关于 CFD 高精度保真的数值模拟研究

本文由四部分组成。第一部分研究了利用高阶格式、网格、物理模型和高性能计算机求解 NS 方程时,计算数据的高精度保真性的要求以及高精度保真的指标。第二部分研究了利用大规模计算开展大涡模拟和直接数值模拟存在的问题。第三部分分析了在高雷诺数下 NS 方程计算方法和网格的关系。最后提出了建立计算数值验证、确认的新方法。     

Boundary discontinuous Fourier analysis of thick beams with clamped and simply supported edges via CUF

This paper presents an analytical solution for static analysis of thick rectangular beams with different boundary conditions.Carrera's Unified Formulation (CUF) is used in order to consider shear deformation theories of arbitrary order.The novelty of the present work is that a boundary discontinuous Fourier approach is used to consider clamped boundary conditions in the analytical solution,unlike Navier-type solutions which are restricted to simply supported beams.Governing equations are obtained by employing the principle of virtual work.The numerical accuracy of results is ascertained by studying the convergence of the solution and comparing the results to those of a 3D finite element solution.Beams subjected to bending due to a uniform pressure load and subjected to torsion due to opposite linear forces are considered.Overall,accurate results close to those of 3D finite element solutions are obtained,which can be used to validate finite element results or other approximate methods.     

Analytical solutions of cracks emanating from an elliptical hole under shear

Based on the complex variable method, the analytical solutions of stress functions and stress intensity factors（SIFs） are provided for the plane problem of two collinear edge cracks emanating from an elliptical hole in an infinite plate under shear. The stress distribution along the horizontal axis is given in graphical forms, which conforms to Saint-Venant＇s principle. The influences of crack length and ellipse shape on the stress intensity factors are evaluated. Comparing the analytical solutions with finite element method（FEM） results shows good coincidence. These numerical examples show that the present solutions are accurate.     

High-order accurate,low numerical diffusion methods for aerodynamics

In recent years numerical methods have been widely used to effectively resolve complex flow features of aerodynamics flows with meshes that are reasonable for today's computers. High-order numerical methods were used mainly in direct numerical simulations and aeroacoustics. For many aeronautical applications, accurate computation of vortex-dominated flows is important because the vorticity in the flow field and the wake of swept wings at an incidence and rotor blades largely determines the distribution of loading. The main deficiency of widely available, second-order accurate methods for the accurate computation of these flows is the numerical diffusion of vorticity to unacceptable levels. Application of high-order accurate, low-diffusion numerical methods can significantly alleviate this deficiency of traditional second order methods. Furthermore, higher-order space discretizations have the potential to improve detached eddy simulation predictions of separated flows with significant unsteadiness. Recently developed high-order accurate finite-difference, finite-volume, and finite-element methods are reviewed. These methods can be used as an attractive alternative of traditional low-order central and upwind computational fluid dynamics methods for improved predictions of vortical and other complex, separated, unsteady flows. The main features of these methods are summarized, from a practical user's point of view, their applicability and relative strength is indicated, and examples from recent applications are presented to illustrate their performance on selected problems.     

一个非线性拟协调退化壳有限元

 根据非线性协调有限元列式方法,构造了几何非线性拟协调9结点四边形退化壳有限元。首先给出9结点四边形退化壳单元的几何描述和位移模式;接着讨论了非线性协调有限元列式方法;假设应力和应变;然后用所构造的壳单元,进行了方板、圆拱、球壳和圆柱壳的数值分析,并同精确解以及其他单元的解答进行了比较。结果表明本文壳单元是准确的和有效的。     

横向载荷作用下缺陷加筋板有效板宽的一个计算方法

 基于大挠度理论给出一个含初始挠度、焊接残余应力缺陷加筋板格在横向载荷作用下有效带板宽度的计算公式,分析缺陷加筋板格的极限强度。并对 Faulkner型焊接残余应力板在均布载荷作用下进行了实际数值算例,分析表明上述诸因素均对极限强度有一定影响,这与实际情况是相符的。     

近水面飞行气动特性数值计算方法研究

根据对水面波的数学描述，给出了其对流场影响的精确解析解。针对地(水)面效应飞行器的特点，分析了近水面波飞行时的流场特征，利用线性叠加原理，提出了飞行器与水面波耦合影响的非定常速度势修正项概念。分析了非定常气动特性的数值计算方法。对某实用型地效飞行器进行了计算，并对计算结果与试验结果进行了分析总结。     

计算谐振机翼气动力的激波膨胀波级数展开法

本文根据激波-膨胀波理论,忽略了反射波对翼面压强分布的影响,把斜激波之后和通过一族主特征线的压强展成级数,给出了沉浮和俯仰谐振翼型表面压强分布的近似解析解。然后应用片条理论导得三维机翼振动导数的闭式解。文中给出三角形机翼俯仰导数的几个实例,数值结果与现有其它方法的结果有很好的一致性。     

高超声速化学非平衡粘性激波层方程的数值解

本文讨论了高超声速粘性激波层方程数值计算时差分格式引起的物理失真问题。具体分析了全隐格式格式粘性的影响,并作了数值试验。为了验证隐式结果的可靠性。在超声速激波风洞中测量了钝锥的表面压力分布,并与计算结果作了比较,两者基本一致。 本文采用隐式有限差分法数值计算了高超声速化学非平衡粘性激波层绕细长球锥的流动。计算时采用连续方程和法向动量方程耦合求解的方法以解决细长体远后身区计算中的问题。应用网格技术和加强系数矩阵主对角元素优势的方法提高了化学非平衡流计算的雷诺数范围。文中给出了高超声速化学非平衡流的计算结果,并与其它文献的结果作了比较。     

高阶精度间断Galerkin有限元方法研究

在二维非结构网格上,对高阶精度间断Galerkin有限元方法求解跨音速欧拉方程进行研究。运用间断有限元理论,采用施密特正交化多项式基函数对流场解进行近似描述,使用HLLC近似黎曼解方法计算网格单元边界处的数值通量,积分项通过高斯积分求解,时间推进采用经典四步Runge-Kutta方法,并引入斜率限制器,抑制数值振荡。对NACA0012翼型跨音速无粘流动进行数值模拟,数值结果表明：间断Galerkin有限元方法具有较高的精度,较小的数值耗散和较强的激波捕捉能力。     

虚构解方法程序验证

对求解偏微分方程问题的程序的严格验证,一直以来由于其精确解有限,较难进行,针对这种情况,本文给出了一种新的程序验证方法,虚构解方法,该方法旨在解决大型科学计算程序如何较严格地进行程序验证这一问题;该方法通过构造虚构解,修改原控制方程,然后通过对计算结果的分析处理达到对程序的精确验证;文中给出了一组通用的虚构解的选取办法,解决了虚构解方法验证过程中确定虚构解的问题;同时还给出了运用该方法对非结构二维Euler计算程序进行验证的具体例子,网格收敛分析结果表明该方法是一种有效的程序验证方法,并且具有较好的通用性。     

利用紧致格式捕捉间断的数值方法研究

将通量限制或加权的思想引入到紧致格式中,构造了两类传统方法与紧致格式混合组成的差分格式:通量限制与加权型差分格式。通过方波、组合波、定常激波、非定常Sod问题、Shu问题和Lax问题上的计算,以及与精确解的比较,结果表明这两种方法在间断的捕捉上具有高精度、高分辨率,而在计算方波、组合波或Shu问题和Lax问题上,加权格式具有更大的优势。     

结构细节多裂纹扩展分析的新方法──变量优化法

以确定性疲劳裂纹扩展分析为基础,推出了一种多裂纹扩展分析的新方法———变量优化法．给出了两种典型结构细节多裂纹扩展分析结果,结果表明：变量优化法比工程试凑法更有效,精度更高,比解非线性方程组法更符合工程实际,更容易被人们所接受。     

大曲率缺口奇异有限元计算模型及其数值分析

 研究了大曲率缺口的位移场基本理论,构造了一种新的大曲率缺口位移模式;建立含大曲率缺口损伤结构有限元方程和相应的缺口奇异单元;提出了求解大曲率缺口应力与应力强度因子等断裂参量一种的新数值计算方法。算例说明本方法是一种有效的数值计算分析方法,其研究成果对众多的材料破坏试验极有参考价值。     

The contribution of observations of satellites to the determination of the Earth's gravitational potential

The history of the determination of the external gravitational potential of the Earth is sketched briefly. A discussion of the principles by which the potential may be derived from the observations of changes in the orbits of artificial satellites is followed by outlines of the principal theories and by detailed consideration of the formal differences between them that arise from differences in the ways that the orbits are described and it is shown that those formulae on which most of the numerical results depend are equivalent in the principal theories. The usual methods of treatment break down in certain special conditions and the analysis of these cases is also considered although they are not of great practical importance in the derivation of the potential; similarly a short account is given of the behaviour of a satellite having an orbital angular velocity commensurable with the spin angular velocity of the Earth. Methods by which satellites are observed are mentioned and the main numerical results on the external potential of the Earth are discussed critically. Finally the results are compared with those derived from observations of gravity on the surface of the Earth and the application of the results to problems of geodesy, of the physical state of the Earth and of the motion of the Moon are described.     

高超音速化学非平衡钝劈绕流数值计算

 自1970年Davis提出粘性激波层方法以来,用数值方法求解高超音速轴对称钝体绕流问题国内外已做了大量工作,但至今仍未见到关于平面问题的计算结果。对于平面问题,虽然方程在形式上比轴对称简单,但由于二维效应,激波层较厚,用文献[2]的方法向下游区推进有困难。另外,在驻点线上采用极限关系式虽能克服方程的奇性,但驻点解对流向步长Δξ有依赖。     

任意回转面亚、跨音流场计算方法

本文所设计的任意回转面亚、跨音流场的计算软件 ,能根据叶型和进出口条件分析流动特性 ,并自动选择精确和节省机时的合适的数值解法。用户在给出叶型坐标和定解条件后 ,可以得到叶面马赫数分布或压力分布 ,全流场的等马赫数或等压图     

Real-time trajectory optimization for powered planetary landings based on analytical shooting equations

Traditionally, numerical trajectory integration for shooting equation calculation and iterations for shooting with randomly guessed initial solutions deteriorate the real-time performance of indirect methods for on-board applications. In this study, the indirect method is improved to achieve real-time trajectory optimization of fuel-optimal powered planetary landings with the help of analytical shooting equation derivations and a practical homotopy technique. Specifically, the contributions of t...     

带冠空心冷却叶片的三维应力分析

 带冠的高温空心冷却叶片,由于它的形状复杂,工作时所承受的离心力大,温度高,气动力分布极不均匀,因此到目前为止,尚未见有准确可靠的计算方法,一般只能靠实验或统计的方法来对付生产使用中出现的问题。 为试图解决此一问题,我们采用高阶的三维等参元素来离散复杂的叶片形状。用节省内存空间而精度又高的波前法来求解此特大型方程组。用高阶双三次Coons样条插值函数来拟合叶型的空间曲面。为验证本方法和程序的可靠性,计算了各种例题,做了真实叶片的高速旋转实验,它们都证明了本方法的可靠性和计算精度是满意的。 本方法的适应性也较强,用它可以计算实心和空心的、带冠和不带冠的、伸根和非伸根的、高温和常温的各种类型叶片。