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。     

Direct numerical and large eddy simulation of longitudinal flow along triangular array of rods using the lattice Boltzmann method

Results of direct numerical (DNS) and large eddy simulation (LES) of turbulent longitudinal flow in rod bundles are presented using the lattice Boltzmann method with the Bhatnagar–Gross–Krook collision operator [P.L. Bhatnagar, E.P. Gross, M. Krook, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev. 94 (1954) 511; Y.H. Qian, d’Humiéres, P. Lallemand, Lattice BGK models for Navier-Stokes equation, Europhys. Lett. 17 (1992) 479] as a computational framework. The problem requires the accurate modeling of curved walls, to which the method proposed by Yu et al. [D. Yu, M.R. Luo, W. Shyy, Viscous flow computations with the method of lattice Boltzmann equation, Prog. Aerospace Sci. 39 (2003) 329] has been applied. The computational domain is a regular hexagonal prism around the rod. Opposite sides of the prism are coupled periodically. In the longitudinal direction periodical boundary conditions are applied and the flow is driven by a body force. Simulations were carried out using two three-dimensional lattices. It has been found that the application of the model with 19 velocities (D3Q19) gives qualitatively false result. However, we have found that the application of the model with 27 links (D3Q27) can provide the proper mean axial velocity profile, and it also predicts the secondary flow patterns deduced from measurements [A.C. Trupp, R.S. Azad, The structure of turbulent flow in triangular array rod bundles, Nucl. Eng. Des. 32 (1975) 47]. Flow pulsation phenomenon is also observed in our simulations just like in some recent measurements of Krauss and Meyer [T. Krauss, L. Meyer, Experimental investigation of turbulent transport of momentum and energy in heated rod bundle, Nucl. Eng. Des. 180 (1998) 185].     

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.     

Multi-agent simulation on multiple GPUs

Multi-agent simulation is widely used in many areas including biology, economic, political, and environmental science to study complex systems. Unfortunately, it is computationally expensive. In this paper, we shall explore the implementation of a general multi-agent simulation system on a system with multiple GPUs acting as accelerators. In particular, we have ported the popular Java multi-agent simulation framework MASON to a nVidia CUDA-based multi-GPU setting. We evaluated our implementation over different numbers and types of nVidia GPUs. For our evaluation, we ported three models in the original version of MASON. On the well-known Boids model, we achieved a speedup of $187\times$. Using a fictional model, we showed that speedup of up to $468\times$ is possible. In the paper, we shall also describe the detailed internals of our system, and the various issues we encountered and how they were solved.     

Entropic lattice Boltzmann method for simulation of binary mixtures

A new kinetic model for binary mixtures and its lattice Boltzmann (LB) discretization is formulated. In the hydrodynamic limit, the model recovers the Navier–Stokes and the Stefan–Maxwell binary diffusion equations, satisfies the indifferentiability principle, and is thermodynamically consistent. The present model is able to simulate mixtures with different Schmidt numbers and with a large molecular weight ratio of the components.     

Memory transfer optimization for a lattice Boltzmann solver on Kepler architecture nVidia GPUs

The Lattice Boltzmann method (LBM) for solving fluid flow is naturally well suited to an efficient implementation for massively parallel computing, due to the prevalence of local operations in the algorithm. This paper presents and analyses the performance of a 3D lattice Boltzmann solver, optimized for third generation nVidia GPU hardware, also known as ‘Kepler’. We provide a review of previous optimization strategies and analyse data read/write times for different memory types. In LBM, the time propagation step (known as streaming), involves shifting data to adjacent locations and is central to parallel performance; here we examine three approaches which make use of different hardware options. Two of which make use of ‘performance enhancing’ features of the GPU; shared memory and the new shuffle instruction found in Kepler based GPUs. These are compared to a standard transfer of data which relies instead on optimized storage to increase coalesced access. It is shown that the more simple approach is most efficient; since the need for large numbers of registers per thread in LBM limits the block size and thus the efficiency of these special features is reduced. Detailed results are obtained for a D3Q19 LBM solver, which is benchmarked on nVidia K5000M and K20C GPUs. In the latter case the use of a read-only data cache is explored, and peak performance of over 1036 Million Lattice Updates Per Second (MLUPS) is achieved. The appearance of a periodic bottleneck in the solver performance is also reported, believed to be hardware related; spikes in iteration-time occur with a frequency of around 11 Hz for both GPUs, independent of the size of the problem.     

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.     

Large eddy simulation of turbulent open duct flow using a lattice Boltzmann approach

Large eddy simulations of turbulent open duct flow are performed using the lattice Boltzmann method (LBM) in conjunction with the Smagorinsky sub-grid scale (SGS) model. A smaller value of the Smagorinsky constant than the usually used one in plain channel flow simulations is used. Results for the mean flow and turbulent fluctuations are compared to experimental data obtained in an open duct of similar dimensions. It is found that the LBM simulation results are in good qualitative agreement with the experiments.     

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。     

Lattice Boltzmann large eddy simulation of subcritical flows around a sphere on non-uniform grids

In this work, the suitability of the lattice Boltzmann method is evaluated for the simulation of subcritical turbulent flows around a sphere. Special measures are taken to reduce the computational cost without sacrificing the accuracy of the method. A large eddy simulation turbulence model is employed to allow efficient simulation of resolved flow structures on non-uniform computational meshes. In the vicinity of solid walls, where the flow is governed by the presence of a thin boundary layer, local grid-refinement is employed in order to capture the fine structures of the flow. In the test case considered, reference values for the drag force in the Reynolds number range from 2000 to 10 000 and for the surface pressure distribution and the angle of separation at a Reynolds number of 10 000 could be quantitatively reproduced. A parallel efficiency of 80% was obtained on an Opteron cluster.     

A scalable interface-resolved simulation of particle-laden flow using the lattice Boltzmann method

We examine the scalable implementation of the lattice Boltzmann method (LBM) in the context of interface-resolved simulation of wall-bounded particle-laden flows. Three distinct aspects relevant to performance optimization of our lattice Boltzmann simulation are studied. First, we optimize the core sub-steps of LBM, the collision and the propagation (or streaming) sub-steps, by reviewing and implementing five different published algorithms to reduce memory loading and storing requirements to boost performance. For each, two different array storage formats are benchmarked to test effective cache utilization. Second, the vectorization of the multiple-relaxation-time collision model is discussed and our vectorized collision and propagation algorithm is presented. We find that careful use of Intel’s Advance Vector Extensions and appropriate array storage formats can significantly enhance performance. Third, in the presence of many finite-size, moving solid particles within the flow field, three different communication schemes are proposed and compared in order to optimize the treatment of fluid-solid interactions. These efforts together lead to a very efficient LBM simulation code for interface-resolved simulation of particle-laden flows. Overall, the optimized scalable code of particle-laden flow is a factor of 4.0-to-8.5 times faster than our previous implementation.     

An improved entropic lattice Boltzmann model for parallel computation

In this paper, we suggest two kinds of approximation methods based on Taylor series expansion which can solve the non-linear equation in entropic lattice Boltzmann model without using any iteration methods such as Newton–Raphson method. The advantage of our methods is to be able to avoid the load imbalance in parallel computation which occurs due to the differences of iteration number on each calculation grid. In this study, ELBM simulations using our methods were compared with those using Newton–Raphson method for the channel flow past a square cylinder in Re = 1000 and the validity of the results and computational effort were investigated. As a result, it was found that the solutions obtained by our methods are qualitatively and quantitatively reasonable and CPU time is shorter than those obtained by Newton–Raphson method.     

Adaptive large eddy simulation

Several a posteriori indicators in the framework of local grid adaptation and large eddy simulation (LES) are evaluated. In LES indicators must be capable to bound not only the discretisation error, but also the modeling error. Moreover, the numerical method must be able to adapt the computational grid dynamically, as the regions requiring different resolution are not static. The performance of different indicators is evaluated in two flow configurations. It turns out that the classic residual based error indicator and the newly introduced heuristic indicator perform best.     

Inlet conditions for large eddy simulation: A review

The treatment of inlet conditions for LES is a complex problem, but of extreme importance as, in many cases, the fluid behaviour within the domain is determined in large part by the inlet behaviour. The reason why it is so difficult to formulate inlet conditions is because the inlet flow must include a stochastically-varying component: ideally this component should ‘look’ like turbulence whilst at the same time be as simple as possible to implement and modify. We review methods for accomplishing this reported in the literature, these being ‘precursor simulation’ methods and ‘synthesis’ methods, and implement our own novel versions of these using the code OpenFOAM. Conclusions have been drawn about the relative merits of the different approaches, based on the physical realism of the results and the ease of construction and use.     

A direct-forcing immersed boundary method for the thermal lattice Boltzmann method

In this study, a direct-forcing immersed boundary method (IBM) for thermal lattice Boltzmann method (TLBM) is proposed to simulate the non-isothermal flows. The direct-forcing IBM formulas for thermal equations are derived based on two TLBM models: a double-population model with a simplified thermal lattice Boltzmann equation (Model 1) and a hybrid model with an advection–diffusion equation of temperature (Model 2). As an interface scheme, which is required due to a mismatch between boundary and computational grids in the IBM, the sharp interface scheme based on second-order bilinear and linear interpolations (instead of the diffuse interface scheme, which uses discrete delta functions) is adopted to obtain the more accurate results. The proposed methods are validated through convective heat transfer problems with not only stationary but also moving boundaries – the natural convection in a square cavity with an eccentrically located cylinder and a cold particle sedimentation in an infinite channel. In terms of accuracy, the results from the IBM based on both models are comparable and show a good agreement with those from other numerical methods. In contrast, the IBM based on Model 2 is more numerically efficient than the IBM based on Model 1.     

Bluff body flow simulation using lattice Boltzmann equation with multiple relaxation time

Numerical simulations using multiple-relaxation-time lattice Boltzmann model (MRT-LBM) are carried out for a long slender rigid circular cylinder in a cross flow to examine three-dimensional wake effect on the flow-induced forces. A mesh refinement technique is applied in the MRT-LBM calculation. The aim is to assess the validity and efficiency of the MRT-LBM model in three-dimensional calculation. In order to simulate the practical situation correctly, wall boundary conditions are specified at both ends of the cylinder. The aspect ratio of the slender cylinder is 16. The calculation is compared with results obtained from a finite volume method (FVM) and a lattice BGK model [Bhatnagar PL, Gross EP, Krook M. A model for collision processes in gases. 1. Small amplitude processes in charged and neutral one-component systems. Phys Rev 1954;94:511–25] with refined grid. Good agreement is obtained. It is found that the MRT-LBM is more efficient and faster in three-dimensional calculations.     

大规模流场模拟中壁面距离的并行计算方法研究

采用MPI多进程和Open MP多线程两级并行相结合的方式,实现了循环盒子法的并行计算,并对其预处理算法进行了改进。在国家超算广州中心的"天河-2"系统上,完成了对亿级网格量的超燃冲压发动机燃烧室算例的测试。结果分析表明,进程盒子法和边界盒子法不存在盒子切割数的选择问题,边界盒子法较其他算法具有更好的加速比,可显著提高壁面距离的计算效率。     

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。     

Solving the Boltzmann equation on GPUs

We show how to accelerate the direct solution of the Boltzmann equation using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we choose a method of solution which combines a finite difference discretization of the free-streaming term with a Monte Carlo evaluation of the collision integral. The efficiency of the code is demonstrated by solving the two-dimensional driven cavity flow. Computational results show that it is possible to cut down the computing time of the sequential code of two order of magnitude. This makes the proposed method of solution a viable alternative to particle simulations for studying unsteady low Mach number flows.     

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.