基于Boltzmann模型方程的气体运动论HPF并行算法

从修正的BGK-Blotzmann模型方程出发，引入离散速度坐标技术对气体分子速度分量进行离散降维，基于非定常时间分裂数值计算方法和无波动、无自由参数的NND耗散差分格式，发展直接求解气体分子速度分布函数的气体运动论有限差分数值格式，提出了一套能有效模拟各流域三维绕流问题的气体运动论统一算法，在分析研究气体运动论数值算法内在并行度的基础上，开展各流域三维绕流问题统一算法的HPF（高性能FORTRAN）并行化程度设计，建立一套能有效模拟各流域复杂外形体绕流的HPF并行算法软件，并进行了不同Knudsen(克努森）数下三维球体绕流及类“神舟号”返回舱外形体绕流的初步数值实验，将计算结果与过渡区有关实验数据及各流域气体绕流现象进行比较分析，证实了发展的气体运动论HPF并行算法在求解稀薄流到连续流不同流域复杂绕流问题方面的可行性。     

跨流域高超声速绕流环境Boltzmann模型方程统一算法研究

如何准确可靠地模拟从外层空间高稀薄流到近地面连续流的航天器高超声速绕流环境与复杂流动变化机理是流体物理的前沿基础科学问题. 基于对Boltzmann方程碰撞积分的物理分析与可计算建模, 确立了可描述自由分子流到连续流区各流域不同马赫数复杂流动输运现象统一的Boltzmann模型速度分布函数方程, 发展了适于高、低不同马赫数绕流问题的离散速度坐标法和直接求解分子速度分布函数演化更新的气体动理论数值格式, 建立了模拟复杂飞行器跨流域高超声速飞行热环境绕流问题的气体动理论统一算法. 对稀薄流到连续流不同Knudsen数0.002 ≤Kn_∞ ≤1.618、不同马赫数下可重复使用卫星体再入过程(110–70 km)中高超声速绕流问题进行算法验证分析, 计算结果与典型文献的Monte Carlo直接模拟值及相关理论分析符合得较好. 研究揭示了飞行器跨流域不同高度高超声速复杂流动机理、绕流现象与气动力/热变化规律, 提出了一个通过数值求解介观Boltzmann模型方程, 可靠模拟高稀薄自由分子流到连续流跨流域高超声速气动力/热绕流特性统一算法.     

气体运动论统一算法在跨流域转动非平衡效应模拟中的应用

从考虑转动松弛变化特性的Rykov模型出发,基于Boltzmann模型方程求解跨流域气体运动论统一算法原理与计算规则,采用转动惯量描述气体分子自旋运动,研究考虑转动非平衡影响的Boltzmann模型方程数值求解方法.通过对氮气激波结构、二维钝头体和三维尖双锥跨流域绕流的模拟分析,验证该算法的跨流域一致适用性.     

考虑转动能的一维/二维Boltzmann-Rykov模型方程数值算法

研究考虑转动能的Boltzmann-Rykov模型方程,基于转动自由度对气体分子速度分布函数矩积分,引入约化速度分布函数,应用离散速度坐标法与数值积分技术,将气体运动论模型方程化为在离散速度坐标点处关于三个约化速度分布函数的联立方程组.应用拓展计算流体力学有限差分方法,数值计算考虑转动自由度的双原子气体一维、二维Boltzmann模型方程,得到高、低Knudsen数一维激波管内流动和二维竖直平板绕流问题的流场,分析验证考虑转动能的Boltzmann-Rykov模型方程全流域统一算法求解一维/二维气体流动问题的可靠性.结果表明,气体稀薄程度与分子内自由度对流场具有较大影响,且Knudsen数较高的稀薄气体流动呈现严重的非平衡流动特点.     

流动和传热问题的分区并行计算

针对交错网格下的SIMPLE数值算法实施了分区并行计算方法,在小型局域网下实现了流动和传热问题的并行数值计算.对两个经典的流动和传热问题的数值模拟实验表明,所建立的并行计算环境和分区并行算法能够得到正确的和收敛的数值结果.但与串行计算结果相比,并行计算误差明显大于串行计算误差.对并行算法做出的性能分析表明,所给出的并行算法得到了明显的加速效率.随着计算规模的增大,加速比和并行效率提高更显著.     

涡流管内三维强旋转流场数值模拟与分析

涡流管内可压缩气体的强旋转流动是涡流管能量分离的根本原因和驱动力,因而涡流管内流场研究是揭示涡流管能量分离物理机制的首要关键问题。由于涡流管内可压缩气体的三维强旋转湍流流动,实验测量中存在诸多问题,而CFD数值模拟技术对此具有很大的优势。文中以涡流管内部流场为研究对象,建立了涡流管计算域模型并进行网格划分,讨论了边界条件、湍流模型以及线性方程组求解策略等问题,对不同冷气流率下的涡流管内三维强旋流流场结构特性进行数值模拟,获得了不同冷气流率下的旋转运动、轴向运动、径向运动和循环流的分布特性。研究表明Realizableκ-ε湍流模型能够充分反映强旋流动特点,数值模拟结果与文献中实验值基本吻合。     

一种可扩展的三维半导体器件并行数值模拟算法

在基于漂移-扩散模型的三维半导体器件数值模拟中,通过有限体积法进行数值离散,采用完全耦合的牛顿迭代求解非线性代数方程组,并使用基于代数多重网格预条件子的GMRES方法求解牛顿迭代中的线性方程组,构造一种稳健且高度可扩展的非结构四面体网格上求解半导体方程的并行算法.基于PHG平台实现该算法的并行计算程序,并对PN结和MOS场效应晶体管等问题进行了最大网格规模达到5亿单元、最大并行规模达到1 024进程的大规模数值模拟实验,结果表明,该算法计算效率高,可扩展性好.     

一种含运动固壁超声速流动的Descartes网格算法

提出一种Descartes网格算法,用于数值求解含任意复杂及运动固壁的超声速流动问题.采用位标集函数确定和跟踪流-固界面.引入虚网格技术处理流-固边界条件,并沿法向和切向分别进行计算.该算法简单、稳健,可与高阶有限差分格式并用.选取一组一维/二维静止或运动物体绕流算例,验证其有效性.     

惯性约束聚变内爆中基于多块结构网格的高效辐射扩散并行算法

针对三维球形靶丸内爆高效模拟需求和传统笛卡尔正交网格上辐射加源困难的问题, 发展一种多块结构非正交网格生成方法, 并基于此种计算网格提出高效的三维扩散格式并行算法, 将其应用于辐射流体方程组的求解和三维内爆不对称性的数值模拟, 数值结果显示了算法的有效性。并行性能测试显示该算法可扩展到5400个核上, 并行效率达到69%。     

隐式格式求解拟压缩性非定常不可压Navier-Stokes方程

采用Rogers发展的双时间步拟压缩方法,数值求解不可压非定常问题.数值通量分别采用三阶精度Roe格式和二阶精度Harten-Yee的TVD格式离散.为了加快收敛,提高求解效率,试验了几种隐式格式(ADI-LU,LGS,LU-SGS).针对经典的低雷诺数(Re=200)圆柱绕流问题,比较了不同隐式方法的计算结果和求解效率,以及两种数值离散格式计算结果的异同.最后采用Roe格式数值求解了两种典型的低速非定常流动问题:绕转动圆柱(ω=1)低雷诺数流动;NACA0015翼型等速拉起数值模拟.     

Study on the unified algorithm for three-dimensional complex problems covering various flow regimes using Boltzmann model equation

The Boltzmann simplified velocity distribution function equation describing the gas transfer phenomena from various flow regimes will be explored and solved numerically in this study. The discrete velocity ordinate method of the gas kinetic theory is studied and applied to simulate the complex multi-scale flows. Based on the uncoupling technique on molecular movement and colliding in the DSMC method, the gas-kinetic finite difference scheme is constructed to directly solve the discrete velocity distribution functions by extending and applying the unsteady time-splitting method from computational fluid dynamics. The Gauss-type discrete velocity numerical quadrature technique for different Mach number flows is developed to evaluate the macroscopic flow parameters in the physical space. As a result, the gas-kinetic numerical algorithm is established to study the three-dimensional complex flows from rarefied transition to continuum regimes. The parallel strategy adapted to the gas-kinetic numerical algorithm is investigated by analyzing the inner parallel degree of the algorithm, and then the HPF parallel processing program is developed. To test the reliability of the present gas-kinetic numerical method, the three-dimensional complex flows around sphere and spacecraft shape with various Knudsen numbers are simulated by HPF parallel computing. The computational results are found in high resolution of the flow fields and good agreement with the theoretical and experimental data. The computing practice has confirmed that the present gas-kinetic algorithm probably provides a promising approach to resolve the hypersonic aerothermodynamic problems with the complete spectrum of flow regimes from the gas-kinetic point of view of solving the Boltzmann model equation. Supported by the National Natural Science Foundation of China (Grant Nos. 90205009 and 10321002) and the National Parallel Computing Center     

Gas-kinetic numerical studies of three-dimensional complex flows on spacecraft re-entry

The gas-kinetic numerical algorithm solving the Boltzmann model equation is extended and developed to study the three-dimensional hypersonic flows of spacecraft re-entry into the atmosphere in perfect gas. In this study, the simplified velocity distribution function equation for various flow regimes is presented on the basis of the kinetic Boltzmann–Shakhov model. The discrete velocity ordinate technique and numerical quadrature methods, such as the Gauss quadrature formulas with the weight function 2/π^1/2exp(?V²) and the Gauss–Legendre numerical quadrature rule, are studied to resolve the barrier in simulating complex flows from low Mach numbers to hypersonic problems. Specially, the gas-kinetic finite-difference scheme is constructed for the computation of three-dimensional flow problems, which directly captures the time evolution of the molecular velocity distribution function. The gas-kinetic boundary conditions and numerical procedures are studied and implemented by directly acting on the velocity distribution function. The HPF (high performance fortran) parallel implementation technique for the gas-kinetic numerical method is developed and applied to study the hypersonic flows around three-dimensional complex bodies. The main purpose of the current research is to provide a way to extend the gas-kinetic numerical algorithm to the flow computation of three-dimensional complex hypersonic problems with high Mach numbers. To verify the current method and simulate gas transport phenomena covering various flow regimes, the three-dimensional hypersonic flows around sphere and spacecraft shape with different Knudsen numbers and Mach numbers are studied by HPF parallel computing. Excellent results have been obtained for all examples computed.     

Numerical study on the gas-kinetic high-order schemes for solving Boltzmann model equation

The high-order compact finite difference technique is introduced to solve the Boltzmann model equation, and the gas-kinetic high-order schemes are developed to simulate the different kinetic model equations such as the BGK model, the Shakhov model and the Ellipsoidal Statistical (ES) model in this paper. The methods are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the inner flows of normal shock wave for different Mach numbers, and the two-dimensional flows past ...     

Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation

~~Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation1. Feynman, R., There's plenty of room at the bottom, Journal of Microelectromechanical Systems, 1992, 1: 60 -66. 2. Piekos, E. S., Breuer, K. S., Numerical modeling of micromechanical devices using the direct simulation Monte Carlo method, Transactions of the ASME, Journal of Fluids Engineering, 1996, 118: 464-469. 3. Beskok, A., Karniadakis, G. E., Trimmer, W., Rarefaction and …     

Rivulet flow on the outer surface of an inclined cylinder

A study of the three-dimensional flow of a liquid film (rivulet) over the external part of an inclined cylinder was conducted for liquids with various physical properties. Patterns of the flow regimes were constructed. Good agreement is observed between the experimental data on the thickness and wall friction with the calculation with an asymptotic model in the case of a waveless rivulet. A comparison of the evolution of natural waves on rivulets with the theory of waves of maximal growth shows good agreement for small Re numbers. During the experiments, the wave characteristics of excited waves on a rivulet were investigated. The thickness, amplitude, frequency, and phase velocity of the waves over a wide range of variable parameters are given. Phase velocity integrated functions of the amplitude are constructed for various liquids. The friction on the cylinder wall is measured in the presence of natural and excited waves. The effects of wave regimes on the average values and RMS (root-mean-square) friction pulsations are studied.     

A Switch Function-Based Gas-Kinetic Scheme for Simulation of Inviscid and Viscous Compressible Flows

In this paper, a switch function-based gas-kinetic scheme (SF-GKS) is presented for the simulation of inviscid and viscous compressible flows. With the finite volume discretization, Euler and Navier-Stokes equations are solved and the SF-GKS is applied to evaluate the inviscid flux at cell interface. The viscous flux is obtained by the conventional smooth function approximation. Unlike the traditional gas-kinetic scheme in the calculation of inviscid flux such as Kinetic Flux Vector Splitting (KFVS), the numerical dissipation is controlled with a switch function in the present scheme. That is, the numerical dissipation is only introduced in the region around strong shock waves. As a consequence, the present SF-GKS can well capture strong shock waves and thin boundary layers simultaneously. The present SF-GKS is firstly validated by its application to the inviscid flow problems, including 1-D Euler shock tube, regular shock reflection and double Mach reflection. Then, SF-GKS is extended to solve viscous transonic and hypersonic flow problems. Good agreement between the present results and those in the literature verifies the accuracy and robustness of SF-GKS.     

面向结构网格并行应用的一类快速通信算法

通信算法需要在相邻子区域间传输数据.通过求解子区域间的相交问题可以寻找相邻区域.针对子区域的求交问题,基于区间树,结合结构网格应用的特点,构造近似线性时间复杂度的算法.数值实验表明该算法具有较高的计算效率和可扩展性,能够支持百万量级矩形子区域的并行计算.     

基于I.MX6的数字化仪表设计与实现

为了向工业应用环境提供一种通用化的人机交互工具,以I.MX6处理器为核心设计高性能数字化仪表,集成COM、CAN、以太网、USB总线通信接口和视频采集、数字量输入输出等功能。在Linux操作系统上适配CoDeSys组态运行平台,实现了现场总线通信、图形化人机交互、数据存储、安防监控等多种功能。仪表具有显示界面清晰、可靠性高、应用软件开发灵活、通用性好等优点,能够广泛应用于移动机械、矿山、井下、船舶等恶劣工作环境中。