基于Matlab分布式工具箱的流场计算及其可视化

讨论了格子Boltzmann方法LBGK D2Q9模型的计算过程和计算特点。通过该模型模拟了一类典型的流体绕流问题的计算及其可视化,研究并实现了利用Matlab分布式计算工具箱进行分布式并行处理的问题。讨论了利用虚拟目录及文件的方式传递数据的过程,实现了跟踪方式的LBGK流体计算模型科学计算可视化系统。     

基于Matlab分布式工具箱的流场计算及其可视化

讨论了格子Boltzmann方法LBGK D2Q9模型的计算过程和计算特点。通过该模型模拟了一类典型的流体绕流问题的计算及其可视化，研究并实现了利用Matlab分布式计算工具箱进行分布式并行处理的问题。讨论了利用虚拟目录及文件的方式传递数据的过程，实现了跟踪方式的LBGK流体计算模型科学计算可视化系统。     

LBGK模型的分布式并行计算

以二维9速模型D2Q9(LBGK)为例,针对不同集合形状的流场,研究了数据分布与通信量及并行效率之间的关系。在“自强3000”集群式超级计算机上就流场网格的不同规模、多种数据分布及通信方案进行了数值实验。测试结果表明,LBGK模型的并行效率高、可扩展性好,在数据分布方案与流场网格形状相似时,并行效率最高。该结论与理论分析相吻合。     

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。     

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.     

异构平台下格子Boltzmann方法实现及性能分析

对CPU+GPU异构平台下的多种并行编程模式进行了研究,并针对格子Boltzmann方法实现了CUDA,MPI+CUDA,MPI+OpenMP+CUDA多级并行算法。结果表明,算法具有较好的加速性能;提出的根据计算量比例参数调节CPU和GPU之间负载均衡的方法,对于在异构平台上实现多级并行处理及资源的有效利用具有一定的参考和应用价值。     

LBM在流体渗透率计算中的应用与优化

格子Boltzmann方法广泛应用于流体计算领域,针对其应用中计算规模过大的问题提出了一种粒子空间压缩算法,改善了格子Boltzmann并行算法空间消耗过大的问题;合并了迁移与碰撞过程,减少了内存的I/O次数,加快了计算速度;该算法拥有良好的可扩展性。实验结果表明,优化后的程序空间消耗明显减少,性能提高50%以上。     

LBM在多核并行编程模型中的应用

LBGK(Lattice Bhatnagar-Gross-Krook)模IV不仅是LBM(Lattice Boltzmann Method)理论及应用上的新突破,而且是一种非常新颖的数值计算方法,适合大规模并行计算.多线程并行编程接11库(Multi-Thread Interface,MTI)充分利用多核处理器的资源来提升计算的性能,为在多核环境下方便地开发高效的并行程序提供了一个接口,大大地减轻了开发人员的负担.MTI提供了使用cache块技术划分数据集实现单任务数据并行计算,以及采用任务密取调度策略实现多任务并行处理.应用MI实现了LBGK模型模拟斑图形成的并行计算,并获得了较高的并行效率.     

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。     

基于MPI的二维稳态温度场的并行计算

作为颗粒离散元软件并行化的前期研究,对二维稳态导热问题的有限差分法求解程序进行了并行化处理.并行算法将计算域划分为若干个子域,并将各子域上的迭代计算任务分配给相应的处理器执行.同时,算法考虑负载平衡,并采用计算和通信的重叠技术,提高并行算法的效率.通过对二维稳态温度场导热问题的串/并行程序在曙光TC2600刀片服务器上的计算结果进行比较分析,验证了该并行方法的有效性.实验结果表明,计算耗时与通信耗时的比值越大,并行效率越高.     

Artificial compressibility method and lattice Boltzmann method: Similarities and differences

The artificial compressibility method and the lattice Boltzmann method yield the solutions of the incompressible Navier–Stokes equations in the limit of the vanishing Mach number. The inclusion of the bulk viscosity is considered to be one of the reasons for the success of the lattice Boltzmann method at least in the 2D case. In the present paper, the robustness of the artificial compressibility method is enhanced by introducing a new dissipation term, which makes high cell-Reynolds number computation possible. The increase of the stability is also confirmed in the linear stability analysis; the magnitude of the eigenvalues are drastically reduced for low resolution. Comparisons are made with the lattice Boltzmann method. It is confirmed that the fortified ACM is more robust as well as more accurate than the lattice Boltzmann method.     

Lattice Boltzmann Models for Anisotropic Diffusion of Images

The lattice Boltzmann method has attracted more and more attention as an alternative numerical scheme to traditional numerical methods for solving partial differential equations and modeling physical systems. The idea of the lattice Boltzmann method is to construct a simplified discrete microscopic dynamics to simulate the macroscopic model described by the partial differential equations. The use of the lattice Boltzmann method has allowed the study of a broad class of systems that would have been difficult by other means. The advantage of the lattice Boltzmann method is that it provides easily implemented fully parallel algorithms and the capability of handling complicated boundaries. In this paper, we present two lattice Boltzmann models for nonlinear anisotropic diffusion of images. We show that image feature selective diffusion (smoothing) can be achieved by making the relaxation parameter in the lattice Boltzmann equation be image feature and direction dependent. The models naturally lead to the numerical algorithms that are easy to implement. Experimental results on both synthetic and real images are described.     

Adjoint-based fluid flow control and optimisation with lattice Boltzmann methods

A lattice Boltzmann (LB) framework to solve fluid flow control and optimisation problems numerically is presented. Problems are formulated on a mesoscopic basis. In a side condition, the dynamics of a Newtonian fluid is described by a family of simplified Boltzmann-like equations, namely BGK–Boltzmann equations, which are linked to an incompressible Navier–Stokes equation. It is proposed to solve the non-linear optimisation problem by a line search algorithm. The needed derivatives are obtained by deriving the adjoint equations, referred to as adjoint BGK–Boltzmann equations. The primal equations are discretised by standard lattice Boltzmann methods (LBM) while for the adjoint equations a novel discretisation strategy is introduced. The approach follows the main ideas behind LBM and is therefore referred to as adjoint lattice Boltzmann methods (ALBM). The corresponding algorithm retains most of the basic features of LB algorithms. In particular, it enables a highly-efficient parallel implementation and thus solving large-scale fluid flow control and optimisation problems. The overall solution strategy, the derivation of a prototype adjoint BGK–Boltzmann equation, the novel ALBM and its parallel realisation as well as its validation are discussed in detail in this article. Numerical and performance results are presented for a series of steady-state distributed control problems with up to approximately 1.6 million unknown control parameters obtained on a high performance computer with up to 256 processing units.     

Multi-thread implementations of the lattice Boltzmann method on non-uniform grids for CPUs and GPUs

Two multi-thread based parallel implementations of the lattice Boltzmann method for non-uniform grids on different hardware platforms are compared in this paper: a multi-core CPU implementation and an implementation on General Purpose Graphics Processing Units (GPGPU). Both codes employ second order accurate compact interpolation at the interfaces, coupling grids of different resolutions. Since the compact interpolation technique is both simple and accurate, it produces almost no computational overhead as compared to the lattice Boltzmann method for uniform grids in terms of node updates per second. To the best of our knowledge, the current paper presents the first study on multi-core parallelization of the lattice Boltzmann method with inhomogeneous grid spacing and nested time stepping for both CPUs and GPUs.     

一类偏微分方程的格子Boltzmann模型

研究了对流扩散方程、Burgers方程和Modified-Burgers方程等具有相同形式的一类偏微分方程。并且构建了带修正函数项的D1Q3格子Boltzmann模型求解这类方程。为了能准确地恢复出此宏观方程,利用Chapman-Enskog展开和多尺度分析技术,推导出了各个方向的平衡态分布函数和修正函数的具体表达式。数值计算结果表明该模型是稳定、有效的。     

On improving the performance of large parallel lattice Boltzmann flow simulations in heterogeneous porous media

Classical Cartesian domain decompositions for parallel lattice Boltzmann simulations of fluid flow through heterogeneous porous media are doomed to workload imbalance as the number of processors increases, thus leading to decreasing parallel performance. A one-lattice lattice Boltzmann method (LBM) implementation with vector data structure combined with even fluid node partitioning domain decomposition and fully-optimized data transfer layout is presented. It is found to provide nearly-optimal workload balance, lower memory usage and better computational performance than classical slice decomposition techniques using sparse matrix data structures. Predictive memory usage and parallel performance models are also established and observed to be in very good agreement with data corresponding to numerical fluid flow simulations performed through 3-dimensional packings of cylinders and polydisperse spheres.     

Verification of surface tension in the parallel free surface lattice Boltzmann method in waLBerla

The free surface lattice Boltzmann method in the parallel software framework waLBerla solves a wide range of two-phase flow scenarios efficiently by neglecting the gas flow and only taking the gas pressure into account. To obtain a good parallel efficiency, an extensive algorithm computes the curvature needed to calculate the surface tension pressure by using only a restricted set of neighboring data, reducing the communication effort. This, however, is assumed to be the main limitation of the accuracy of the surface tension computation. Nevertheless, this work shows that this method is able to simulate typical two-phase applications accurately enough. It is validated by comparing the evolution of capillary waves to analytical solution, and checking the agreement of a rising bubble’s velocity with experiments. The results show that the method differs less than 10% from theory in the micro-scale, and lies well within the confidence interval of experimental measurements.     

Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow

Over the last decade, lattice Boltzmann methods have proven to be reliable and efficient tools for the numerical simulation of complex flows. The specifics of such methods as turbulence solvers, however, are not yet completely documented. This paper provides results of direct numerical simulations (DNS), by a lattice Boltzmann scheme, of fully developed, incompressible, pressure-driven turbulence between two parallel plates. These are validated against results from simulations using a standard Chebyshev pseudo-spectral method. Detailed comparisons, in terms of classical one-point turbulence statistics at moderate Reynolds number, with both numerical and experimental data show remarkable agreement.

Consequently, the choice of numerical method has, in sufficiently resolved DNS computations, no dominant effect at least on simple statistical quantities such as mean flow and Reynolds stresses. Since only the method-independent statistics can be credible, the choice of numerical method for DNS should be determined mainly through considerations of computational efficiency. The expected practical advantages of the lattice Boltzmann method, for instance against pseudo-spectral methods, are found to be significant even for the simple geometry and the moderate Reynolds number considered here. This permits the conclusion that the lattice Boltzmann approach is a promising DNS tool for incompressible turbulence.     

A front-tracking lattice Boltzmann method to study flow-induced deformation of three-dimensional capsules

In this paper, a hybrid method is proposed to study the flow-induced deformation of three-dimensional capsules. The capsules consist of Newtonian liquid drops enclosed by thin elastic membranes. In the proposed approach, the front-tracking method is coupled with the lattice Boltzmann method. The fluids inside and outside the capsule is treated as one fluid with varying physical properties, and is modeled by the lattice Boltzmann equation. The capsule membrane is explicitly tracked by the membrane nodes that are advected by the flow. The multi-block strategy of the lattice Boltzmann method is employed to refine the mesh near the capsule, which greatly increase the accuracy and efficiency of the three-dimensional computation. The capsule membrane is discretized into unstructured flat triangular elements, and a finite element model is incorporated to account for the membrane mechanics. With the present method, the transient deformation of initially spherical capsules with membrane following Neo-Hookean constitutive laws is simulated in shear flow, under various dimensionless shear rates and ratios of internal to surrounding liquid viscosities. The present results, including the Taylor shape parameter, the capsule inclination angle and the tank-treading frequency, agree well with previously published numerical results.