共查询到16条相似文献,搜索用时 234 毫秒
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基于从稀薄流到连续流的跨流域气体动理论统一算法(gas-kinetic unified algorithm,GKUA),通过数值求解考虑转动自由度激发的Boltzmann-Rykov模型方程,得到了一种跨流域非定常流动数值模拟的方法.该求解方法以Boltzmann模型方程为控制方程,在常温状态下如果考虑转动能激发的情况则选用Rykov模型.文中数值求解Rykov模型时,首先基于转动能模对速度分布函数积分以消去分子转动能量这一自变量,在速度空间应用自适应离散速度坐标法与数值积分演化更新计算技术,在位置空间应用3阶WENO空间离散格式和3阶显式Runge-Kutta时间推进.针对经典的二维Karman涡街流动现象进行数值模拟,说明该跨流域非定常流动模拟算法对于连续流区低速流动的适应性. 相似文献
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为模拟研究高温高马赫数下多原子气体内能激发对跨流域非平衡流动的影响,将转动能、振动能分别作为气体分子速度分布函数的自变量,把转动能和振动能处理为连续分布的能量模式,将Boltzmann方程的碰撞项分解成弹性碰撞项和非弹性碰撞项,同时将非弹性碰撞按一定松弛速率分解为平动-转动能松弛过程和平动-转动-振动能松弛过程,构造了一类考虑振动能激发的Boltzmann模型方程,并证明了其守恒性和H定理.基于内部能量变量对分布函数无穷积分,引入三个约化速度分布函数,得到一组考虑振动能激发的约化速度分布函数控制方程组,使用离散速度坐标法,基于LU-SGS隐式格式和有限体积法求解离散速度分布函数,建立含振动能激发的气体动理论统一算法.通过开展高稀薄流到连续流圆柱绕流问题统一算法与直接模拟蒙特卡罗法模拟结果对比分析,特别是过渡流区平动、转动、振动非平衡效应对绕流流场与物面力热特性的影响机制,证实了所建立的含振动能激发的Boltzmann模型方程及气体动理论统一算法的准确可靠性. 相似文献
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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. 相似文献
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基于Boltzmann模型方程的气体运动论HPF并行算法 总被引:1,自引:1,他引:0
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。 相似文献
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离散速度方向模型是一种简化Boltzmann方程的新方法。该方法通过减少Boltzmann方程的维数来降低数值求解的计算量。在DVD模型中,分子速度的方向是离散的,而分子的速率仍然是连续的,这样就可以用一组三维的速率分布函数来代替Boltzmann方程中六维的速度分布函数。由于减少了三个动量维,同Boltzmann方程相比,DVD模型的数值计算量可以降低几个数量级。本文用数值的方法对DVD模型进行了研究。数值结果显示,在广泛的Knudsen数下,DVD方法可给出精确的计算结果。同线性化Boltzmann方程的计算结果相比,最大的误差不超过6%,在连续介质领域中,误差甚至不超过1%。 相似文献
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针对最新发展的气-固界面作用物理模型,提出一种确定性计算方法。算法的核心是:针对离散速度空间分布函数,采用确定性算法计算出单轮气-固碰撞作用的散射核函数矩阵,并通过考虑吸引势阱作用和迭代累加多次气-固碰撞作用,物理地反映气体分子入射/反射速度分布函数在气-固界面上的变化。与现有基于Monte Carlo随机采样的实现方法对比,该确定性实现方法可以快速且准确地计算边界上气体分子入射/反射速度分布函数的映射关系。因此,该方法可为以离散速度空间为基础的稀薄气体流动模拟方法提供先进的边界条件。 相似文献
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Numerical Simulations of Unsteady Flows from Rarefied Transition to Continuum Using Gas-Kinetic Unified Algorithm 下载免费PDF全文
Junlin Wu Zhihui Li Aoping Peng & Xinyu Jiang 《advances in applied mathematics and mechanics.》2015,7(5):569-596
Numerical simulations of unsteady gas flows are studied on the basis of
Gas-Kinetic Unified Algorithm (GKUA) from rarefied transition to continuum flow
regimes. Several typical examples are adopted. An unsteady flow solver is developed
by solving the Boltzmann model equations, including the Shakhov model and
the Rykov model etc. The Rykov kinetic equation involving the effect of rotational
energy can be transformed into two kinetic governing equations with inelastic and
elastic collisions by integrating the molecular velocity distribution function with the
weight factor on the energy of rotational motion. Then, the reduced velocity distribution
functions are devised to further simplify the governing equation for one- and two-dimensional
flows. The simultaneous equations are numerically solved by the discrete
velocity ordinate (DVO) method in velocity space and the finite-difference schemes in
physical space. The time-explicit operator-splitting scheme is constructed, and numerical
stability conditions to ascertain the time step are discussed. As the application
of the newly developed GKUA, several unsteady varying processes of one- and two-dimensional
flows with different Knudsen number are simulated, and the unsteady
transport phenomena and rarefied effects are revealed and analyzed. It is validated
that the GKUA solver is competent for simulations of unsteady gas dynamics covering
various flow regimes. 相似文献
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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 相似文献
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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/π1/2exp(?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. 相似文献
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研究各流域三维流动问题的Boltzmann模型方程计算方法,建立直接求解分子速度分布函数的气体运动论耦合迭代数值格式;基于变量依赖关系、数据通信与并行可扩展性分析,使用区域分解并行化方法,建立气体运动论数值算法并行方案,发展求解各流域三维绕流问题的气体运动论并行算法.拟定高低不同马赫数下来自不同流域的三维球体及返回舱绕流算例,进行高性能Fortran(HPF)大规模并行计算,将计算结果与有关实验数据、相关理论预测等进行比较分析,研究揭示不同流区复杂绕流现象及流动机理.研究表明,所发展的气体运动论并行算法具有很好的并行独立性,基本达到线性加速的并行效果,显示出良好的并行可扩展性. 相似文献
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LI Zhihui ZHANG Hanxin & FU Song ⒈ National Laboratory for CFD Hypervelocity Aerodynamics Institute China Aerodynamics Research Development Center Mianyang China .Department of Engineering Mechanics Tsinghua University Beijing China 《中国科学G辑(英文版)》2005,48(4):496-512
~~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 … 相似文献
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LI ZhiHui PENG AoPing ZHANG HanXin & DENG XiaoGang National Laboratory for Computational Fluid Dynamics Beijing China China Aerodynamics Research Development Center Mianyang 《中国科学:物理学 力学 天文学(英文版)》2011,(9)
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 ... 相似文献