相对论磁化等离子体的广义玻尔兹曼方程碰撞项

本文采用Ｋｌｉｍｏｎｔｏｖｉｃｈ方法导出了相对论磁化等离子体的广义玻尔兹曼方程碰撞项，计算出带电粒子间的感应电磁力对碰撞项的贡献。     

用格子Boltzmann方法模拟MKDV方程

用精确到0(ε)的5速格子Boltzmann模型模拟MKDV方程:u_t+6u²u_x+u_xxx=0,并与MKDV方程的孤子解比较,二者精确吻合. 关键词： 格子Boltzmann方法 MKDV方程 孤子解     

SOME PROGRESS IN THE LATTICE BOLTZMANN MODEL

A lattice Boltzmann equation model has been developed by using the equilibrium distribution function of the Maxwell－Boltzmann-like form, which is third order in fluid velocity u_α. The criteria of energy conservation between the macroscopic physical quantities and the microscopic particles are introduced into the model, thus the thermal hydrodynamic equations containing the effect of buoyancy force can be recovered in terms of the Taylor and Chapman－Enskog asymptotic expansion methods. The two-dimensional thermal convection phenomena in a square cavity and between two concentric cylinders have been calculated by implementing a heat flux boundary condition. Both numerical results are in good agreement with the conventional numerical results.     

格子Boltzmann方法求解Burgers方程

众所周知,格子方法（包括格子气和格子Ｂｏｌｔｚｍａｎｎ方法）在计算物理领域取得巨大进展。与之形成鲜明对比,格子方法的数学理论始终处于停滞前的状况。为求解Ｂｕｒｇｅｒｓ方程,一类带有ＢＧＫ模型格子方法被构造出来,经过变量替换,发现他们属于三层非性差分方法。使用极值原理,给出此类格式稳定性的严格证明,最后,从数值实验中可以看出,使用ＬＢＭ得到的结果,与经典二阶守恒差分方法的结果符合得非常好。     

用格子Boltzmann方法模拟高雷诺数下的热空腔黏性流

对13速六方格子Bhatnagar-Gross-Krook模型进行改进,适当地选取弛豫时间τ和k,使得热流体的切黏滞系数μ与热导系数λ只与内能有关,流体的Prandtl数可调.用该模型模拟了高雷诺数下的各种边界空腔流 关键词： 格子Boltzmann方法 Bhatnagar-Gross-Krook模型 Prandtl数 空腔流     

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.     

三维十五点格子Boltzmann模型仿真

格子气和格子Ｂｏｌｔｚｍａｎｎ方法的迅速发展提供了一类求解流体力学问题的新方法。格子Ｂｏｌｔｚｍａｎｎ方法在保留了格子气模型优点的同时,克服了它的不足之处。本文讨论了一种三维十五点格子Ｂｏｌｔｚｍａｎｎ模型,通过选择适当的平衡分布及参数,并用Ｃｈａｐｍａｎ－Ｅｎｓｋｏｇ展开和多尺度技术导出了Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程．在微机上模拟了工程中比较常见的管排绕流问题,并与实验观察到的结果进行了比较,结果表明该模型能较好的模拟复杂流动现象,并具有较好的工程应用背景。     

十三点格子Boltzmann模型仿真

格子气和格子Boltzmann方法的迅速发展提供了一类求解流体力学问题的新方法。格子Boltzmann方法在保留了格子气模型优点的同时,克服了它的不足之处。本文讨论了一种三迭加HPP十三点模型,通过选择适当的平衡分布及参数,并用Chapman－Enskog展开和多尺度技术导出了Navier－Stokes方程。在微机上模拟了空腔流的流动问题,并与传统方法的计算结果进行了比较,结果表明该模型能较好的模拟复杂流动现象,并具有较好的工程应用背景。     

振荡流共轭换热格子-Boltzmann模拟

振荡流共轭换热现象广泛存在于热声热机等工程应用中.基于双分布格子-Boltzmann模型,对平行平板间振荡流共轭换热进行了数值模拟.通过假定共轭界面处流体和固体的未知内能分布函数均为对应的平衡态滑移修正格式,提出了一种处理共轭换热边界的新方法.模拟结果表明,该方法可以保证共轭界面上温度连续和热流连续.分析了不同流体与固体导热系数比情况下振荡流共轭换热的速度场、温度场以及热流分布的特点.     

梯度磁场下磁流体三维结构的格子-Boltzmann方法模拟

考虑磁性颗粒受到的各种内力与外力包括重力、布朗力、van der、Waaks力、磁偶极-偶极作用力以及外磁场作用力,建立了描述磁流体结构的两相格子-Boltzmann三维模型,对外加梯度磁场条件下磁流体的介观结构进行了模拟.模拟结果表明:外加梯度磁场时磁流体粒子沿梯度方向聚集并出现分层现象,且随时间推移和外加磁场增大,分层现象越来越明显.     

LATTICE BOLTZMANN EQUATION MODEL IN THE CORIOLIS FIELD

In a large-scale field of rotational fluid, various unintelligible and surprising dynamic phenomena are produced due to the effect of the Coriolis force. The lattice Boltzmann equation (LBE) model in the Coriolis field is developed based on previous works.^[1-4] Geophysical fluid dynamics equations are derived from the model. Numerical simulations have been made on an ideal atmospheric circulation of the Northern Hemisphere by using the model and they reproduce the Rossby wave motion well. Hence the applicability of the model is verified in both theory and experiment.     

利用多松弛格子Boltzmann方法预测多孔介质的渗透率

多孔介质内的流动问题在工程热物理领域有着重要的研究价值和应用背景。本文利用多松弛格子Boltzmann方法详细预测了两种二维多孔介质中的渗透率。研究结果表明:一方面,多松弛模型可以用来克服由单松弛模型带来的一些不足;另一方面,借助于达西定律,多松弛模型可以准确预测多孔介质的渗透率,并将计算结果与已有文献做了对比。     

用格子Boltzmann模型模拟非等温流场

根据微观和宏观之间的质量、动量、能量守恒准则和在原格子Boltzmann模型基础上,建立了几个新的格子Boltzmann模型,使得在外力场中的格子Boltzmann模型得到进一步完善.通过还原宏观流体力学方程,捕捉到了浮力强迫系数与Grashof数之间的关系.所得动量方程和Navier Stokes方程相比,在黏性输运项上有明显的改进,说明黏性应力不但与流体的速度梯度和流体的压缩性有关,而且还与非定常的内能梯度和动量通量有关.该模型对非等温流场的数值结果证明了其具有很好的数值稳定性和适用性. 关键词： Boltzmann模型 平衡分布函数 流体力学方程     

A study on the inclusion of body forces in the lattice Boltzmann BGK equation to recover steady-state hydrodynamics

When the lattice Boltzmann (LB) method is used to solve hydrodynamic problems containing a body force term varying in space and/or time, its modelling at the mesoscopic scale must be verified in terms of consistency in order to avoid the appearance of non-hydrodynamic error terms at the macroscopic scale. In the present work it is shown that the modelling of spatially varying steady body force terms in the LB equation must be different from the time-dependent case, when a steady-state flow solution is sought. For that, the Chapman-Enskog analysis is used to derive the LB body force model for the LB BGK equations in a steady-state flow problem. The theoretical findings are supported by numerical tests performed on two different 2D steady-state laminar flows driven by spatially varying body forces with known analytical solutions.     

A Discrete Effect of the Thermal Lattice BGK Model

In this article, a discrete effect in the thermal Lattice BGK two-speed model is studied. These effects are due to the non-equilibrium state in the particle distribution function, and the non-equilibrium occurs near walls. The mechanism of the LBM counterpart of the thermal creep flow, which appears due to the temperature gradient of the boundary in rarefied gases, is clarified analytically and numerical calculations are performed for some cases. A technique for eliminating this effect is also shown.     

玻耳兹曼分布定律对固相表面短程引力场的应用

把玻耳兹曼分布定律应用于固相表现短程引力场并结合平均的概念给出了范德瓦耳斯方程,讨论了固相表现短程引力场对固－气相间压力的影响。     

类氖锗基态到n＝3精细能级的碰撞激发强度

使用扭曲波方法计算了Ｇｅ￣（２２＋）从基态到ｎ＝３精细能级的碰撞强度，考察了不同组态以及相对论修正对碰撞强度的影响，并与平面波，库仑波和其它扭曲波方法计算的结果进行了比较。     

A higher order lattice BGK model for simulating some nonlinear partial differential equations

In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux + βunux - γuxx + δuxxx = F(u). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective.     

一个不容忽视的教学问题——巧用柯尼希定理求解两体碰撞

从柯尼希定理出发,给出了两体碰撞前后的机械能关系,并以两个具体习题为例,说明了利用柯尼希定理求解两体碰撞问题的方法,要比用动量守恒结合能量守恒的方法更为简洁、可行.揭示了加强柯尼希定理的习题教学对培养学生一题多解的发散思维能力的重要性.     

二维氢原子的相对论修正

求解了二维氢原子的Ｄｉｒａｃ方程,得到了精确的相对论能级与波函数,并详细讨论了非相对论极限。