热动力学格子Boltzmann模型

提出了一类热动力学格子Boltzmann模型,其分布函数中含有内能项与高阶速度项。以三个HPP模型为基础,建立了一个三迭加HPP格子Boltzmann模型,并给出其局部平衡分布函数。设计了热动力学现象模拟中的外力处理方法和温度边界条件处理方法,用该模型成功地模拟了Benard热对流现象。     

大雷诺数Navier-Stokes方程的两水平亚格子模型稳定化方法

基于两重网格离散方法,提出三种求解大雷诺数定常Navier-Stokes方程的两水平亚格子模型稳定化有限元算法.其基本思想是首先在一粗网格上求解带有亚格子模型稳定项的Navier-Stokes方程,然后在细网格上分别用三种不同的校正格式求解一个亚格子模型稳定化的线性问题,以校正粗网格解.通过适当的稳定化参数和粗细网格尺寸的选取,这些算法能取得最优渐近收敛阶的有限元解.最后,用数值模拟验证三种算法的有效性.     

热声发动机的格子气模拟

在传统的9-bit格子气模型中引入了温度区的概念,并应用于热声发动机的模拟研究.利用改进后的格子气模型,模拟了热声谐振管中的自激振荡和二维温度场的分布及温度随时间的演化过程,同时,对热声板叠的长度和在声场中的位置对声幅的影响也进行了数值研究,所得结果对板叠的优化设计是有价值的.通过对模拟和实验结果的比较,验证了热声机格子气模型的有效性,表明格子气方法适用于热声模拟.     

凝固前沿和气泡相互作用的大密度比格子玻尔兹曼方法模拟

建立了二维双组分两相流的大密度比格子玻尔兹曼方法 (lattice Boltzmann method, LBM)模型. 该模型基于改进的Shan-Chen伪势多相流LBM模型, 结合采用不同时间步长的方法, 实现密度比达800以上的气液两相流模拟. 为了对模型进行验证, 模拟了在不同气液相互作用系数和密度比条件下气泡内外压力差与其半径之间的关系, 其结果满足Laplace定律. 将所建立的大密度比LBM与介观尺度的元胞自动机(cellular automaton, CA)和有限差分法(FDM)相耦合, 用LBM模拟气液两相流, 用CA方法模拟固相生长, 用有限差分法模拟温度场, 采用LBM-CA-FDM耦合模型对定向凝固过程中凝固前沿的气泡与液-固界面之间的相互作用进行模拟研究. 结果表明, 绝热气泡的存在影响了温度场分布, 使得凝固前沿接近气泡时, 液-固界面凸起, 在不同的固相生长速度条件下, 出现凝固前沿淹没气泡或气泡脱离凝固前沿的不同情况, 模拟结果与实验结果符合良好. 关键词： 格子玻尔兹曼方法 元胞自动机 凝固 气泡     

二维平板通道中流动与传热的格子-Boltzmann模拟

格子-Boltzmann数值模拟方法(LBM),在最近十几年来得到迅速发展。本文发展了LBM的流动与传热模型,并对二维平板通道中的流动与传热进行了模拟,采用密度分布函数得到速度场,用单独的内能分布函数得到温度场,并与传统FVM方法所得到的多个特征量结果进行了比较,模拟结果与FVM解均吻合很好。鉴于LBM边界条件处理简单和易于实施等特点,该方法可望成为求解流动与传热的一种有效数值模拟手段。     

格子气的声振荡衰减

采用格子气数值方法模拟了共振腔中气体声振荡衰减过程．计算结果表明：格子气中声振荡衰减的规律和经典理论结果一致；衰减系数随频率增加而减小，并且随密度增加而减小．该结果可以用来说明一些大学统计物理教科书中的一个经典例子存在不完善之处．本中采用了一种新的扭转9-bit格子气模型和并行计算方法，这些结果对今后研究格子气中的热声问题有参考价值．     

过渡区微尺度流动的有效黏性多松弛系数格子Boltzmann模拟

为提高采用二维九速离散速度模型的格子Boltzmann方法 (LBM)模拟微尺度流动中非线性现象的精度和效率,引入Dongari等提出的有效平均分子自由程对黏性进行修正(Dongari N,Zhang Y H,Reese J M2011 J.Fluids Eng.133 071101);并针对以往研究微尺度流动时采用边界处理格式含有离散误差的问题,采用多松弛系数格子Boltzmann方法结合二阶滑移边界条件,对微尺度Couette流动和周期性Poiseuille流动进行模拟,并将速度分布以及质量流量等模拟结果与直接模拟蒙特卡罗方法模拟数据、线性Boltzmann方程的数值解以及现有的LBM模型模拟结果进行对比.结果表明,相对于现有的LBM模型,引入新的修正函数所建立的有效黏性多松弛系数LBM模型有效提高了LBM模拟过渡区的微尺度流动中的非线性现象的能力.     

格子Boltzmann方法分布函数重构算子的应用

给出了格子Boltzmann方法(LBM)密度分布函数和温度分布函数的两个重构算子,解决了LBM与其它方法耦合的关键难题.构造了LBM与有限容积法(FVM)以及LBM与分子动力模拟方法(MD)的两个耦合模型.通过方腔自然对流以及平板通道内的泊肃叶流动对耦合模型进行验证.结果表明,基于重构算子的耦合模型可以正确地应用于L...     

低阶格式在大涡模拟计算中的适用性

采用三维Taylor-Green涡作为研究对象,利用工程中常用的低阶数值格式,研究格式本身的数值误差对大涡模拟计算的影响.结果表明:三种数值格式的数值耗散行为都与亚格子模型行为类似,即在小雷诺数下,流场比较光滑时,耗散很小,当雷诺数增加,流动转捩为湍流,流场梯度增大,耗散显著增大.对于MUSCL格式和二阶有界中心格式,在高雷诺数下,亚格子尺度模型没有明显改善计算结果,但也没有使计算结果恶化.中心格式相比其它两种格式,数值耗散最小,但是在高雷诺数湍流情况下,中心格式的数值耗散仍然主导了能量的耗散,再添加亚格子模型,计算结果反而变得稍差.对于工程中的低阶格式而言,采用中心格式计算大涡模拟是比较好的选择,而且在计算不存在稳定性问题时,采用不添加亚格子模型的隐式大涡模拟效果更好.     

基于修正格子Boltzmann方法的大雷诺数Herschel-Bulkley流动分析

传统LBM方法在用来分析大雷诺数非牛顿流体时,体现出较低的稳定性和精度,当逐步增大雷诺数到一定数值时,此种现象更为突出。文中针对这个问题,提出一种修正LBM可以有效提高大雷诺数的Herschel-Bulkley流体流动分析时的稳定性和精度,将Herschel-Bulkley流体的非牛顿性看作一项特殊的外力项,并将上述提出的方法应用于顶盖驱动流的数值模拟分析中,讨论了在剪切变稀和剪切增稠两种情况下,逐步增大雷诺数时流线图以及主涡中心位置的变化,结果证明提出的方法可以有效应用于大雷诺数Herschel-Bulkley流体流动的分析中。为了验证此方法的可行性,利用泊肃叶流的理论解与上述方法的数值解进行对比,并分析了初始屈服应力,幂律指数以及格子大小对LBM数值模拟结果的影响。     

Numerical analysis of the averaged flow field in a turbulent lattice Boltzmann simulation

A direct numerical simulation of a turbulent flow field with a lattice BGK method is presented. A spatial coarse graining of the numerical results is compared with the expected LBGK dynamics for a flow field on a reduced lattice size. This comparison permits to exhibit subgrid properties of the fluid which are not resolved on the coarse lattice. As expected from existing subgrid models, an effective viscosity can be measured that increases when the lattice is coarse grained. Turbulence models based on an effective viscosity are particularly interesting in a lattice Boltzmann simulation, due to the linearity of the propagation operator.     

Lattice Boltzmann computational fluid dynamics in three dimensions

The recent development of the lattice gas method and its extension to the lattice Boltzmann method have provided new computational schemes for fluid dynamics. Both methods are fully paralleled and can easily model many different physical problems, including flows with complicated boundary conditions. In this paper, basic principles of a lattice Boltzmann computational method are described and applied to several three-dimensional benchmark problems. In most previous lattice gas and lattice Boltzmann methods, a face-centered-hyper-cubic lattice in four-dimensional space was used to obtain an isotropic stress tensor. To conserve computer memory, we develop a model which requires 14 moving directions instead of the usual 24 directions. Lattice Boltzmann models, describing two-phase fluid flows and magnetohydrodynamics, can be developed based on this simpler 14-directional lattice. Comparisons between three-dimensional spectral code results and results using our method are given for simple periodic geometries. An important property of the lattice Boltzmann method is that simulations for flow in simple and complex geometries have the same speed and efficiency, while all other methods, including the spectral method, are unable to model complicated geometries efficiently.     

多孔介质模型在管壳式换热器数值模拟中的应用

本文详细讨论了多孔介质模型在管壳式换热器数值模拟中的应用,开发了一套能自动生成多孔介质特性参数的通用程序。该程序主要基于三维交错网格及SIMPLE算法,然后运用该模型,采用改进的κ-ε模型和壁面函数法,对换热器壳侧的湍流流动进行了数值模拟。计算结果与换热器冷态实验结果符合良好,表明该模型和计算方法是切实可行的。     

Lattice Boltzmann Simulation of Shear-Thinning Fluids

It is shown how shear-thinning flow can be simulated without the need for numerical differentiation by following a lattice Boltzmann approach. The basic idea of is to combine the Cross model of viscosity with a 3D multiple relaxation time lattice Boltzmann method and to extract the required velocity derivatives from intrinsic quantities of the lattice Boltzmann scheme. Computational results are presented for a simple benchmark and for the simulation of liquid composite moulding.     

Lattice Bhatnagar-Gross-Krook Simulations in 2-D Incompressible Magnetohydrodynamics

Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.     

Lattice Bhatnagar-Gross-Krook Simulations in 2-D Incompressible Magnetohydrodynamics

Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice.Bhatnagar-Gross-Krook （LBGK） model for two-dimensional incompressible magnetohydrodynamics （IMHD） is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.     

Entropic lattice Boltzmann models for hydrodynamics in three dimensions

Efficient, nonlinearly stable entropic lattice Boltzmann models for computational fluid dynamics are presented. A new method of fast evaluation of equilibria to machine precision is proposed. Analytical solution is found for the collision step which guarantees stability and thermodynamic consistency of the scheme. As an example, a novel 15-velocity lattice Boltzmann model is derived and validated with a simulation of a three-dimensional backward-facing step flow.     

Simulation of natural convection under high magnetic field by means of the thermal lattice Boltzmann method

The thermal lattice Boltzmann method (TLBM), which was proposed by J. G. M. Eggels and J. A. Somers previously, has been improved in this paper. The improved method has introduced a new equilibrium solution for the temperature distribution function on the assumption that flow is incompressible, and it can correct the effect of compressibility on the macroscopic temperature computed. Compared to the previous method, where the half-way bounce back boundary condition was used for non-slip velocity and temperature, a non-equilibrium extrapolation scheme has been adopted for both velocity and temperature boundary conditions in this paper. Its second-order accuracy coincides with the ensemble accuracy of lattice Boltzmann method. In order to validate the improved thermal scheme, the natural convection of air in a square cavity is simulated by using this method. The results obtained in the simulation agree very well with the data of other numerical methods and benchmark data. It is indicated that the improved TLBM is also successful for the simulations of non-isothermal flows. Moreover, this thermal scheme can be applied to simulate the natural convection in a non-uniform high magnetic field. The simulation has been completed in a square cavity filled with the aqueous solutions of KCl (11wt%), which is considered as a diamagnetic fluid with electrically low-conducting, with Grashof number Gr=4.64× 10^4 and Prandtl number Pr=7.0. And three cases, with different cavity locations in the magnetic field, have been studied. In the presence of a high magnetic field, the natural convection is quenched by the body forces exerted on the electrically low-conducting fluids, such as the magnetization force and the Lorentz force. From the results obtained, it can be seen that the quenching efficiencies decrease with the variation of location from left, symmetrical line, to the right. These phenomena originate from the different distributions of the magnetic field strengths in the zones of the symmetrical central line of the magnetic fields. The results are also compared with those without a magnetic field. Finally, we can conclude that the improved TLBM will enable effective simulation of the natural convection under a high magnetic field.     

Non-negativity and stability analyses of lattice Boltzmann method for advection–diffusion equation

Stability is one of the main concerns in the lattice Boltzmann method (LBM). The objectives of this study are to investigate the linear stability of the lattice Boltzmann equation with the Bhatnagar–Gross–Krook collision operator (LBGK) for the advection–diffusion equation (ADE), and to understand the relationship between the stability of the LBGK and non-negativity of the equilibrium distribution functions (EDFs). This study conducted linear stability analysis on the LBGK, whose stability depends on the lattice Peclet number, the Courant number, the single relaxation time, and the flow direction. The von Neumann analysis was applied to delineate the stability domains by systematically varying these parameters. Moreover, the dimensionless EDFs were analyzed to identify the non-negative domains of the dimensionless EDFs. As a result, this study obtained linear stability and non-negativity domains for three different lattices with linear and second-order EDFs. It was found that the second-order EDFs have larger stability and non-negativity domains than the linear EDFs and outperform linear EDFs in terms of stability and numerical dispersion. Furthermore, the non-negativity of the EDFs is a sufficient condition for linear stability and becomes a necessary condition when the relaxation time is very close to 0.5. The stability and non-negativity domains provide useful information to guide the selection of dimensionless parameters to obtain stable LBM solutions. We use mass transport problems to demonstrate the consistency between the theoretical findings and LBM solutions.