基于格子Boltzmann方法的一维Burgers方程的数值模拟

基于格子Boltzmann方法(LBM)的一维Burgers方程的数值解法,已有2-bit和4-bit模型。文中通过选择合适的离散速度模型构造出恰当的平衡态分布函数; 然后, 利用单松弛的格子Bhatnagar-Gross-Krook模型、Chapman-Enskog展开和多尺度技术, 提出了用于求解一维Burgers方程的3-bit的格子Boltzmann模型,即D1Q3模型,并进行了数值实验。实验结果表明,该方法的数值解与解析解吻合的程度很好,且误差比现有文献中的误差更小,从而验证了格子Boltzamnn模型的有效性。     

多松弛时间格子Boltzmann方法在GPU上的实现

近年来,随着统一计算设备构架(CUDA)的出现,高端图形处理器(GPU)在图像处理、计算流体力学等科学计算领域的应用得到了快速发展.属于介观数值方法的格子Boltzmann方法(LBM)是1种新的计算流体力学(CFD)方法,具有算法简单、能处理复杂边界条件、压力能够直接求解等优势,在多相流、湍流、渗流等领域得到了广泛应用.LBM由于具有内在的并行性,特别适合在GPU上计算.采用多松弛时间模型(MRT)的LBM,受松弛因子的影响较小并且数值稳定性较好.本文实现了MRT-LBM在基于CUDA的GPU上的计算,并通过计算流体力学经典算例--二维方腔流来验证计算的正确性.在雷诺数Re=[10,104]之间,计算了多达26种雷诺数的算例,并将Re=102,4×102,103,2×103,5×103,7.5×103算例对应的主涡中心坐标与文献中结果进行了对比.计算结果与文献数值实验符合较好,从而验证了算法实现的正确性,并显示出MRT-LBM具有更优的数值稳定性.本文还分析了在GPU上MRT-LBM的计算性能并与CPU的计算进行了比较,结果表明,GPU可以极大地加快MRT-LBM的计算,NVIDIA Tesla C2050相对于单核Intel Xeon 5430 CPU的加速比约为60倍.     

基于格子Boltzmann方法的换热器优化模拟

为优化换热器的结构设计,用格子Boltzmann方法(Lattice Boltzmann Method,LBM)结合多孔介质模型模拟换热器内的换热,研究雷诺数、普朗特数和热扩散率比的变化对温度场和换热性能的影响.模拟结果表明:在小雷诺数范围内,随着雷诺数的增加,努塞尔数先增加后减小,即存在一个使换热性能达到最好的雷诺数;随着普朗特数的增加,努塞尔数减小,换热性能降低;随着热扩散率比的增加,换热性能提高.分析不同管柱排列方式对换热性能的影响,结果表明:叉排的换热效果明显优于顺排,当横向节距等于2时,对于均匀顺排或叉排,努塞尔数均随纵向节距的增加而减小,这与实验结果相符;对于非均匀叉排,采用"前密"或"中间密"的排布方式有利于换热.     

有限体积格子Boltzmann方法的算法改进及性能分析

有限体积格子Boltzmann方法(LBM)能够将标准LBM的应用范围扩展到非结构网格,但是比起标准的LBM这个方法需要更多的内存用量和计算量。针对此问题采用了优化计算顺序、简化计算方程的方法对有限体积LBM算法进行改进。科学的分析和实验的结果表明,改进后的算法能够在不增加计算量的基础上减少内存用量,在一些情况下还可以大量减少计算时间。     

多重网格格子Boltzmann方法的并行算法

针对复杂流动数值模拟中的格子Boltzmann方法存在计算网格量大、收敛速度慢的缺点,提出了基于三维几何边界的多重笛卡儿网格并行生成算法,并基于该网格生成方法提出了多重网格并行格子Boltzmann方法（LBM）。该方法结合不同尺度网格间的耦合计算,有效减少了计算网格量,提高了收敛速度;而且测试结果也表明该并行算法具有良好的可扩展性。     

LBGK模型的分布式并行算法及实现

在计算流体力学领域中,由于流场求解的复杂性,设计出高效的并行算法成为了流场并行化计算的研究重点.以格子Boltzmann方法的理论应用为研究背景,把并行思想和格子Boltzmann方法在模拟流体流动中的计算问题结合起来,讨论了格子Boitzmann方法LBGK D2Q9模型的计算过程和计算特点.研究并实现了LBGK模型的分布式并行算法,并在自强3000上进行了算法的并行性能的分析和测试.结果表明,格子Boltzmann方法LBGKD2Q9模型适合大规模的并行计算,能提高计算的精度和速度,解决复杂流场计算问题.     

非均匀分布颗粒群中的曳力分布

本文采用格子Boltzmann方法(LBM)在图形处理器(GPU)上计算了由静止圆柱阵列组成的团聚物周期单元内的不可压缩流体流动,流固交界面处采用直接反弹以实现无滑移边界,每个圆柱上的曳力通过统计动量交换直接求得。根据LBM求得的流体速度,对于团聚物中的单圆柱按能量最小多尺度(EMMS)模型计算平均曳力系数,并考察了将聚团近似为均匀悬浮的临界条件。对颗粒雷诺数Re_p在0～10之间的80种固相份额的模拟结果表明,密相空隙率可以表征这种临界条件。当固相份额恒定时,该临界空隙率随着Re_p的增加而降低;当Re_p恒定时,该临界空隙率随着固相份额的增加而降低。     

基于格子Boltzmann方法和大涡模拟的颈动脉分叉狭窄流动并行计算

颈动脉斑块的形成与复杂的血流动力学因素密切相关,血液流动状况的精确模拟对颈动脉斑块的临床诊断具有重要意义。为了精确模拟脉动流场,在格子Boltzmann方法（LBM）的基础上,添加大涡模拟（LES）模型,建立了LBM-LES颈动脉模拟算法。利用医学图像重构软件,建立颈动脉狭窄真实几何模型,对颈动脉狭窄脉动流动进行了数值模拟,通过计算血液流动速度、壁面剪切应力（WSS）等,得出了有意义的流动结果,验证了LBM-LES对颈动脉狭窄后段血液流动研究的有效性。基于OpenMP编程环境,在高性能集群机全互联胖节点上进行了千万量级网格的并行计算,结果表明LBM-LES颈动脉模拟算法具有较好的并行性能。     

巷道热流蔓延及阻滞的分块耦合LBM仿真

为了掌握地下矿火灾发生后遇到易燃物蔓延、障碍物阻滞的规律,提出用分块耦合格子Boltzmann方法(LBM)进行巷道热流蔓延与阻滞的仿真方法.该方法使用分块耦合算法将巷道分为若干相对规则的块,并应用速度-温度双分布LBM对巷道热流蔓延及阻滞过程进行仿真.仿真时,在巷道随机设置多处易燃物,当热流流经巷道时采用热流蔓延模型使得易燃物在一定条件下被引燃,产生热流与原有热流共同传播;在巷道随机设置障碍物,采用热流阻滞模型分析热流遇到障碍物后其方向和温度变化状况.仿真结果表明,该仿真方法可得到关于热流流动速度、热流温度和压力的详细数据,获得关于巷道热流流态的直观信息,从而为制定有效的规避热流的方案提供依据.     

面向超大规模并行模拟的LBM计算流体力学软件

格子玻尔兹曼方法(Lattice Boltzmann Method,LBM)是一种基于介观模拟尺度的计算流体力学方法,已被广泛用于理论研究和工程领域。提高LBM计算流体软件的并行模拟能力,是高性能计算及应用研究中的一项重要内容。该研究基于“神威·太湖之光”超级计算系统,设计并实现了一套高效扩展的LBM计算流体力学软件。针对国产众核处理器SW26010的架构,文中设计了以下几种提高SWLBM方针速度和可扩展性的多级并行技术,包括面向19点stencil的数据复用、碰撞过程向量化、主从异步并行通信计算隐藏等。基于以上并行优化方案,文中测试了高达56000亿网格的数值模拟,SWLBM软件持续浮点计算性能达到4.7 PFlops,软件模拟速度提高了172倍。相比百万核心10000*10000*5000网格风场模拟,SWLBM整机千万核心的并行效率可达87%。测试结果表明,SWLBM有能力为工业应用提供实用的大规模并行模拟解决方案。     

Non-body-fitted Cartesian-mesh simulation of highly turbulent flows using multi-relaxation-time lattice Boltzmann method

This paper presents a lattice Boltzmann method (LBM) based study aimed at numerical simulation of highly turbulent and largely inclined flow around obstacles of curved geometry using non-body-fitted Cartesian meshes. The approach features (1) combining the interpolated bounce-back scheme with the LBM of multi-relaxation-time (MRT) type to enable the use of simple Cartesian mesh for the flow cases even with complex geometries; and (2) incorporating the Spalart–Allmaras (SA) turbulence model into LBM in order to represent the turbulent flow effect. The numerical experiments are performed corresponding to flows around an NACA0012 airfoil at Re=5×10⁵ and around a flat plate at Re=2×10⁴, respectively. The agreement between all simulation results obtained from this study and the data provided by other literature demonstrates the reliability of the enhanced LBM proposed in this paper for simulating, simply on Cartesian meshes, complex flows that may involve bodies of curved boundary, high Reynolds number, and large angle of attack.     

A fractional step lattice Boltzmann method for simulating high Reynolds number flows

A fractional step lattice Boltzmann scheme is presented to greatly improve the stability of the lattice Boltzmann method (LBM) in modelling incompressible flows at high Reynolds number. This method combines the good features of the conventional LBM and the fractional step technique. Through the fractional step, the flow at an extreme case of infinite Reynolds number (inviscid flow) can be effectively simulated. In addition, the non-slip boundary condition can be directly implemented.     

Modelling solute transport in shallow water with the lattice Boltzmann method

The lattice Boltzmann method is used to investigate the solute transport in shallow water flows. Shallow water equations are solved using the lattice Boltzmann equation on a D2Q9 lattice with multiple-relaxation-time (MRT-LBM) and Bhatnagar–Gross–Krook (BGK-LBM) terms separately, and the advection–diffusion equation is also solved with a LBM-BGK on a D2Q5 lattice. Three cases: open channel flow with side discharge, shallow recirculation flow and flow in a harbour are simulated to verify the described methods. Agreements between predictions and experiments are satisfactory. In side discharge flow, the reattachment length for different ratios of side discharge velocity to main channel velocity has been studied in detail. Furthermore, the performance of MRT-LBM and BGK-LBM for these three cases has been investigated. It is found that LBM-MRT has better stability and is able to satisfactorily simulate flows with higher Reynolds number. The study shows that the lattice Boltzmann method is simple and accurate for simulating solute transport in shallow water flows, and hence it can be applied to a wide range of environmental flow problems.     

A flow topology optimization method for steady state flow using transient information of flow field solved by lattice Boltzmann method

A topology optimization method for fluid flow using transient information is proposed. In many conventional methods, the design domain is updated using steady state information which is obtained after solving the flow field equations completely. Hence we must solve the flow field at each iterative which leads to high computational cost. In contrast, the proposed method updates the design domain using transient information of flow field. Hence the flow field is solved only once. The flow field is solved by lattice Boltzmann method (LBM). It is found that, by using LBM, the flow field is stably computed even though the design domain drastically changes during the computation. The design domain is updated according to sensitivity analysis. In many conventional methods, the sensitivity of objective functionals under lattice Boltzmann equations is obtained using additional adjoint equations. However, in the proposed method, the sensitivity is explicitly formulated and computed without using adjoint variables. In this paper, we show some numerical examples for low Reynolds number flows. The results demonstrate good convergence property in small computation time.     

A Coupled Lattice Boltzmann Method to Solve Nernst–Planck Model for Simulating Electro-osmotic Flows

In this paper, we focus on the nonlinear coupling mechanism of the Nernst–Planck model and propose a coupled lattice Boltzmann method (LBM) to solve it. In this method, a new LBM for the Nernst–Planck equation is developed, a multi-relaxation-time (MRT)-LBM for flow field and an LBM for the Poisson equation are used. And then, we discuss the choice of the model and found that the MRT-LBM is much more stable and accurate than the LBGK model. A reasonable iterative sequence and evolution number for each LBM are proposed by considering the properties of the coupled LBM. The accuracy and stability of the presented coupled LBM are also discussed through simulating electro-osmotic flows (EOF) in micro-channels. Furthermore, to test the applicability of it, the EOF with non-uniform surface potential in micro-channels based on the Nernst–Planck model is simulated. And we investigate the effects of non-uniform surface potential on the pattern of the EOF at different external applied electric fields. Finally, a comparison of the difference between the Nernst–Planck model and the Poisson–Boltzmann model is presented.     

Application of lattice Boltzmann method in free surface flow simulation of micro injection molding

The filling flow in micro injection molding was simulated by using the lattice Boltzmann method (LBM). A tracking algorithm for free surface to handle the complex interaction between gas and liquid phases in LBM was used for the free surface advancement. The temperature field in the filling flow is also analyzed by combining the thermal lattice Boltzmann model and the free surface method. To simulate the fluid flow of polymer melt with a high Prandtl number and high viscosity, a modified lattice Boltzmann scheme was adopted by introducing a free parameter in the thermal diffusion equation to overcome the restriction of the thermal relaxation time. The filling flow simulation of micro injection molding was successfully performed in the study.     

Bifurcation phenomenon in the wake of a 3-D cylinder

Numerical simulations are carried out for a long slender rigid circular cylinder in a cross flow to investigate the effect of end-plates on the bifurcation phenomenon in the near wake. A multiple relaxation time lattice Boltzmann method (MRT-LBM) is used for the solution of three-dimensional unsteady flow. At the Reynolds number of 200, there exists shedding frequency bifurcation along the span which is resulted from the shedding phase oscillation.     

求解Navier-Stokes方程的一类有限元有限体积迎风方法及其实现

Navier-Stokes方程是一类非线性的鞍点问题,在高Reynolds数流的情形下,标准Galerkin有限元方法会导致数值伪震荡.迎风有限元方法在算法结构上表征了流体＂上游＂决定＂下游＂的流动性态,它能够有效地消除高Reynolds数流的对流占优扩散所产生的非物理震荡.基于此,将Navier-Stokes方程的对流项采用有限体积框架下的迎风离散,对其它项仍使用Galerkin有限元离散,研究了二维定常Navier-Stokes方程的数值求解,编程藉助于有限元程序自动生成软件FEPG.通过对方腔流动和圆柱绕流问题与基准测试已有数值结果的比较,验证了所构造方法的可行性和有效性.     

Topology optimization of flow domains using the lattice Boltzmann method

We consider the optimal design of two- (2D) and three-dimensional (3D) flow domains using the lattice Boltzmann method (LBM) as an approximation of Navier-Stokes (NS) flows. The problem is solved by a topology optimization approach varying the effective porosity of a fictitious material. The boundaries of the flow domain are represented by potentially discontinuous material distributions. NS flows are traditionally approximated by finite element and finite volume methods. These schemes, while well established as high-fidelity simulation tools using body-fitted meshes, are effected in their accuracy and robustness when regular meshes with zero-velocity constraints along the surface and in the interior of obstacles are used, as is common in topology optimization. Therefore, we study the potential of the LBM for approximating low Mach number incompressible viscous flows for topology optimization. In the LBM the geometry of flow domains is defined in a discontinuous manner, similar to the approach used in material-based topology optimization. In addition, this non-traditional discretization method features parallel scalability and allows for high-resolution, regular fluid meshes. In this paper, we show how the variation of the porosity can be used in conjunction with the LBM for the optimal design of fluid domains, making the LBM an interesting alternative to NS solvers for topology optimization problems. The potential of our topology optimization approach will be illustrated by 2D and 3D numerical examples.