用粘性体力方法计算轴流叶轮机械内部流场

阐述了一种用于叶轮机械内部三维粘性流场计算程序。该程序以有限体积显式时间推进方法为基础,用Baldwin-Lomax模型模拟湍流流动,用局部时间步长和多重网格方法提高计算效率。使用上述方法计算了NASA 37^#跨音速压气机转子流场,并与实验结果进行了比较,从而证明文中提出的方法能够快速、准确地模拟轴流叶轮机械内部复杂三维流场,该方法具有较强的工程实用意义。     

用隐式方法和WENO格式计算悬停旋翼跨声速无粘流场

寻找一种能够准确计算以涡为主要特征的复杂流场和克服尾迹耗散问题的数值方法,一直是旋翼空气动力学研究的热点和难点。本文发展了一种基于高阶迎风格式计算悬停旋翼无粘流场的隐式数值方法。无粘通量采用Roe通量差分分裂格式,为提高精度,使用五阶WENO格式进行左右状态插值,并与MUSCL插值进行比较。为提高收敛到定常解的效率,时间推进采用LU-SGS隐式方法。用该方法对一跨声速悬停旋翼无粘流场进行了数值计算,数值结果表明WENO-Roe的激波分辨率高于MUSCL-Roe,体现出了格式精度的提高对计算结果的改善,LU-SGS隐式方法的计算效率比5步Runge-Kutta显式方法的高。     

含分流叶片的离心压缩机级内三维流场数值分析

使用Fine/Turbo三维粘性计算程序对含分流叶片半开式叶轮的离心压缩机级内三维粘性流场进行数值分析.该程序应用Jameson的中心差分格式结合Yang&Shih k-ε湍流模型,使用时间推进法求解雷诺平均N-S方程,用四阶显式Runge-Kutta法进行时间推进.计算中CFL数取2.5,残差收敛至10-4数量级、计算域进出口质量流量误差小于0.05%时认为收敛.并为进一步的产品优化设计及改进研究打下基础.计算结果表明该模级的数值模拟曲线与实验值吻合良好;叶轮出口截面上两个通道的速度分布极不均匀,右通道的速度比左通道的变化剧烈.为了加快收敛,计算时采用了隐式残差平均法及完全多重网格技术.     

不可压缩流动的移动粒子半隐式法数值模拟

介绍了一种新的移动粒子半隐式方法。该方法采用Lagrange描述,用一系列离散粒子代替流体,通过半隐式求解和时间推进法来进行计算,弥补了传统网格法对复杂形状、大变形、高速撞击等情况下网格划分和重构过于繁琐的缺点,在模拟不可压缩流动问题中得到了较好的效果。     

近似平衡多项式加速度动力显式算法

利用已知初始时刻的信息，建立一种可以取到任意阶高精度的多项式加速度单步隐式算法。在该隐式方法中，待采解方程纽系数矩阵中质量阵的系数远远大于阻尼阵和剐度阵的系数，略去非对角阻尼阵和非对角刚度阵对方程组的影响，得到一种近似平衡多项式加速度动力显式计算方法。此方法的精度主要由加速度多项式插值的项数、步长、质量阵的每件数、质量刚度比（质量阵和刚度阵的范数之比）决定。在此基础上给出了这种算法的通式，进行了精度分析，结果表明：如果时间步长h足够短，n次加速度近似平衡动力显式算法的精度可以达到O（hn＋1）。算例采用5次加速度近似平衡显式算法，计算结果的精确性证明了本算法的可行性。     

气体动理学统一算法的隐式方法研究

目前的气体动理学统一算法(unified gas kinetic scheme, 简称UGKS) 在求解高速流动问题时的计算效率,难以满足求解复杂工程问题的需求. 为了提高该算法的计算效率, 本文对模型方程的对流项和碰撞项进行了隐式处理, 并针对UGKS 界面通量与演化时间相关的特点, 引入了演化时间平均界面通量, 通过对控制方程矩阵进行近似LU 分解(lower-upper decomposition), 实现了隐式UGKS. 不同来流马赫数的圆柱绕流算例测试表明, 只要演化时间选取得当, 隐式方法可以得到与显式方法完全相同的结果, 且计算效率可以提高1~2 个量级.      

推进－迭代算法计算效率的研究

本文对求解三维定常超音速动性流场的一次空间推进，在每一个推进站沿伪时间层局部迭代的推进－迭代算法作了进一步的研究．在每一推进站（侧向平面）沿伪时间层局部迭代时，给出了四种不同的隐式迭代方法，即沿侧面两个方向（法向和周向）全用隐式；法向隐式而周向采用Ｇａｕｓｓ－Ｓｉｌｄｌｅ来回扫描迭代；法向隐式而周向显式及以系数矩阵谱半径代替系数矩阵的简化标量隐式算法．用这四种算法模拟了三维球锥黏性绕流，给出了四种不同算法的计算效率和收敛特性比较．     

全机绕流Euler方程多重网格分区计算方法

全机三维复杂形状绕流数值求解只能采用分区求解的方法,本文采用可压缩Euler方程有限体积方法以及多重网格分区方法对流场进行分区计算。数值方法采用改进的van Leer迎风型矢通量分裂格式和MUSCL方法,基于有限体积方法和迎风型矢通量分裂方法,建立一套处理子区域内分界面的耦合条件。各个子区域之间采用显式耦合条件,区域内部采用隐式格式和局部时间步长等,以加快收敛速度。计算结果飞机表面压力分布等气动力特性与实验值进行了比较,二者基本吻合。计算结果表明采用分析“V”型多重网格方法,能提高计算效率,加快收敛速度达到接近一个量级。根据全机数值计算结果和可视化结果讨论了流场背风区域旋涡的形成过程。     

多重网格法求解轴流压气机内部流场

提出了一种能够与显式时间推进法、有限体积差分格式、粘性体积力法有效地配合使用的有效地配合使用的多重网格法来解轴流压气机内部流场。作者对美国NASA37^#跨音速轴流压气机转子内部流场的数值计算表明,多重网格法的计算结果与试验结果吻合, 同时该多重网格法的收敛速度比不用多重网格法加快了1．5倍。     

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.      

A discussion and comparison of numerical techniques used to solve the Navier–Stokes and Euler equations

This paper is intended to provide some background to a number of widely used methods for solving the Navier–Stokes and Euler equations. The difference between coupled and uncoupled iterative schemes is discussed together with methods for solving the equations. Methods covered include time marching (both explicit and implicit), pressure correction and a Newton–Raphson technique. The relationship between the methods is illustrated.     

Stabilization of explicit methods for hyperbolic partial differential equations

It is well known that explicit methods are subject to a restriction on the time step. This restriction is a drawback if the variation of the solution in time is so small that accuracy considerations would allow a larger time step. In this case, implicit methods are more appropriate because they do allow large time steps. However, in general, they require more storage and are more difficult to implement than explicit methods. In this paper we propose a technique by which it is possible to stabilize explicit methods for quasi-linear hyperbolic equations. The stabilization turns out to be so effective that explicit methods become a good alternative to unconditionally stable implicit methods.     

带约束多体系统动力学方程的隐式算法

研究了带约束多体系统隐式算法,用子矩阵的形式推导出了多体系统正则方程的Ｊａｃｏｂｉ矩阵,它适用于多种隐式算法并给出了隐式Ｒｕｎｇｅ－Ｋｕｔｔａ算法,最后用一算例表明了隐式算法的计算效率和精度明显优于算法。     

A space-time lower–upper symmetric Gauss–Seidel scheme for the time-spectral method

The time-spectral method (TSM) offers the advantage of increased order of accuracy compared to methods using finite-difference in time for periodic unsteady flow problems. Explicit Runge–Kutta pseudo-time marching and implicit schemes have been developed to solve iteratively the space-time coupled nonlinear equations resulting from TSM. Convergence of the explicit schemes is slow because of the stringent time-step limit. Many implicit methods have been developed for TSM. Their computational efficiency is, however, still limited in practice because of delayed implicit temporal coupling, multiple iterative loops, costly matrix operations, or lack of strong diagonal dominance of the implicit operator matrix. To overcome these shortcomings, an efficient space-time lower–upper symmetric Gauss–Seidel (ST-LU-SGS) implicit scheme with multigrid acceleration is presented. In this scheme, the implicit temporal coupling term is split as one additional dimension of space in the LU-SGS sweeps. To improve numerical stability for periodic flows with high frequency, a modification to the ST-LU-SGS scheme is proposed. Numerical results show that fast convergence is achieved using large or even infinite Courant–Friedrichs–Lewy (CFL) numbers for unsteady flow problems with moderately high frequency and with the use of moderately high numbers of time intervals. The ST-LU-SGS implicit scheme is also found to work well in calculating periodic flow problems where the frequency is not known a priori and needed to be determined by using a combined Fourier analysis and gradient-based search algorithm.     

具有奇异位置的多体系统动力学方程的隐式算法

本文研究了在运动过程中具有奇异位置的多体系统动力学方程的隐式算法，给出了隐式算法所用的Ｊａｃｏｂｉ矩阵，并建立了该矩阵中各子矩阵间的计算关系，提高了计算效率，计算结果表明隐式算法的计算速度和精度明显优于显式算法。     

金属刚粘塑性变形的能量泛函与动力显式算法有限元分析

设计出刚粘塑性动态变形场的能量泛函，采用罚函数法和Ｌａｇｒａｎｇｉａｎ乘子法取消对运动容许速度场满足体积不可压缩的约束条件，运用虚功原理和广义变分原理，推导出刚粘塑性变形的动力分析显式算法有限元方程，以及速率形式的中心差分求解的时间积分显式，给出了两个金属变形的算例。     

Gel Placement in Porous Media: Constant Injection Rate

In this paper we analyse advective transport of polymers, crosslinkers and gel, taking into account non-equilibrium gelation, gel adsorption and crosslinker precipitation. In absence of diffusion/dispersion the resulting model consists of hyperbolic transport-reaction equations. These equations are studied in several steps using mainly analytical techniques. For simple cases, we obtain explicit travelling wave solutions, whereas for more complicated cases we rely on analytical techniques to analyse the problem qualitatively. Finally, a numerical solution for the full system of equations is obtained. The results developed in this study can be used to validate numerical solutions obtained from commercial simulators.     

Implicit preconditioned high‐order compact scheme for the simulation of the three‐dimensional incompressible Navier–Stokes equations with pseudo‐compressibility method

This paper combines the pseudo‐compressibility procedure, the preconditioning technique for accelerating the time marching for stiff hyperbolic equations, and high‐order accurate central compact scheme to establish the code for efficiently and accurately solving incompressible flows numerically based on the finite difference discretization. The spatial scheme consists of the sixth‐order compact scheme and 10th‐order numerical filter operator for guaranteeing computational stability. The preconditioned pseudo‐compressible Navier–Stokes equations are marched temporally using the implicit lower–upper symmetric Gauss–Seidel time integration method, and the time accuracy is improved by the dual‐time step method for the unsteady problems. The efficiency and reliability of the present procedure are demonstrated by applications to Taylor decaying vortices phenomena, double periodic shear layer rolling‐up problem, laminar flow over a flat plate, low Reynolds number unsteady flow around a circular cylinder at Re = 200, high Reynolds number turbulence flow past the S809 airfoil, and the three‐dimensional flows through two 90°curved ducts of square and circular cross sections, respectively. It is found that the numerical results of the present algorithm are in good agreement with theoretical solutions or experimental data. Copyright © 2011 John Wiley & Sons, Ltd.     

亚、跨、超音速及不可压流动的数值分析方法的研究

为了对亚、跨、超音速及不可压无粘流动进行数值模拟,将LU－SGS方法与预处理方法结合,给出了PLU－SGS方法。方程离散基于有限体积法,采用高阶精度AUSMPW格式。方程求解采用了特征边界条件。通过典型算例的数值试验对比分析,表明PLU－SGS方法可以有效地对亚、跨、超音速及不可压流动进行数值模拟,并具有较高的计算精度和收敛速度。