统一气体动理学方法研究进展

在临近空间高超声速飞行器气动载荷、航天飞行器变轨/调姿、微尺度元器件传质/传热等科学和工程实践中，存在着大量的时序多流域（多尺度）流动问题以及位于单一流场中的复杂多流域问题（局部稀薄问题），对数值预测工作提出挑战.因此，近年来从介观气体动理学基础上发展出了一大类将连续流与稀薄流进行统一计算的高效数值方法，包括确定论形式的UGKS，GKUA和DUGKS方法，以及粒子形式的USP-BGK和UGKWP方法.文章围绕着确定论和统计粒子两类统一方法的最新研究进展进行回顾和分析，重点关注在每种方法中全流域统一性质的来源与实现方式、目前已取得的关键进展以及该方法的扩展性和应用价值.      

表征体元尺度渗流的离散统一动理学格式

结合表征体元尺度的通用渗流模型,提出离散统一动理学格式（DUGKS）渗流方法,分别用均匀网格和非均匀网格计算二维Poiseuille、Couette、方腔流等经典渗流问题,检验DUGKS渗流方法的有效性和非均匀网格应用的优势,将DUGKS渗流方法应用到裂缝系统中.     

气体动理学格式模拟多孔介质流动的可行性

将气体动理学格式（GKS）拓展到模拟多孔介质内的低速渗流,并检验在孔隙尺度上模拟不可压缩低速流动的可行性与有效性.结果表明：GKS具有二阶空间精度,能够较精确地计算多孔介质的渗透率;相比于单松弛格子玻尔兹曼方法,GKS能够精确实现壁面无滑移边界条件,从而正确反映渗透率与黏性无关的特性;对于Berea砂岩切片结构中的复杂流动,模拟结果与实验吻合较好,能较精确地计算渗透率.给出GKS模拟达西渗流的马赫数选取准则,为研究多孔介质流动提供新的工具.     

精细平衡气体动理学格式

流体系统在重力作用下,流体压力可与重力相平衡,达到静力平衡状态.常规的有限差分和有限体积方法无法在离散尺度上保持这种平衡态,常常产生虚假速度等非物理现象.通过将重力源项的体积分改写为网格界面值的加权平均,实现离散条件下压力与重力的精细平衡,得到一种Navier-Stokes （NS）方程的精细平衡气体动理学格式.该格式可以在机器精度上精确地保持等温条件下的静力平衡态以及捕捉平衡态附近的小扰动传播.同时,该格式还能求解自然界中更常见的非等温平衡态.此类平衡态除了要求静力平衡还要求热流平衡.利用提出的格式求解NS方程,可以得到静止（机器精度下的零速度）的非等温平衡态,并且密度和温度分布都具有二阶精度.通过多个算例验证格式的有效性,表明该格式可更好地模拟重力场下的温度、密度的分层流动.     

圆柱界面不稳定性的多组分气体动理学数值计算

在假定单元内各组分同温同速的条件下,采用气体动理学格式(Gas-Kinetic Scheme,GKS)对空气/He和空气/R22圆柱界面不稳定性进行了数值计算,得到不同时刻的密度分布以及界面上特征位置的位移历史和平均速度。当激波穿过界面后,界面上特征位置的位移随时间逐渐增大,特征位置的平均速度与前人的实验结果和数值模拟结果吻合很好。对比结果表明,从微观气体运动角度出发的GKS方法对于界面不稳定性问题具有良好的模拟能力。     

指数型谐振管的二维气体动理学格式模拟

本文构造了适合模拟变截面谐振管的非结构三角形网格上的二维气体动理学BGK模型,采用该模型研究了包括圆直谐振管在内的八种不同形状的指数型谐振管内声场及流场的分布,分析了谐振管形状对压力分布和瞬时流场的影响。研究发现,从抑制激波、高次谐波以提高压力振幅和压比方面综合分析,形状参数m=2.2的指数型谐振管具有更好的性能。研究中也发现了一些新的物理现象,并对这些现象做了详细的解释。     

基于SIMPLE算法的时间离散格式比较

本文在具有高精度空间离散格式的SIMPLE算法计算代码的基础上研究比较了非稳态计算的时间离散格式.分别采用一阶全隐和二阶全隐格式对非稳态的控制方程进行离散,通过方腔驱动流和圆柱绕流两个经典算例的分析,比较了这两种格式在计算精确性和计算效率等方面的性能。     

多车种LWR交通流模型的半离散中心迎风格式

对多车种LWR交通流模型,给出一种半离散中心迎风格式,该格式以五阶WENO-Z重构和半离散中心迎风数值通量为基础.WENO-Z重构方法的引入提高了格式的精度,并保证格式具有基本无振荡的性质.时间的离散采用保持强稳定性的Runge-Kutta方法.通过数值算例验证了格式的有效性.     

离散速度方向模型在微尺度气体流动中的应用

离散速度方向模型是一种简化Boltzmann方程的新方法。该方法通过减少Boltzmann方程的维数来降低数值求解的计算量。在DVD模型中,分子速度的方向是离散的,而分子的速率仍然是连续的,这样就可以用一组三维的速率分布函数来代替Boltzmann方程中六维的速度分布函数。由于减少了三个动量维,同Boltzmann方程相比,DVD模型的数值计算量可以降低几个数量级。本文用数值的方法对DVD模型进行了研究。数值结果显示,在广泛的Knudsen数下,DVD方法可给出精确的计算结果。同线性化Boltzmann方程的计算结果相比,最大的误差不超过6%,在连续介质领域中,误差甚至不超过1%。     

Free-Energy-Based Discrete Unified Gas Kinetic Scheme for van der Waals Fluid

The multiphase model based on free-energy theory has been experiencing long-term prosperity for its solid foundation and succinct implementation. To identify the main hindrance to developing a free-energy-based discrete unified gas-kinetic scheme (DUGKS), we introduced the classical lattice Boltzmann free-energy model into the DUGKS implemented with different flux reconstruction schemes. It is found that the force imbalance amplified by the reconstruction errors prevents the direct application of the free-energy model to the DUGKS. By coupling the well-balanced free-energy model with the DUGKS, the influences of the amplified force imbalance are entirely removed. Comparative results demonstrated a consistent performance of the well-balanced DUGKS despite the reconstruction schemes utilized. The capability of the DUGKS coupled with the well-balanced free-energy model was quantitatively validated by the coexisting density curves and Laplace’s law. In the quiescent droplet test, the magnitude of spurious currents is reduced to a machine accuracy of 10−15. Aside from the excellent performance of the well-balanced DUGKS in predicting steady-state multiphase flows, the spinodal decomposition test and the droplet coalescence test revealed its stability problems in dealing with transient flows. Further improvements are required on this point.     

Three-Dimensional Simulations of Anisotropic Slip Microflows Using the Discrete Unified Gas Kinetic Scheme

The specific objective of the present work study is to propose an anisotropic slip boundary condition for three-dimensional (3D) simulations with adjustable streamwise and spanwise slip length by the discrete unified gas kinetic scheme (DUGKS). The present boundary condition is proposed based on the assumption of nonlinear velocity profiles near the wall instead of linear velocity profiles in a unidirectional steady flow. Moreover, a 3D corner boundary condition is introduced to the DUGKS to reduce the singularities. Numerical tests validate the effectiveness of the present method, which is more accurate than the bounce-back and specular reflection slip boundary condition in the lattice Boltzmann method. It is of significance to study the lid-driven cavity flow due to its applications and its capability in exhibiting important phenomena. Then, the present work explores, for the first time, the effects of anisotropic slip on the two-sided orthogonal oscillating micro-lid-driven cavity flow by adopting the present method. This work will generate fresh insight into the effects of anisotropic slip on the 3D flow in a two-sided orthogonal oscillating micro-lid-driven cavity. Some findings are obtained: The oscillating velocity of the wall has a weaker influence on the normal velocity component than on the tangential velocity component. In most cases, large slip length has a more significant influence on velocity profiles than small slip length. Compared with pure slip in both top and bottom walls, anisotropic slip on the top wall has a greater influence on flow, increasing the 3D mixing of flow. In short, the influence of slip on the flow field depends not only on slip length but also on the relative direction of the wall motion and the slip velocity. The findings can help in better understanding the anisotropic slip effect on the unsteady microflow and the design of microdevices.     

辐射流体力学的分子动理学自适应加密方法(英文)

通过构造新的平衡分布函数和结合分区自适应网格加密方法,对不带扩散项的平衡辐射流体力学方程,构造二阶的分子动理学BGK-AMR格式.一方面在关心的计算区域中局部加密计算网格,提高计算精度的同时大大节省了计算网格数量和计算时间;另一方面,不同于已有的参数强耦合平衡分布函数,新构造的平衡分布函数中各参数不相互依赖,简化了辐射流体力学分子动理学格式的计算.一维和二维的数值算例显示了格式的性能.     

Experimental and Numerical Investigation of Convective Heat Transfer in a Multiple-ventilated Enclosure with Discrete Heat Sources

The experimental and numerical investigation of convective heat transfer in a rectangular cavity of aspect ratio (L/H) = 5 has been presented in this study. The comparison of experimental results is done with a two-dimensional numerical model considered with steady and turbulent flow conditions. Six different arrangements (bottom/bottom/bottom, top/top/top, right/top/left, bottom/top/right, bottom/top/left, and bottom/right/left) were considered. The lowest and highest hotspot temperatures were observed in bottom/bottom/bottom and bottom/right/left arrangements, respectively. For similar configurations, the bottom/bottom/bottom arrangement displays better heat transfer performance, while heat transfer performance is inferior for the bottom/right/left arrangement than all other configurations.     

A Lattice Boltzmann Kinetic Model for Microflow and Heat Transfer

In this paper, we propose a lattice Boltzmann BGK model for simulation of micro flows with heat transfer based on kinetic theory and the thermal lattice Boltzmann method (He et al., J. Comp. Phys. 146:282, 1998). The relaxation times are redefined in terms of the Knudsen number and a diffuse scattering boundary condition (DSBC) is adopted to consider the velocity slip and temperature jump at wall boundaries. To check validity and potential of the present model in modelling the micro flows, two two-dimensional micro flows including thermal Couette flow and thermal developing channel flow are simulated and numerical results obtained compare well with previous studies of the direct simulation Monte Carlo (DSMC), molecular dynamics (MD) approaches and the Maxwell theoretical analysis     

Radiative-Convective Heat Transfer in Discharge Chamber at Turbulent Gas Flow

In the paper radiative-convective heat transfer in electric arc flowed through by Ar in the discharge chamber is studied. The equation system for heat, mass and momentum transfer in boundary layer approximation is considered, and the turbulence model with radiation pulsation and electrodynamic values is suggested. By solution of the equation system with the help of finite differences method distributions of temperature, heat flows and turbulent transfer coefficients over chamber length were obtained. The radiation and turbulence influence on the electric arc characteristics is analysed.