一维元胞自动机随机交通流模型的宏观方程分析

在一维局部作用元胞自动机交通流模型中引入刹车噪声与产生、消失概率,得到一完全随机的元胞自动机交通流模型.利用玻耳兹曼近似,建立了该模型的宏观动力学方程,并对宏观方程在特殊条件下的解进行了理论分析和计算机模拟. 关键词： 元胞自动机 交通流 Burgers方程 激波     

用格子Boltzmann模型模拟激波现象

根据微观和宏观之间的质量、动量、能量守恒准则,建立了一个两维的D2Q13格子Boltzmann模型,可从该D2Q13模型出发推导出宏观的流体力学方程,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,用该模型对冲击波在障碍物表面上的折射和反射现象的数值模拟都得到了比较满意的结果,而且数值稳定性也很好.证明了D2Q13模型的适宜性 关键词： Boltzmann模型 分布函数 冲击波 流体力学方程     

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     

Burgers-Korteweg-de Vries复合方程的格子Boltzmann方法模拟

针对Burgers-Korteweg-de Vries(cBKdV)复合方程提出一种格子Boltzmann模型.通过恰当地处理色散项u_xxx并运用Chapman-Enskog展开从格子Boltzmann方程推导出宏观方程,从而得到联系微观量与宏观量的局部平衡分布函数.对不同微分方程进行数值实验,数值解与解析解非常吻合,相比于其它数值结果,该格子Boltzmann模型的数值结果更精确,说明该数值模型的高效性.     

Burgers-Korteweg-de Vries复合方程的格子Boltzmann方法模拟（英文）

针对Burgers-Korteweg-de Vries(cBKdV)复合方程提出一种格子Boltzmann模型.通过恰当地处理色散项uxxx并运用Chapman-Enskog展开从格子Boltzmann方程推导出宏观方程,从而得到联系微观量与宏观量的局部平衡分布函数.对不同微分方程进行数值实验,数值解与解析解非常吻合,相比于其它数值结果,该格子Boltzmann模型的数值结果更精确,说明该数值模型的高效性.     

三维颗粒有序列阵多孔介质湍流方程改进研究

本文首先对三维颗粒有序列阵孔隙单元内的湍流特性进行数值研究,并在此基础上采用体积平均方法对多孔介质宏观湍流方程进行改进。结果表明:三维颗粒有序列阵内的湍流特性与二维棒束模型存在较大差异,在相同雷诺数及孔隙率下,颗粒有序列阵多孔介质内由颗粒骨架导致的宏观湍动能及耗散率附加净产生项明显偏低;传统基于二维棒束模型得到的多孔介质宏观湍流模型(N-K模型)高估了湍流方程中k_∞/|V_D|~2和ε~∞H/|V_D|~3项的值,本文对此进行了修正和改进。     

一维空间Riesz分数阶对流扩散方程的格子Boltzmann方法

建立格子Boltzmann方法（LBM）的D1Q3演化模型,研究一类Riesz空间分数阶对流扩散方程的数值求解问题。对分数阶微积分算子中的积分项离散化处理,得到逼近的标准对流扩散方程。结合Taylor展式和Chapman-Enskog多尺度展开技术得到模型的各个方向上的平衡态分布函数,通过D1Q3演化模型正确恢复所要求解的宏观方程。数值算例验证该方法的有效性。     

不同精度格式的格子Boltzmann热模型的传热分析

通过在格子Boltzmann (LBM)热模型中添加参数项,使得在对应的宏观传热方程中,消除了一阶非线性误差项,具备二阶精度.通过Rayleigh-Benard对流数值试算,初步探索该二阶精度格式及其对应的一阶精度格式三个热模型的传热特征和适应性,并做出相应对比分析.针对一二阶精度模型在Ra数极高或热传导系数极大时,Nu数的计算与经验值相比出现较大偏差,分析LBM对应宏观热传导方程的截断误差后,在平衡分布函数中引进一个调节因子.通过调节对应宏观传热方程的截断误差项系数,校正Nu数的计算偏差,提高模拟精度,拓展模拟范围,增强了LBM作为一个数值方法在传热中的适应性.     

弱相对论电子等离子体的宏观非寻常模稳定性

本文利用宏观冷流体模型及麦克斯韦方程研究了磁约束在圆柱形导体容器内的弱相对论电子等离子体的宏观非寻常模稳定性，寻出了槽纹扰动下（ｋｚ＝０）的普遍本征方程，分析中包含平衡自洽场。在低频扰动情况下，简化了本征方程，并仔细研究了电子等离子体在矩形分布下的稳定性质。     

基于宏观方程数值本构关系的气体动理论加速收敛方法

在跨流域复杂流动问题的模拟中,基于求解速度分布函数演化方程的气体动理论方法的效率问题一直受到工程应用领域关注.研究提升气体动理论方法在定常流动模拟中的计算效率具有重要意义.为了提升定常流动计算收敛速度,本文提出了一种耦合宏观方程数值本构关系的气体动理论加速收敛方法.通过求解Boltzmann模型方程,将应力、热流高阶项的数值解与宏观方程耦合,实现了宏观方程的封闭;另一方面,宏观方程的计算结果被用来更新Boltzmann模型方程的当地平衡态速度分布函数中的宏观物理量,以此构造求解Boltzmann模型方程的全隐式数值格式.通过跨流域方腔流动、超声速圆柱绕流及双圆柱干扰绕流案例的数值模拟,对方法进行了广泛考核.计算结果与常规气体动理论统一算法、直接模拟蒙特卡罗法符合良好,证明该方法很好地描述了稀薄流动中的非线性本构关系,以及激波、强壁面剪切、流动分离等强非平衡特征.进一步,对于低努森数Kn的流动,方法能显著加速收敛过程,提升计算效率;随着努森数Kn增加,气体对流输运效应减弱,方法的加速收敛效果降低.与此同时,如何减少内迭代耗时,进一步提升效率有待更多研究.     

Two velocity difference model for a car following theory

In the light of the optimal velocity model, a two velocity difference model for a car-following theory is put forward considering navigation in modern traffic. To our knowledge, the model is an improvement over the previous ones theoretically, because it considers more aspects in the car-following process than others. Then we investigate the property of the model using linear and nonlinear analyses. The Korteweg-de Vries equation (for short, the KdV equation) near the neutral stability line and the modified Korteweg-de Vries equation (for short, the mKdV equation) around the critical point are derived by applying the reductive perturbation method. The traffic jam could be thus described by the KdV soliton and the kink-anti-kink soliton for the KdV equation and mKdV equation, respectively. Numerical simulations are made to verify the model, and good results are obtained with the new model.     

电光调QCO_2激光器的六温度模型理论与速率方程理论比较分析

分别利用速率方程理论和六温度模型理论对Q开关CO2 激光器动力学过程进行了理论分析比较 ,实验上测得电光调Q射频波导CO2 激光器脉冲激光建立时间及峰值功率与速率方程理论和六温度模型理论计算结果一致 .但速率方程理论计算的激光脉冲宽度较“窄” ,并且几乎没有拖尾 ,而六温度模型理论计算的脉冲激光波形有明显的拖尾 ,符合实际测量的波形 .另外 ,六温度模型理论可以全面反映激光器工作气体中不同分子能级的能量转移过程 ,因此六温度模型理论分析更全面     

染料激光色立方模型的第一通过时间分布

本文首先把Ｊｕｎｇ和Ｈａｎｇｇｉ提出的统一色噪声近似推广到多维情形，从而导出了这一近似下单模染料激光色立方模型的朗之万方程和福克－普朗克方程；得到了该模型第一通过时间分布的平均值，协方差和偏斜率的近似解析式并将其和数值模拟进行比较。     

Image reconstruction in diffuse optical tomography using the coupled radiative transport-diffusion model

The coupled radiative transport-diffusion model can be used as light transport model in situations in which the diffusion equation is not a valid approximation everywhere in the domain. In the coupled model, light propagation is modelled with the radiative transport equation in sub-domains in which the approximations of the diffusion equation are not valid, such as within low-scattering regions, and the diffusion approximation is used elsewhere in the domain. In this paper, an image reconstruction method for diffuse optical tomography based on using the coupled radiative transport-diffusion model is developed. In the approach, absorption and scattering distributions are estimated by minimising a regularised least-squares error between the measured data and solution of the coupled model. The approach is tested with simulations. Reconstructions from different cases including domains with low-scattering regions are shown. The results show that the coupled radiative transport-diffusion model can be utilised in image reconstruction problem of diffuse optical tomography and that it produces as good quality reconstructions as the full radiative transport equation also in the presence of low-scattering regions.     

Sigma model for Ernst equation: Lax representation,Bäcklund transformation and divergence-free currents

A sigma model associated with the Ernst equation is derived. This sigma model is described by the Belinsky-Zakharov-type completely integrable equation and is formally equivalent to the usual sigma model in curved two-dimensional space. The corresponding Lax representation, BÄcklund transformation, and divergence-free currents are obtained.     

电光调QCO2激光器的六温度模型理论与速率方程理论比较分析

分别利用速率方程理论和六温度模型理论对Q开关CO₂激光器动力学过程进行了理论分析比较,实验上测得电光调Q射频波导CO₂激光器脉冲激光建立时间及峰值功率与速率方程理论和六温度模型理论计算结果一致.但速率方程理论计算的激光脉冲宽度较“窄”,并且几乎没有拖尾,而六温度模型理论计算的脉冲激光波形有明显的拖尾,符合实际测量的波形.另外,六温度模型理论可以全面反映激光器工作气体中不同分子能级的能量转移过程,因此六温度模型理论分析更全面 关键词： 2激光器')" href="#">电光调QCO₂激光器 六温度模型理论 速率方程理论     

两相湍流色噪声扩维法PDF模型及数值模拟

由颗粒运动的朗之万方程出发,对流体脉动速度采用扩维方法,得到两个不同层次的PDF输运方程.通过对颗粒运动方程求解和高斯分布假设,解决PDF方程的封闭问题,获得颗粒二阶矩模型,然后将颗粒应力方程简化成代数方程,建立代数应力模型.将对流扩散方程的有限分析法运用到求解两相流模型中,对壁面两相射流进行数值模拟,对比分析数值结果与实验结果.     

Kinetic theory based lattice Boltzmann equation with viscous dissipation and pressure work for axisymmetric thermal flows

A lattice Boltzmann equation (LBE) for axisymmetric thermal flows is proposed. The model is derived from the kinetic theory which exhibits several features that distinguish it from other previous LBE models. First, the present thermal LBE model is derived from the continuous Boltzmann equation, which has a solid foundation and clear physical significance; Second, the model can recover the energy equation with the viscous dissipation term and work of pressure which are usually ignored by traditional methods and the existing thermal LBE models; Finally, unlike the existing thermal LBE models, no velocity and temperature gradients appear in the force terms which are easy to realize in the present model. The model is validated by thermal flow in a pipe, thermal buoyancy-driven flow, and swirling flow in vertical cylinder by rotating the top and bottom walls. It is found that the numerical results agreed excellently with analytical solution or other numerical results.     

Equation of State of Quark-Gluon Plasma Using a Simple Statistical Model

A statistical model is discussed to study the equation of state with the finite size effect. Finite-size effects are taken into account by using Multiple Reflection Expansion (MRE). It modifies the free energy by expanding it, in volume, surface and curvature terms. To incorporate finite size effects in the calculation of equation of state, model needs to consider the surface part as effective contribution factor. The equation of state produced by the model matches well with the lattice results.     

Spline-Galerkin Solution of Dynamic Equations for Particle Comminution and Collection

The population balance equation is solved for particles undergoing a combination of growth, comminution, and collection. The approximation method is to use a weighted Galerkin technique with cubic B-splines and an implicit scheme for solving the system of ordinary differential equations. The cubic splines are defined on a graded mesh. The performance of the method is investigated by solving a model problem with simple but nonsmooth kernels. The weight function is chosen so that singularities in the equation can be easily treated. A self-similar solution for comminuted particles is shown to be a useful representation for the solution of the population balance equation provided that this equation is solved over a sufficiently long time interval. Stationary solutions of the equation are obtained for a model that describes both particle comminution and collection.