硬球-拟颗粒耦合模拟超声速流动

超声速流动广泛存在于航天航空和能源动力等领域,其中连续介质假设往往不再适用,需要充分考虑介质的离散性质。但传统上基于软球模型的分子动力学(MD)方法对于流动过程的模拟计算量过大,难以实际应用。本文利用硬球-拟颗粒耦合方法克服了软球MD方法计算量大和硬球MD方法可扩展性差的缺点,高效实现了超声速流动的微观离散模拟。通过超声速单球绕流和充气式返回舱实验装置等算例表明了该方法模拟含激波等剧烈变化的流场的可行性,以及在航空航天等工程领域的应用前景。     

乏燃料组件跌落速度的理论计算和数值模拟

针对乏燃料组件在乏燃料池的水中吊运时有可能发生跌落的情况,通过理论近似解和CFD数值模拟两种方法计算乏燃料组件跌落速度.结果表明两种方法得到的跌落速度相近,最大误差小于5%,都可以用于跌落过程的模拟;采用CFD数值模拟还可以得到乏燃料组件下降过程中周围流场和压强的变化.虽然乏燃料组件的跌落速度逐渐增大,但跌落加速度变化不大,表明水对组件的阻力影响较小.     

碰撞C20-C20富勒烯分子的聚合与分裂

针对碳富勒烯制备过程中普遍存在的碳原子团簇与碳原子团簇的相撞、聚合与生长现象,采用分子动力学与量子力学相结合的方法,对C20富勒烯分子之间碰撞后的聚合与分裂过程进行了理论模拟。模拟结果表明,(1)当碰撞速度较小时,分子间发生弹性碰撞;当碰撞速度较高时,分子间发生聚合;当碰撞速度非常高时,分子间碰撞后发生分裂。(2)C20分子碰撞后的聚合与分裂行为,不仅与分子之间的初始碰撞速度有关,而且还与分子的碰撞形式有关。     

不同错开位置锯齿翅片热力特性的三维仿真

对通道壁面沿流动方向周期性地错开而在横向上通道壁面有几组不同错开位置的强化换热翅片的层流流动和传热情况进行了三维仿真分析。这类翅片经常被应用在汽车和电子设备的冷却系统中。三维有限元方法用来模拟Re数在100-1500范围时翅片的速度场和温度场，考虑了通道壁面的不同错开位置(SSP)对翅片传热性能的影响。仿真结果与以前的试验数据也进行了比较研究。     

气体在水中扩散过程的分子模拟

用分子动力学(MD)模拟法模拟正则系综下氧气、甲烷等4种气体,在水中的扩散过程.计算扩散系数采用微分--区限变分法.结果表明:水分子数目相同下计算不同分子数气体的扩散系数差别较大.与氨基酸相比,其扩散系数模拟值并不总是随着浓度的增加而减小,而是先增大后减小.4种气体在水中的扩散系数与文献值相对比,模拟结果与实验结果吻合较好.研究结果表明采用分子模拟手段可以获得具有工业应用价值的扩散系数,从而有助于计算传质学的发展.     

LB-SGS方法和MRT-LBM方法对高雷诺数顶盖驱动流的数值模拟对比

针对格子Boltzmann方法(Lattice Boltzmann Method,LBM)广泛采用的LBGK模型虽然简单易行,但对高雷诺数流动模拟稳定性不佳的问题,分别采用结合亚格子模型的LBM(LBM with Sub Grid Scale(SGS),LB-SGS)方法和多松驰时间LBM(Multiple Relaxation Time(MRT)LBM,MRT-LBM)方法对高雷诺数顶盖驱动流进行数值模拟.取Re=7 500对比2种方法得到的涡位置与标准解之间的误差,结果表明LB-SGS方法更接近标准解;保持雷诺数和顶盖速度不变并减少格点数观察收敛情况,结果表明MRT-LBM方法更稳定.     

几种复合型数值方法的算法模拟与性能比较

浅水波问题的数值模拟一直是计算数学、计算流体力学的研究热点之一,采用低阶方法和高阶方法相复合的数值方法引起了人们的注意,并在水力学的数值模拟中取得了很大的成功。文中对三种复合型的数值方法,即Lax-Wendroff(LW)格式与Lax-Friedrichs(LF)格式的复合算法,Upwind格式与Lax-Wendroff(LW)格式的复合算法,WENO格式与LW格式的复合算法,进行了分析比较和改进,并就计算流体力学中的一维浅水波方程的两个算例分别做了数值对比试验,在解的光滑性、锐利性,计算速度等几个方面做了比较,模拟结果表明三种方法均能准确捕捉激波又不产生非物理震荡。     

几种复合型数值方法的算法模拟与性能比较

浅水波问题的数值模拟一直是计算数学、计算流体力学的研究热点之一,采用低阶方法和高阶方法相复合的数值方法引起了人们的注意,并在水力学的数值模拟中取得了很大的成功.文中对三种复合型的数值方法,即Lax-Wendroff(LW)格式与Lax-Friedrichs(LF)格式的复合算法,Upwind格式与Lax-Wendroff(LW) 格式的复合算法,WENO格式与LW格式的复合算法,进行了分析比较和改进,并就计算流体力学中的一维浅水波方程的两个算例分别做了数值对比试验,在解的光滑性、锐利性,计算速度等几个方面做了比较,模拟结果表明三种方法均能准确捕捉激波又不产生非物理震荡.     

微孔隙中流体扩散系数分子动力学模拟的并行算法研究

扩散系数计算量非常大,为提高计算效率研究采用并行计算替代单机计算：用非阻塞通信替代阻塞通信;利用元胞分解的成果创建要拷贝的外层粒子列表;用拷贝粒子和移动粒子的重叠部分来减少通信量,在空间分解(SD)算法的基础上对MD模拟的并行算法进行了改进,使并行计算的效率提高了28．64％。用改进的SD并行计算方法,以RedHat Linux 8．0位操作系统和基于Message Passing Interface(MPI)消息传递界面的四节点计算机集群系统(PC Cluster)。对水分子在宏量条件下以及受限于硅酸岩狭缝中的速度自相关函数进行了MD模拟计算。结果表明,并行算法可以使速度自相关函数及相应的自扩散系数的MD模拟时间大为缩短。     

矩形腔内Stokes流动混合过程追踪模拟

基于涡量-速度方法建立了矩形腔上盖拖动的数学模型,采用交错网格,对腔内Stokes流动进行了有限体积数值模拟研究,得到了不同长高比的矩形腔内速度场及流函数分布.发现随着长高比的增大,中垂线的水平速度分布逐渐向无限大长高比得到解析解抛物线分布靠近.采用4阶Runge-Kutta方法对示踪剂混合过程进行前锋追踪模拟,得到了不同时刻示踪剂的混合图像.结果表明,示踪剂界面随时间呈线性增长,而且长高比越大,示踪剂界面的增长越快.     

Numerical simulation of gas flow in rough microchannels: hybrid kinetic–continuum approach versus Navier–Stokes

The flow field in a rough microchannel is numerically analyzed using a hybrid solver, dynamically coupling kinetic and Navier–Stokes solutions computed in rarefied and continuum subareas of the flow field, respectively, and a full Navier–Stokes solver. The rough surface is configured with triangular roughness elements, with a maximum relative roughness of 5 % of the channel height. The effects of Mach number, Knudsen number (or Reynolds number) and roughness height are investigated and discussed in terms of Poiseuille number and mass flow rate. Discrepancies between full Navier–Stokes and hybrid solutions are analyzed, assessing the range of validity of Navier–Stokes equations provided with first-order slip boundary conditions for modeling gas flow along a rough surface. Results indicate that the roughness increases Poiseuille number and decreases mass flux in comparison with those for the smooth microchannel. Increasing rarefaction results in further enhancement of roughness effect. At the same time, the compressibility effect is more noticeable than the roughness one, although the compressibility effect is alleviated by increase in the rarefaction. It was found that, although the Navier–Stokes solution of the flow in a smooth channel is accurate up to Kn = 0.1, when relative roughness height is higher than 1.25 % significant errors already appear at Kn = 0.02.     

A high order Discontinuous Galerkin Finite Element solver for the incompressible Navier–Stokes equations

The paper presents an unsteady high order Discontinuous Galerkin (DG) solver that has been developed, verified and validated for the solution of the two-dimensional incompressible Navier–Stokes equations. A second order stiffly stable method is used to discretise the equations in time. Spatial discretisation is accomplished using a modal DG approach, in which the inter-element fluxes are approximated using the Symmetric Interior Penalty Galerkin formulation. The non-linear terms in the Navier–Stokes equations are expressed in the convective form and approximated through the Lesaint–Raviart fluxes modified for DG methods.Verification of the solver is performed for a series of test problems; purely elliptic, unsteady Stokes and full Navier–Stokes. The resulting method leads to a stable scheme for the unsteady Stokes and Navier–Stokes equations when equal order approximation is used for velocity and pressure. For the validation of the full Navier–Stokes solver, we consider unsteady laminar flow past a square cylinder at a Reynolds number of 100 (unsteady wake). The DG solver shows favourably comparisons to experimental data and a continuous Spectral code.     

A partially structure-preserving algorithm for the permanents of adjacency matrices of fullerenes

A partially structure-preserving method for sparse symmetric matrices is proposed. Computational results on the permanents of adjacency matrices arising from molecular chemistry are presented. The largest adjacency matrix of fullerenes computed before is that of C₆₀ with a cost of several hours on supercomputers, while only about 6 min on an Intel Pentium PC (1.8 GHz) with our method. Further numerical computations are given for larger fullerenes and other adjacency matrices with n=60,80. This shows that our method is promising for problems from molecular chemistry.     

Kinetic-based numerical schemes for incompressible Navier–Stokes equations

Numerical schemes for incompressible Navier–Stokes equations based on low Mach number limits of kinetic equations are presented. Discretizations of the incompressible Navier–Stokes equations are derived based on discretizations of the Boltzmann equation and consideration for the low Mach number limit. In the incompressible Navier–Stokes limit the discretizations reduce to explicit high-order numerical schemes. Numerical results for several test cases and comparisons with other well-known approaches are also presented.     

Microchannel miter bend effects on pressure equalization and vortex formation

Simulations have been carried out for water flow in a square microchannel with a miter bend. The simulation considered a pressure-driven flow in a channel-hydraulic diameter of 5 μm for series of Reynolds number (Re) range from 0.056 to 560, in order to investigate water flow at bends. The result shows formation of two vortices after the miter bend, which are more discernible above Re 5.6. The critical inlet velocity for the generation of vortex in this particular geometry occurs at 1 m/s. A simple energy mechanism is postulated to explain the vortex formation as well as core skew direction. The high pressure region at the outer wall before and after the bend is a major factor for vortex formation since the liquid needs to reduce the additional energy effected by the high pressure region. Navier–Stokes equation is utilized with a no slip boundary condition for a total microchannel centerline length of 795 μm which is sufficient to produce a laminar flow pattern at the outlet.     

Determination of water activities and osmotic and activity coefficients of the system NaCl–BaCl2–H2O at 298.15 K

The water activities of the mixed aqueous electrolyte NaCl–BaCl₂(aq) are measured at total molalities from 0.25 mol kg⁻¹ to about saturation for different ionic strength fractions (y) of NaCl with y=0.33,0.50,0.67. The results allow the deduction of osmotic coefficients. The experimental results are compared with the predictions of the Zdanovskii, Stokes, and Robinson (ZSR), Kusik and Meissner (KM), Robinson and Stokes (RS), Lietzke and Stoughton (LSII), Reilly, Wood, and Robinson (RWR), and Pitzer models. From these measurements, the Pitzer mixing ionic parameters are determined and used to predict the solute activity coefficients in the mixture. The excess Gibbs energy is also determined.     

The numerical solution of laminar flow in a re-entrant tube geometry by a Chebyshev spectral element collocation method

A Chebyshev spectral element collocation method is used for the numerical solution of laminar flow in a re-entrant tube geometry. The high accuracy of the method allows the study of the merging process of the vortices in the re-entrant region. Results are presented for values of the Reynolds number up to 400 and for different lengths of the re-entrant tube lip. For low Reynolds number, the observed behaviour of the flow in the re-entrant region may be interpreted by analytical results on Stokes flow from the literature. As the Reynolds number is increased, a vortex that grows in size with the Reynolds number, is detected below the tip of the re-entrant lip.     

Numerical simulations of solutions of a two-level averaged Navier–Stokes system

An averaging procedure for the Navier–Stokes equations has been proposed in an earlier article [I. Moise, R.M. Temam, Renormalization group method. Application to Navier–Stokes Equation, Discrete Contin. Dyn. Syst. 6 (1) (2000) 191–210]. This averaging procedure is based on a two-level decomposition of the solution into low and high frequencies. The aim of the present article is to investigate, with the help of numerical simulations, the behavior of the small scales of the corresponding system. Space-periodic solutions with a non-resonant period are considered. The time evolution of the averaged and standard (non-averaged) small scales are compared at different Reynolds numbers and for different values of the cut-off level used to separate large and small scales of the flow variables. The numerical results illustrate the efficiency of the proposed averaging procedure for the Navier–Stokes equations. The averaged small scales provide an accurate prediction of the time-averaged small scales of the Navier–Stokes solutions. As the computational cost is reduced for the averaged equations, long time integrations on more than 50 eddy-turnover times have been performed for cut-off levels ensuring a proper resolution of the large scales. In these cases, development of instabilities in the averaged small scale equation is observed.