全机跨音速大迎角绕流的数值分析

应用有限体积法求解Ｅｕｌｅｒ方程计算了真实飞机外形的跨音速大迎角绕流流场及空气动力特性。本方法能自动捕获大后掠机翼前缘脱体涡，侧缘涡，机身体涡以及它们间的相互干扰。计算的机翼压力分布及全机气动力系数与实验值符合良好。表明了本文所采用的计算网格生成技术及流场计算方法是有效、可行的。     

三维Euler方程的分区和并行计算

三维全机绕流区域分解成多块子区域,多块区域之间采用迎风型通量守恒内边界耦合条件,分区计算总体区域,形成总体耦合流场的分区数值解。利用PVM并行环境,采用纯结点并行计算编程方式和“先进先出”的同步控制等待机制,对三维复杂流动跨音速流场相应分区实现了多区域并行计算。分析了影响并行效率的主要因素,将并行计算结果与串行计算结果和实验结果作了比较,讨论了多种区域分解数目的并行计算效率。在负载平衡程度较好时,可得到较高的并行效率。     

三维对流扩散方程的高精度全隐式多重网格方法

提出了数值求解三维非定常变系数对流扩散方程的一种高精度全隐紧致差分格式,该格式在空间上具有四阶精度,时间具有二阶精度。为了克服传统迭代法在每一个时间步上迭代求解隐格式时收敛速度慢的缺点,采用多重网格加速技术,建立了适用于本文高精度全隐紧致格式的多重网格算法,从而大大加快了迭代收敛速度。数值实验结果验证了本文方法的精确性、稳定性和对高网格雷诺数问题的强适应性。     

采用自适应直角网格计算三维增升装置绕流

针对三维增升装置绕流，对存在剪刀叉的不连续外形，基于自适应直角网格，提出并介绍了分区和面搭接技术，采用变长宽比网格，进行了直角网格生成和流场Euler方程数值计算. 根据几何外形的特点，在直角网格生成过程中，以外形不连续面作为分区边界，对初始``根'网格实施分区处理，降低了整个网格的生成难度. 通过基于外形的自适应网格加密，详细描述了剪刀叉外形和缝道，提高了网格质量. 在分区边界面上，基于面搭接技术，构造重叠面积切割算法，实现边界两侧网格间的流场信息传递，保证流场计算中的通量守恒. 采用中心有限体积方法，结合双时间推进算法，完成了两段机翼、带增升襟翼翼身组合体绕流流场的Euler方程数值模拟，对计算结果与实验数据进行了对比，验证了所提方法、算法的合理性和实用性.     

二维Euler方程无网格算法的精度分析

在几种典型的点云布点方案中,分析了文献[3]中的无网格算法的计算精度。分析指出影响无网格算法计算精度的主要因素是点云中点的分布是否平衡;增加点云中节点的数目或者采用高阶曲面拟合都不能提高精度;这里的理论分析为无网格算法的布点提供了重要参考。     

基于聚合多重网格方法的跨音速颤振的数值模拟

采用流固耦合方法对跨音速颤振进行了数值模拟。流体方面在非结构网格上用有限体积方法求解了Euler方程;结构方面则求解了后掠机翼典型剖面的结构模态方程。时间推进采用双时间步长：对每一真实时间步,都通过基于聚合多重网格方法的伪时间步推进,对流体和结构方程交替迭代．得到一个稳态的流固耦合的解。文章最后给出了NACA64A010翼型剖面的跨音速颤振边界．与相关文献的计算结果符合良好。     

用拟压缩性方法求解不可压Euler方程

用拟压缩性方法和Ｊａｍｅｓｏｎ的有限体积算法求解了二维和三维定常可可压Ｅｕｌｅｒ方程。分别采用显、隐式时间离散推进求解;分析了人工粘性的阶数对定常解收敛性的影响,应用该方法计算了单个翼型和翼身组合体的低速绕流,结果与实验吻合较好。     

二维对流扩散方程的高精度全隐式多重网格方法

提出了数值求解二维非定常变系数对流扩散方程的一种时间二阶、空间四阶精度的三层全隐紧致差分格式。为了加快迭代求解隐格式时在每一个时间步上的收敛速度,采用多重网格加速技术,建立了适用于本文高精度金隐紧致格式的多重网格算法。数值实验结果验证了本文方法的精确性、稳定性和对高网格雷诺数问题的强适应性。     

不同网格拓扑对细长体绕流计算的影响研究

分别运用扇形(Fan)、阶梯形(Ladder)、交界面形(Interface)网格对细长体小攻角对称、大攻角对称、大攻角非对称绕流流场进行了数值研究．通过涡核位置、涡簇显示、物面压力分布、轴向力分布等的计算结果比较了三种网格的计算精度．数值实验表明：细长体分离涡流场对边界层网格非常敏感,应严格控制边界层网格的正交性;随着攻角增大,流场对网格特性的敏感性有增高的趋势;阶梯形网格可能会对流场带入非物理性扰动,交界面网格对流场捕捉有不连续现象;将三种网格得到的物面压力、侧向力、流动分离位置与实验值进行对比,发现扇形网格误差最小、交界面网格误差最大;大攻角非对称流动时,扇形网格计算的侧向力有整体向细长体头部压缩的趋势,涡脱落位置靠前,第二个及第三个极值更大,说明非对称现象有向尾部发展的趋势．     

自适应网格加密和多重网格求解严重病态方程

本文探讨用自适应网格加密技术结合多重网格法求解由有限元离散导致的病态方程。计算结果表明；自适应多重网格有限元法是求解严重病态方程珠有效方法。     

On the efficiency and quality of numerical solutions in CFD problems using the interface strip preconditioner for domain decomposition methods

In this paper, some pathologies found for simple tests solved by means of preconditioned full iterative schemes are presented. According to these results (Sections 4 and 5), the accuracy deterioration observed should be considered as a warning for the final application given to these solutions. Even though it is well known that full iterative solvers are not the best selection for comparison, they were chosen because they are widely used by the computational fluid dynamic (CFD) community for a diversity of complex fluid dynamics applications. FEM simulated solutions are compared with analytical solutions or measured data for problems that have been considered as ‘benchmarks’ in the CFD literature. For this purpose, the study of the solution obtained via parallelized iterative methods that have been extensively used (e.g. conjugate gradients (CG), GMRes global iteration and its variants, ‘overlapping’ and ‘non‐overlapping’ additive Schwarz domain decomposition schemes) in CFD computations and those obtained with the new interface strip preconditioner (J. Comput. Meth. Sci. Engng 2003; Int. J. Numer. Meth. Engng 2005; 62 (13):1873–1894) for the Schur complement method is carried out. The idea is to present the new solver as an alternative to obtain more accurate and faster solutions in the context of monolithic and non‐monolithic schemes applied to a internal/external viscous compressible/incompressible flows around bodies of complex shapes. Therefore, the target of this work is to show how the reliability of CFD codes is affected by the solver selection and why domain decomposition methods should be viewed not only as a more efficient strategy, but also to guarantee the solution quality. Copyright © 2006 John Wiley & Sons, Ltd.     

Body-Fitted Adjoint Formulation of the Euler Equations

The shape optimization problem governed by the Euler equations is posed in a fixed reference plane. The boundary control is exerted by a parametric mapping from the physical plane to the reference fixed plane. The adjoint equations are derived in such fixed plane. By using this approach remeshing is unnecessary; furthermore, as in many practical applications the parametric mapping can be easily differentiated, the computation of mesh sensitivities is avoided.     

多介质流体非守恒律欧拉方程组的数值计算方法

对多介质流体在界面处满足的Euler方程进行了探讨 ,方程组中增加了描述材料参数间断性质的对流形式非守恒律方程组。以波传播算法为基础 ,通过Roe方程近似求解Riemann问题 ,同时采用相同的数值差分格式求解流体动力学Euler方程组和界面方程组。该方法可以有效消除多介质流体在界面处压力、速度可能出现的非物理振荡。给出了部分典型一维和二维数值计算结果。     

PML absorbing boundary conditions for the linearized and nonlinear Euler equations in the case of oblique mean flow

For the case of uniform mean flow in an arbitrary direction, perfectly matched layer (PML) absorbing boundary conditions are presented for both the linearized and nonlinear Euler equations. Although linear perfectly matched side layers with an oblique mean flow have been studied in previous works, we propose in the present paper a construction of corner layer equations that are dynamically stable. Stability issues are investigated by examining the dispersion relations of linear waves supported by the corner layer equations. For increased efficiency, a pseudo mean flow is included in the derivation of the PML equations for the nonlinear case. Numerical examples are given to support the validity of the proposed equations. Specifically, the linear PML formulation is tested for the case of acoustic, vorticity, and entropy waves traveling with an oblique mean flow. The nonlinear formulation is tested with an isentropic vortex moving diagonally with a constant velocity. Copyright © 2008 John Wiley & Sons, Ltd.     

Hoberman's Sphere, Euler Parameters and Lagrange's Equations

In this classroom note, we explore how the Euler parameters can be used to represent a particular homogeneous deformation of a continuum. One possible application is Hoberman's sphere. With the assistance of the theory of a pseudo-rigid body, we show how the motion of the continuum can be determined. We also present a new derivation of Lagrange's equations for the rotational dynamics of a rigid body where the rotation tensor is parameterized using Euler parameters. This revised version was published online in August 2006 with corrections to the Cover Date.     

Multi‐resolution analysis for high accuracy and efficiency of Euler computation

A multi‐resolution analysis (MRA) is proposed for efficient flow computation with preserving the high‐order numerical accuracy of a conventional solver. In the MRA process, the smoothness of a flow pattern is assessed by the difference between original flow property values, and the values approximated by high‐order interpolating polynomial in decomposition. Insignificant data in smooth region are discarded, and flux computation is performed only where crucial features of a solution exist. The reduction of expensive flow computation improves the overall computational efficiency. In order to maintain the high‐order accuracy, modified thresholding procedure restricts the additional error introduced by the thresholding below the order of accuracy of a conventional solver. The practical applicability of the MRA method is validated in various continuous and discontinuous flow problems. The MRA stably computes the Euler equations for continuous and discontinuous flow problems and maintains the accuracy of a conventional solver. Overall, it substantially enhances the computational efficiency of the conventional third‐order accurate solver. Copyright © 2014 John Wiley & Sons, Ltd.     

New Steady and Self-Similar Solutions of the Euler Equations

Exact steady and self-similar solutions of the Euler equations are considered, which possess the property of partial invariance with respect to a certain six-parameter Lie group. New examples of vortex motion of a swirled liquid in curved channels are presented. A classification is given for self-similar solutions of the reduced system with two independent variables, which admits a three-parameter group of extensions, whereas the initial system of the Euler equations possesses a two-parameter group.