多孔介质中流体流动及扩散的耦合格子Boltzmann模型

多孔介质中高Péclet数和大黏性比下混溶流体的流动和扩散广泛存在于二氧化碳驱油、化工生产等工业过程中.用数值方法对该问题进行研究时,关键在于如何正确描述高Péclet数和大黏性比下多孔介质内流体的行为.为此,提出了一种基于多松弛模型和格子动理模型的耦合格子Boltzmann模型.通过Chapman-Enskog分析,证明该模型能有效求解不可压Navier-Stokes方程和对流扩散方程.数值结果表明,该模型不仅具有二阶精度和良好的稳健性,而且对于高Péclet数和大黏性比的问题具有良好的数值稳定性,为模拟此类问题提供了有效工具.     

二维可压缩流体Kelvin-Helmholtz不稳定性

利用高精度数值格式,研究了二维可压缩流体中的Kelvin-Helmholtz不稳定性,主要研究了可压缩性对Kelvin-Helmholtz稳定性增长率的影响.模拟定量的给出低Mach和高Mach数两种情况下,初始静压和对流Mach数以及Kelvin-Helmholtz不稳定性线性增长率的关系.模拟结果和自由剪切层以及混合层的实验结果以及理论分析一致.模拟表明,对流Mach数是描述流体可压缩性的合适参数,对流Mach数越小流体越不可压,Kelvin-Helmholtz不稳定性的线性增长率随对流Mach数的增加而减小. 关键词： Kelvin-Helmholtz不稳定性 可压缩流体 Mach数 超音速流体     

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     

基于MATLAB对不可压缩粘性流体在流管中的研究

粘性流体是指粘性效应不可忽略的流体,其粘性具有在流体质点间可流层因相对运动而产生摩擦力反抗相对运动效果。粘性流体的研究在医疗领域的心脑血管方面具有重要意义。文中详细介绍了管道中的流动模型和一种解决不可压缩流体的通用算法SIMPLE算法,并使用MATLAB软件进行数值模拟,模拟结果与解析结果进行比较,根据其结果的差异总结了SIMPLE算法的优缺点。     

不可压Navier-Stokes方程的投影方法

不可压Navier-Stokes方程是流体力学的基本控制方程,其高精度数值模拟具有重要的科学意义.本综述性文章回顾了求解Navier-Stokes方程的投影方法,重点介绍了时空一致四阶精度的GePUP方法.该方法用一个广义投影算子对不可压Navier-Stokes方程进行了重新表述,使得投影流速的散度由一个热方程控制,保持了UPPE方法的优点.与UPPE方法不同的是, GePUP方法的推导不依赖于Leray-Helmholtz投影算子的各种性质,并且GePUP表述中的演化变量无需满足散度为零的条件,因此数值近似Leray-Helmholtz投影算子的误差对精度和稳定性的影响非常透明.在GePUP方法中,时间积分和空间离散是完全解耦的,因此对这两个模块都能以"黑匣子"的方式自由替换.时间积分模块的灵活性实现了时间上的高阶精度,并使得GePUP算法能同时适用于低雷诺数流体和高雷诺数流体.空间离散模块的灵活性使得GePUP算法能很好地适应不规则边界.理论分析和数值测试结果都显示,相对于二阶投影方法, GePUP方法无论在精度上还是效率上都具有巨大优势.     

一个高效的离散Boltzmann爆轰模型

构建一个适用于爆轰过程模拟的离散Boltzmann模型.该模型由一个离散Boltzmann方程和一个唯象反应率方程构成;在物理建模上,它等效于一个传统Navier-Stokes模型外加一个关于热动非平衡行为的粗粒化模型.与传统流体模型相比,它能够提供更多的动力学和动理学信息.该模型采用16个离散速度,相比于使用33个离散速度的模型具有更高的运算效率,模型中引入了额外自由度,通过调节额外自由度的数目,可以模拟各种不同比热比的爆轰.采用爆轰问题中的一些经典算例对所建立的模型进行数值验证.结果表明：该模型不仅对传统流体模型所能模拟的爆轰问题有效,而且能够用于一些传统流体模型不能描述的非平衡过程,有利于对爆轰问题的深入研究.     

带运动部件的不可压缩流动MPS法数值模拟

本文对移动粒子半隐式法(MPS),一种适用于计算粘性不可压缩流动的全拉格朗日无网格法进行了研究.在原有MPS方法的基础上建立了移动边界作用模型,实现了由于流体中运动部件的平动或转动而引起的流场变化,扩展了MPS方法的应用范围.将计算结果与精确解进行了比较,验证了带运动部件的MPS方法的正确性.同时对十字搅拌器进行了数值模拟,很好地描述了对液体的搅拌过程.为这一类流体机械问题的研究提供了新的数值研究方法.     

耦合界面力的两相流相场格子Boltzmann模型

提出了一种改进的基于相场理论的两相流格子Boltzmann模型.通过引入一种新的更加简化的外力项分布函数,使得此模型克服了前人工作中界面力尺度与理论分析不一致的问题,并且通过Chapman-Enskog多尺度分析表明,所提出的模型能够准确恢复到追踪界面的Cahn-Hilliard方程和不可压的Navier-Stokes方程,并且宏观速度的计算更为简化.利用所提模型对几个经典两相流问题,包括静态液滴测试、液滴合并问题、亚稳态分解以及瑞利-泰勒不稳定性进行了数值模拟,发现本模型可以获得量级为10^-9极小的虚假速度,并且这些算例获取的数值解与解析解或已有的文献结果相吻合,从而验证了模型的准确性和可行性.最后,利用所发展的两相流格子Boltzmann模型研究了随机扰动的瑞利-泰勒不稳定性问题,并着重分析了雷诺数对流体相界面的影响.发现对于高雷诺数情形,在演化前期,流体界面出现一排“蘑菇”形状,而在演化后期,流体界面呈现十分复杂的混沌拓扑结构.不同于高雷诺数情形,低雷诺数时流体界面变得相对光滑,在演化后期未观察到混沌拓扑结构.     

蒸汽-冷流体接触冷凝流动的数值模拟

介绍了关于蒸汽-冷流体直接接触冷凝流动与传热的数值计算模型与部分研究结果。用Level Set方法确定蒸汽-冷流体接触界面的位置和形状,建立了对蒸汽和冷流体普遍适用的动量、能量和质量守恒方程,在能量和质量寺恒方程中增加了部分项用于计算蒸汽冷凝所产生的影响。用有限差分法在交错网格上离散控制方程,用Runge-Kutta法-五阶WENO组合格式求解Level Set输运方程,用压力修正的迭代Projection方法求解动量方程,而用SIMPLE方法求解温度控制方程。对算例的计算结果表明,本文所建立的数值计算模型能反映物理现象的宏观特性。根据计算结果,分析了本文模型的优缺点,并指出了今后改进的方向。     

微通道中一类生物流体在高Zeta势下的电渗流及传热特性

在高壁面Zeta势下,研究滑移边界条件下满足牛顿流体模型的一类生物流体的电渗流动及传热特性,流体在外加电场、磁场和焦耳加热共同作用下流动.首先,在不使用Debye-Hückel线性近似条件时,利用切比雪夫谱方法给出非线性Poisson-Boltzmann方程和流函数满足的四阶微分方程及热能方程的数值解,将所得结果与利用Debye-Hückel线性近似所得结果进行比较,证明本文数值方法的有效性.其次,讨论电磁环境下壁面Zeta势、哈特曼数H、电渗参数m、滑移参数β对流动特性、泵送特性和捕获现象的影响,并探究焦耳加热参数γ和布林克曼数Br等参数对传热特性的影响.结果表明,壁面Zeta势、电渗参数m、滑移参数β的增大对流体速度有促进作用,而哈特曼数H的增大会抵抗流体流动.研究进一步表明,焦耳加热参数γ和布林克曼数Br的增大会导致温度升高.     

Three-dimensional finite-difference lattice Boltzmann model and its application to inviscid compressible flows with shock waves

In this paper, a three-dimensional (3D) finite-difference lattice Boltzmann model for simulating compressible flows with shock waves is developed in the framework of the double-distribution-function approach. In the model, a density distribution function is adopted to model the flow field, while a total energy distribution function is adopted to model the temperature field. The discrete equilibrium density and total energy distribution functions are derived from the Hermite expansions of the continuous equilibrium distribution functions. The discrete velocity set is obtained by choosing the abscissae of a suitable Gauss–Hermite quadrature with sufficient accuracy. In order to capture the shock waves in compressible flows and improve the numerical accuracy and stability, an implicit–explicit finite-difference numerical technique based on the total variation diminishing flux limitation is introduced to solve the discrete kinetic equations. The model is tested by numerical simulations of some typical compressible flows with shock waves ranging from 1D to 3D. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.     

Three-dimensional coupled double-distribution-function lattice Boltzmann models for compressible Navier–Stokes equations

Two three-dimensional (3D) lattice Boltzmann models in the framework of coupled double-distribution-function approach for compressible flows, in which specific-heat ratio and Prandtl number can be adjustable, are developed in this paper. The main differences between the two models are discrete equilibrium density and total energy distribution function. One is the D3Q25 model obtained from spherical function, and the other is the D3Q27 standard lattice model obtained from Hermite expansions of the corresponding continuous equilibrium distribution functions. The two models are tested by numerical simulations of some typical compressible flows, and their numerical stability and precision are also analysed. The results indicate that the two models are capable for supersonic flows, while the one from Hermite expansions is not suitable for compressible flows with shock waves.     

Three-dimensional non-free-parameter lattice-Boltzmann model and its application to inviscid compressible flows

In this Letter, a three-dimensional (3D) lattice-Boltzmann model is presented following the non-free-parameter lattice-Boltzmann method of Qu et al. [K. Qu, C. Shu, Y.T. Chew, Phys. Rev. E 75 (2007) 036706]. A simple function, which satisfies the zeroth- through third-order moments of the Maxwellian distribution function, is introduced to replace the Maxwellian distribution function as the continuous equilibrium distribution function in 3D space. The function is then discretized to discrete-velocity directions via a 25-point Lagrangian interpolation polynomial. To simulate compressible flows with shock waves, an implicit-explicit finite-difference scheme based on the total variation diminishing flux limitation is adopted to solve the discrete Boltzmann-BGK equation in order to capture the shock waves in compressible flows with a finite number of grid points. The model is validated by its application to some typical inviscid compressible flows ranging from 1D to 3D, and the numerical results are found to be in excellent agreement with the analytical solutions and/or other numerical results.     

Three-Dimensional Lattice Boltzmann Model for High-Speed Compressible Flows

A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for high-speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara [Phys. Rev. E 69 (2004) 056702]. The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative (NND) scheme, which effectively damps oscillations at discontinuities. To be more consistent with the kinetic theory of viscosity and to further improve the numerical stability, an additional dissipation term is introduced. Model parameters are chosen in such a way that the von Neumann stability criterion is satisfied. The new model isvalidated by well-known benchmarks, (i) Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with high Mach number; (ii) reaction of shock wave on droplet or bubble. Good agreements are obtained between LB results and exact ones or previously reported solutions. The model is capable of simulating flows from subsonic to supersonic and capturing jumps resulted from shock waves.     

Simple and efficient relaxation methods for interfaces separating compressible fluids,cavitating flows and shocks in multiphase mixtures

Numerical approximation of the five-equation two-phase flow of Kapila et al. [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10) (2001) 3002–3024] is examined. This model has shown excellent capabilities for the numerical resolution of interfaces separating compressible fluids as well as wave propagation in compressible mixtures [A. Murrone, H. Guillard, A five equation reduced model for compressible two phase flow problems, Journal of Computational Physics 202(2) (2005) 664–698; R. Abgrall, V. Perrier, Asymptotic expansion of a multiscale numerical scheme for compressible multiphase flows, SIAM Journal of Multiscale and Modeling and Simulation (5) (2006) 84–115; F. Petitpas, E. Franquet, R. Saurel, O. Le Metayer, A relaxation-projection method for compressible flows. Part II. The artificial heat exchange for multiphase shocks, Journal of Computational Physics 225(2) (2007) 2214–2248]. However, its numerical approximation poses some serious difficulties. Among them, the non-monotonic behavior of the sound speed causes inaccuracies in wave’s transmission across interfaces. Moreover, volume fraction variation across acoustic waves results in difficulties for the Riemann problem resolution, and in particular for the derivation of approximate solvers. Volume fraction positivity in the presence of shocks or strong expansion waves is another issue resulting in lack of robustness. To circumvent these difficulties, the pressure equilibrium assumption is relaxed and a pressure non-equilibrium model is developed. It results in a single velocity, non-conservative hyperbolic model with two energy equations involving relaxation terms. It fulfills the equation of state and energy conservation on both sides of interfaces and guarantees correct transmission of shocks across them. This formulation considerably simplifies numerical resolution. Following a strategy developed previously for another flow model [R. Saurel, R. Abgrall, A multiphase Godunov method for multifluid and multiphase flows, Journal of Computational Physics 150 (1999) 425–467], the hyperbolic part is first solved without relaxation terms with a simple, fast and robust algorithm, valid for unstructured meshes. Second, stiff relaxation terms are solved with a Newton method that also guarantees positivity and robustness. The algorithm and model are compared to exact solutions of the Euler equations as well as solutions of the five-equation model under extreme flow conditions, for interface computation and cavitating flows involving dynamics appearance of interfaces. In order to deal with correct dynamic of shock waves propagating through multiphase mixtures, the artificial heat exchange method of Petitpas et al. [F. Petitpas, E. Franquet, R. Saurel, O. Le Metayer, A relaxation-projection method for compressible flows. Part II. The artificial heat exchange for multiphase shocks, Journal of Computational Physics 225(2) (2007) 2214–2248] is adapted to the present formulation.     

Development and Comparative Studies of Three Non-Free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows

This paper at first shows the details of finite volume-based lattice Boltzmann method (FV-LBM) for simulation of compressible flows with shock waves. In the FV-LBM, the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model, while the tangential flux is calculated using the same way as used in the conventional Euler solvers. The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM. The platform is formed from the conservation forms of moments. Under the platform, both the equilibrium distribution functions and lattice velocities can be determined, and therefore, non-free parameter model can be developed. The paper particularly presents three typical non-free parameter models, D1Q3, D1Q4 and D1Q5. The performances of these three models for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test problems. Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number. From the results, it seems that D1Q4 model could be the best choice for the FV-LBM simulation of hypersonic flows.     

Limited projections laser speckle tomography of complex flows

Different approaches are discussed applied to reconstruction of local flow parameters using line-of-sight laser probing. The first one is based on single projection measurement and detailed numerical simulation of flow pattern. The second one is based on multi-projectional line-of-sight measurement and reconstructing local flow parameters by solving inverse integral transforms. Holographic interferometry (HI) and speckle photography (SP) are used for laser probing of complex 3D media under study. Computer-assisted tomography (CAT) approach based on Radon integral transform is described and examples of reconstructed flowfields are given including compressible flows with shock waves. Statistical information about flow studied is extracted as well, and maps of local statistical turbulence parameters are quantitatively determined by using obtained SP-data and a new Erbeck–Merzkirch integral transform.     

新型可压缩尺度在跨声速流动中的应用

基于von Karman长度尺度和新型Reynolds应力本构关系对k-ε湍流模型重构,将k方程封闭,采用代数形式对湍流耗散项进行模化.在KDO（kinetic dependent only）模型的基础上,引入可压缩von Karman长度尺度,得到一种适用于复杂可压缩流动的新型湍流模型CKDO（compressible kinetic dependent only）,在CKDO模型中没有任何经验系数,仅有两个来自边界层精细化标定的可调参数.对RAE2822翼型、轴对称圆筒管道凸起流动、ONERA-M6机翼跨声速流动等算例进行数值计算,结果显示CKDO湍流模型对上述算例流场的压力系数模拟结果与实验值吻合较好,表明CKDO模型能够对跨声速流场进行较为准确的模拟.      

一个新的用于不可压磁流体动力学的格子波尔兹曼模型

绝大多数现有的格子波尔兹曼磁流体动力学模型其实是用可压缩方法来模拟不可压磁流体。而这些可压缩效应在数值模拟中往往会带来意想不到的误差。在这篇文章中，我们提出了一个全新的可用于的不可压格子波尔兹曼磁流体动力学模型，并且进行了哈特曼流的数值模拟。模拟结果与哈特曼流的解析解非常吻合。这个方法需要一个假设条件来消除误差。我们做了大量的数值试验，并且与Dellar教授的模型进行了详细的分析与比较。     

A Numerical Study of Characteristic Slow-Transient Behavior of a Compressible 2D Gas-Liquid Two-Fluid Model

The purpose of this paper is to gain some insight into the characteristic behavior of a general compressible two-fluid gas-liquid model in 2D by using numerical computations. Main focus is on mass transport phenomena. Relatively few numerical results in higher dimensions can be found in the literature for this two-fluid model, in particular, for cases where mass transport dynamics are essential. We focus on natural extensions to 2D of known 1D benchmark test cases, like water faucet and gas-liquid separation, previously employed by many researchers for the purpose of testing various numerical schemes. For the numerical investigations, the WIMF discretization method introduced in [SIAM J. Sci. Comput. 26 (2005), 1449] is applied, in combination with a standard dimensional splitting approach. Highly complicated flow patterns are observed reflecting the balance between acceleration forces, gravity, interfacial forces, and pressure gradients. An essential ingredient in these results is the appearance of single-phase regions in combination with mixture regions (dispersed flow). Solutions are calculated and shown from early times until a steady state is reached. Grid refinement studies are included to demonstrate that the obtained solutions are not grid-sensitive.