稀薄流到连续流的气体运动论模型方程算法研究

通过引入碰撞松弛参数和当地平衡态分布函数对BGK模型方程进行修正，确定含流态控制参数可描述不同流域气体流动特性的气体分子速度分布函数的简化控制方程。发展和应用离散速度坐标法于气体分子速度空间，利用一套在物理空间和时间上连续而速度空间离散的分布函数来代替原分布函数对速度空间的连续依赖性。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，建立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方法。推广应用改进的Gauss-Hermite无穷积分法和华罗庚－王元提出的以单和逼近重积分的黄金分割数论积分方法等，对离散速度空间进行宏观取矩获取物理空间各点的气体流动参数，由此发展一套从稀薄流到连续流各流域统一的气体运动论数值算法。通过对不同Knudsen数下一维激波管问题、二维圆柱绕流和三维球体绕流的初步数值实验表明文中发展的数值算法是可行的。     

气体动理学统一算法中相容性条件不满足引起的数值误差及其影响研究

求解玻尔兹曼(Boltzmann) 模型方程的气体动理学统一算法(unified gas kinetic scheme,UGKS) 是为模拟存在显著稀薄气体效应流动而建立的. 在该方法中,如果速度空间离散采用传统的离散速度坐标法(discreteordinate method,DOM),将会导致相容性条件得不到严格满足,从而引入数值误差. 本文从理论分析及数值试验两方面说明了该数值误差,正比于来流马赫数,反比于来流努森数. 引入了守恒型的离散速度坐标法(conservativediscrete ordinate method,CDOM),在离散层面上确保了相容性条件得到严格满足. 圆柱绕流计算结果表明,来流马赫数较高、努森数较小时,相容性条件满足与否对计算结果影响较大,采用CDOM 可以在较稀的速度空间网格上得到网格无关解,缩减计算量最大可达2/3.      

一种可压缩与不可压缩气体流动的统一算法及其应用

本文采用伪时间变化率项及其"预处理"矩阵,并结合LU-SGS离散格式,发展了可压缩与不可压缩气体流动求解的统一算法.该方法有效地消除了采用可压缩方法求解低速流动时容易产生的"刚性"问题,减小了由于压力项在低速情况下产生的舍入误差.同时,在求解低速与高速并存的流场流动时,无需进行预处理矩阵的转换,实现了可压缩与不可压缩气体流动的统一理论求解.作为算法有效性的验证,本文分别计算了低速、高速、高低速混合流动的典型算例.计算值的验证结果比较表明,对求解马赫数大范围变化情况下的流场,具有很好的收敛性与稳定性,而且收敛速度基本不受流动速度的影响.这个算法程序为今后发展用于燃烧反应流动和密度梯度驱动流动的分析建立了方法基础.     

耦合离散流体理论的差分格式及其应用

求解Navier-Stokes方程组,一直是粘性流动计算的主导途径。但在计算中,都是在一定的网格单元上进行离散,而对不同的离散单元,流动的特征并不相同。本文通过离散单元上网格雷诺数的变化分析,采用耦合离散流体理论（CDFT）差分格式,对向后台阶底部超声速流动问题进行数值模拟,得到了满意的结果。     

基于Boltzmann模型方程的气体运动论统一算法研究

模型方程出发,研究确立含流态控制参数可描述不同流域气体流动特征的气体分子速度分布函数方程; 研究发展气体运动论离散速度坐标法, 借助非定常时间分裂数值计算方法和NND差分格式, 结合DSMC方法关于分子运动与碰撞去耦技术, 发展直接求解速度分布函数的气体运动论耦合迭代数值格式; 研制可用于物理空间各点宏观流动取矩的离散速度数值积分方法, 由此提出一套能有效模拟稀薄流到连续流不同流域气体流动问题统一算法. 通过对不同Knudsen数下一维激波内流动、二维圆柱、三维球体绕流数值计算表明, 计算结果与有关实验数据及其它途径研究结果(如DSMC模拟值、N-S数值解)吻合较好, 证实气体运动论统一算法求解各流域气体流动问题的可行性. 尝试将统一算法进行HPF并行化程序设计, 基于对球体绕流及类``神舟'返回舱外形绕流问题进行HPF初步并行试算, 显示出统一算法具有很好的并行可扩展性, 可望建立起新型的能有效模拟各流域飞行器绕流HPF并行算法研究方向. 通过将气体运动论统一算法推广应用于微槽道流动计算研究, 已初步发展起可靠模拟二维短微槽道流动数值算法; 通过对Couette流、Poiseuille流、压力驱动的二维短槽道流数值模拟, 证实该算法对微槽道气体流动问题具有较强的模拟能力, 可望发展起基于Boltzmann模型方程能可靠模拟MEMS微流动问题气体运动论数值计算方法研究途径.      

一种基于块雅可比迭代的高阶FR格式隐式方法

最近, 基于非结构网格的高阶通量重构格式(flux reconstruction, FR)因其构造简单且通用性强而受到越来越多人的关注. 但将FR格式应用于大规模复杂流动的模拟时仍面临计算开销大、求解时间长等问题. 因此, 亟需发展与之相适应的高效隐式求解方法和并行计算技术. 本文提出了一种基于块Jacobi迭代的高阶FR格式求解定常二维欧拉方程的单GPU隐式时间推进方法. 由于直接求解FR格式空间和隐式时间离散后的全局线性方程组效率低下并且内存占用很大. 而通过块雅可比迭代的方式, 能够改变全局线性方程组左端矩阵的特征, 克服影响求解并行性的相邻单元依赖问题, 使得只需要存储和计算对角块矩阵. 最终将求解全局线性方程组转化为求解一系列局部单元线性方程组, 进而又可利用LU分解法在GPU上并行求解这些小型局部线性方程组. 通过二维无黏Bump流动和NACA0012无黏绕流两个数值实验表明, 该隐式方法计算收敛所用的迭代步数和计算时间均远小于使用多重网格加速的显式Runge-Kutta格式, 且在计算效率方面至少有一个量级的提升.      

管系内一维可压缩流动数值建模与特性分析

针对复杂管系内可压缩流体,基于有限体积法,采用HLLC(Harten-Lax-vanLeerContact)格式和黎曼求解器构建了有限控制体数值离散方法,引入虚拟节点用于连接有限控制体,借助虚拟节点给出控制体之间数值通量的计算格式,发展了一种管道内一维流动数值建模方法。针对含有分支管路的管系,在管道连接部位构建了分支管路拟一维流动数值计算模型。基于所发展的一维流动数值方法,建立了变径管道和含60°分支管道内流动计算模型,验证了该方法的收敛性和有效性;基于虚拟节点的数值格式处理变径管激波问题具有一定精度优势。研究了变径管和分支管模型中可压缩流体激波、稀疏波等的传播机理,分析了管径对相邻支管压力的影响,为工程管路设计提供了参考。     

基于制造解的非结构二阶有限体积离散格式的精度测试与验证

随着计算机技术的飞速进步,计算流体力学得到迅猛发展,数值计算虽能够快速得到离散结果,但是数值结果的正确性与精度则需要通过严谨的方法来进行验证和确认.制造解方法和网格收敛性研究作为验证与确认的重要手段已经广泛应用于计算流体力学代码验证、精度分析、边界条件验证等方面.本文在实现标量制造解和分量制造解方法的基础上,通过将制造解方法精度测试结果与经典精确解(二维无黏等熵涡)精度测试结果进行对比,进一步证实了制造解精度测试方法的有效性,并将两种制造解方法应用于非结构网格二阶精度有限体积离散格式的精度测试与验证,对各种常用的梯度重构方法、对流通量格式、扩散通量格式进行了网格收敛性精度测试.结果显示,基于Green-Gauss公式的梯度重构方法在不规则网格上会出现精度降阶的情况,导致流动模拟精度严重下降,而基于最小二乘(least squares)的梯度重构方法对网格是否规则并不敏感.对流通量格式的精度测试显示,所测试的各种对流通量格式均能达到二阶精度,且各方法精度几乎相同;而扩散通量离散中界面梯度求解方法的选择对流动模拟精度有显著影响.     

求解多维双曲守恒律方程组的四阶半离散格式

提出了求解多维双曲守恒律方程组的四阶半离散格式。该方法以中心加权基本无振荡(CWENO)重构为基础,同时考虑到在R iemann扇内波传播的局部速度,从而回避了计算过程中的网格交错,建立了数值耗散较小的介于迎风格式和中心格式之间的半离散格式。本文的四阶半离散格式是Kurganov等人的三阶半离散格式的高阶推广。大量的数值算例充分说明了本文方法的高分辨率和稳定性。     

基于四阶半离散中心迎风格式的虚拟流方法的应用

给出了求解多维无粘可压Euler方程组的四阶半离散中心迎风格式,该格式根据非线性波在网格单元边界上传播的局部速度来更准确地估计局部Riemann的宽度,避免了计算网格的交错,降低了格式的数值粘性。同时,考虑到Level Set函数能隐式地追踪到界面的位置,而虚拟流的构造能隐式地捕捉到界面的边界条件,因此再将新的四阶半离散中心迎风格式与Level Set方法以及虚拟流方法相结合,成功地处理了非反应激波和多介质流中爆轰间断的追踪问题。     

Computations of flow over a flexible plate using the hybrid Cartesian/immersed boundary method

A hybrid Cartesian/immersed boundary code is developed and applied to interactions between a flexible plate and a surrounding fluid. The velocities at the immersed boundary (IB) nodes are reconstructed by interpolations along local normal lines to an interface. A new criterion is suggested to distribute the IB nodes near an interface. The suggested criterion guarantees a closed fluid domain by a set of the IB nodes and it is applicable to a zero‐thickness body. To eliminate the pressure interpolation at the IB nodes, the hybrid staggered/non‐staggered grid method is adapted. The developed code is validated by comparisons with other experimental and computational results of flow around an in‐line oscillating cylinder. Good agreements are achieved for velocity profiles and vorticity and pressure contours. As applications to the fluid–structure interaction, oscillations of flexible plate in a resting fluid and flow over a flexible plate are simulated. The elastic deformations of the flexible plate are modelled based on the equations of motion for plates considering the fluid pressure as the external load on the plate. Two non‐dimensional parameters are identified and their effects on the damping of the plate motion are examined. Grid convergence tests are carried out for both cases. Copyright © 2007 John Wiley & Sons, Ltd.     

Multiple-scale modelling of acoustic sources in low Mach-number flow

The main difficulty in the calculation of sound generated by fluid flow at low Mach numbers is the occurrence of different scales. The fluid flow is characterized by small spatial structures containing a large amount of energy that may propagate with a small convective velocity, such as small vortices in a turbulent flow. The radiated acoustic waves have small amplitudes and carry a small amount of energy, but have a long wavelength due to their fast propagation velocity. In this paper a perturbation method is used to calculate noise generation and propagation in combination with fluid flow based on the incompressible equations. The idea for the numerical modelling is to introduce a fine grid for the resolution of the fluid flow that is embedded into a larger acoustical domain with a coarse grid adapted to the long wavelength acoustics. To get an appropriate restriction of the acoustic source terms from the fine CFD-grid to the coarse CAA-grid, a multi-scale expansion with one time and two space scales is introduced. To cite this article: C.-D. Munz et al., C. R. Mecanique 333 (2005).     

入口速度比对射流拟序结构的影响

为了深入了解湍流流动机理以及湍流拟序结构发现过程的影响因素，本文采用大涡模拟方法对不同入口射流伴流速度比的平面湍射流流动进行了数值模拟。采用分步投影法求解动量方程，亚格子项采用标准Smagorinsky亚格子模式模拟，压力泊松方程采用修正的循环消去法快速求解，空间方程采用二阶精度的差分格式，在时间方向上采用二阶精度的显式差分格式。模拟结果给出了平面射流中湍流拟序结构的瞬态发展演变过程，分析了入口速度比对射流拟序结构发展演化过程及宏观流场形态的影响。为进一步研究射流拟序结构及其在湍流流动中的作用提供了基础。     

Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

三维非均匀不稳定渗流方程的二维不均匀粗化算法

在无源汇条件下,根据流过某一个横截面的流体流量等于流过这一横截面内所有精细网格的流体流量之和这一特点提出了粗化网格等效渗透率的计算方法。在粗化区内,利用直接解法求解二维渗流方程,再用这些解合成粗化网格的三维合成解,并由合成解计算粗化网格的等效渗透率。根据精度的要求采用了不均匀网格粗化,在流体流速大的区域采用精细网格。利用所得等效渗透率计算了粗化网格的某三维非均匀不稳定渗流场的压降解,结果表明三维非均匀不稳定渗流方程的二维不均匀粗化解非常逼近采用精细网格的解,但计算的速度比采用精细网格提高了80倍。     

Local similarity solution for the flow of a “second-grade” viscoelastic fluid above a moving plate

The boundary layer flow of a viscoelastic fluid of the second-grade type over a rigid continuous plate moving through an otherwise quiescent fluid with constant velocity U is studied. Assuming the flow to be laminar and two-dimensional, local similarity solution is found with fluid's elasticity and plate's withdrawal speed as the main variables. Results are presented for velocity profiles, boundary layer thickness, wall skin friction coefficient and fluid entrainment in terms of the local Deborah number. A marked formation of boundary layer is predicted, even at low Reynolds numbers, provided the Deborah number is sufficiently large. The boundary layer thickness and the wall skin friction coefficient are found to scale with fluid's elasticity—both decreasing the higher the fluid's elasticity. The amount of fluid entrained is also predicted to decrease whenever a fluid exhibits elastic behavior.     

A hybrid immersed boundary and material point method for simulating 3D fluid–structure interaction problems

A numerical method is developed for solving the 3D, unsteady, incompressible Navier–Stokes equations in curvilinear coordinates containing immersed boundaries (IBs) of arbitrary geometrical complexity moving and deforming under forces acting on the body. Since simulations of flow in complex geometries with deformable surfaces require special treatment, the present approach combines a hybrid immersed boundary method (HIBM) for handling complex moving boundaries and a material point method (MPM) for resolving structural stresses and movement. This combined HIBM & MPM approach is presented as an effective approach for solving fluid–structure interaction (FSI) problems. In the HIBM, a curvilinear grid is defined and the variable values at grid points adjacent to a boundary are forced or interpolated to satisfy the boundary conditions. The MPM is used for solving the equations of solid structure and communicates with the fluid through appropriate interface‐boundary conditions. The governing flow equations are discretized on a non‐staggered grid layout using second‐order accurate finite‐difference formulas. The discrete equations are integrated in time via a second‐order accurate dual time stepping, artificial compressibility scheme. Unstructured, triangular meshes are employed to discretize the complex surface of the IBs. The nodes of the surface mesh constitute a set of Lagrangian control points used for tracking the motion of the flexible body. The equations of the solid body are integrated in time via the MPM. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at stationary curvilinear grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. The influence of the fluid on the body is defined through pressure and shear stresses acting on the surface of the body. The HIBM & MPM approach is validated for FSI problems by solving for a falling rigid and flexible sphere in a fluid‐filled channel. The behavior of a capsule in a shear flow was also examined. Agreement with the published results is excellent. Copyright © 2007 John Wiley & Sons, Ltd.     

Performance analysis and application of grid interpolation techniques for fluid flows

Although it is common for automated image processing techniques to claim subpixel accuracy in the identification of particles, or centroids of displacements of groups of particles, additional errors are inevitably introduced when and if these data are reinterpolated back onto a grid mesh whose nodes lie at different locations from the original data. Moreover, these errors can be large compared to the errors introduced in the original image processing step.Two different techniques, convolution with an adaptive Gaussian window (AGW), and a two-dimensional thin-shell spline (STS), have been compared and contrasted for interpolating irregularly spaced data onto a regular grid. Both techniques are global interpolators; the Gaussian kernel applies an ad hoc choice of smooth function, while the thin-shell spline minimises a global functional proportional to the Laplacian of the velocity field. In this way, the smoothness constraint on the spline coefficients may be thought of as akin to a viscous smoothing of the fluid flow.Performance curves are given, enabling the investigator to make an informed choice of interpolating routine and grid interpolation parameters to minimise the interpolation errors, given various external constraints. Some illustrative example applications on real experimental data are described. In general, the importance of matching the interpolation technique to the characteristics of the original data is stressed. It is also pointed out that a correct interpretation of grid interpolated data must be based on a basic knowledge of the performance characteristics of that interpolator. Finally, recommendations are made concerning the development of surface spline techniques for problems involving large numbers of data points.     

A hybrid time stepping scheme combining explicit Runge–Kutta with implicit LU‐SGS for Navier–Stokes equations

A hybrid time stepping scheme is developed and implemented by a combination of explicit Runge–Kutta with implicit LU‐SGS scheme at the level of system matrix. In this method, the explicit scheme is applied to those grid cells of blocks that have large local time steps; meanwhile, the implicit scheme is applied to other grid cells of blocks that have smaller allowable local time steps in the same flow field. As a result, the discretized governing equations can be expressed as a compound of explicit and implicit matrix operator. The proposed method has been used to compute the steady transonic turbulent flow over the RAE 2822 airfoil. The numerical results are found to be in excellent agreement with the experimental data. In the validation case, the present scheme saved at least 50% of the memory resources compared with the fully implicit LU‐SGS. Copyright © 2015 John Wiley & Sons, Ltd.     

Accelerating fully resolved simulation of particle-laden flows on heterogeneous computer architectures

An efficient computing framework, namely PFlows, for fully resolved-direct numerical simulations of particle-laden flows was accelerated on NVIDIA General Processing Units (GPUs) and GPU-like accelerator (DCU) cards. The framework is featured as coupling the lattice Boltzmann method for fluid flow with the immersed boundary method for fluid-particle interaction, and the discrete element method for particle collision, using two fixed Eulerian meshes and one moved Lagrangian point mesh, respectively. All the parts are accelerated by a fine-grained parallelism technique using CUDA on GPUs, and further using HIP on DCU cards, i.e., the calculation on each fluid grid, each immersed boundary point, each particle motion, and each pair-particle collision is responsible by one computer thread, respectively. Coalesced memory accesses to LBM distribution functions with the data layout of Structure of Arrays are used to maximize utilization of hardware bandwidth. Parallel reduction with shared memory for data of immersed boundary points is adopted for the sake of reducing access to global memory when integrate particle hydrodynamic force. MPI computing is further used for computing on heterogeneous architectures with multiple CPUs-GPUs/DCUs. The communications between adjacent processors are hidden by overlapping with calculations. Two benchmark cases were conducted for code validation, including a pure fluid flow and a particle-laden flow. The performances on a single accelerator show that a GPU V100 can achieve 7.1–11.1 times speed up, while a single DCU can achieve 5.6–8.8 times speed up compared to a single Xeon CPU chip (32 cores). The performances on multi-accelerators show that parallel efficiency is 0.5–0.8 for weak scaling and 0.68–0.9 for strong scaling on up to 64 DCU cards even for the dense flow (φ = 20%). The peak performance reaches 179 giga lattice updates per second (GLUPS) on 256 DCU cards by using 1 billion grids and 1 million particles. At last, a large-scale simulation of a gas-solid flow with 1.6 billion grids and 1.6 million particles was conducted using only 32 DCU cards. This simulation shows that the present framework is prospective for simulations of large-scale particle-laden flows in the upcoming exascale computing era.