framework of Newtonian gravity. Our analysis examines whether and under what conditions magnetohydrodynamic flows can be represented as hydrodynamic ones and then as Newtonian-type gravitational motions. In the latter case we define a generalised effective density and an effective Poisson-type potential, which include the magnetic input and determine the dynamics of the magnetised system. Introducing the dynamical equivalence of the aforementioned two representations, we use it to test mass measurements based on purely gravitational motions. We also provide the generalised Raychaudhuri equation corresponding to the aforementioned effective potential and discuss its implications for the kinematics of the fluid.