HyperFLOW软件非结构网格亚跨声速湍流模拟的验证与确认

计算流体力学(computational fluid dynamics,CFD)数值模拟在航空航天等领域发挥越来越重要的作用,然而CFD数值模拟结果的可信度仍然需要通过不断地验证与确认来提高.本文给出了从制造解精度测试、简单到复杂外形湍流模拟网格收敛性研究等三个方面开展CFD软件验证与确认的方法,并对自主研发的CFD软件平台HyperFLOW在非结构网格上模拟亚跨声速湍流问题的能力进行了验证与确认.首先通过基于Euler方程和标量扩散方程的制造解精度测试,分别验证了HyperFLOW在非结构网格上对Euler方程和黏性项的求解精度,结果表明其能够在任意非结构网格上达到设计的二阶精度. 其次,通过NASATurbulence Modeling Resource中的湍流平板、二维翼型近尾迹流动、二维Bump等几个典型的亚声速湍流算例的网格收敛性研究,量化考察了数值结果的观测精度阶和网格收敛性指数,并与国外知名CFD解算器CFL3D,FUN3D的计算结果进行了对比,验证了HyperFLOW对简单湍流问题的模拟能力,且具有良好的网格收敛性和计算精度(阶). 最后,通过NASA CommonResearchModel标模定升力系数的网格收敛性研究和升阻极曲线预测,验证了软件在复杂外形亚跨声速湍流流动数值模拟中也具有良好的可信度.      

THE DETERMINATION OF THE COMPUTATIONAL DEGREES OF FREEDOM OF BAR SYSTEMS1)

为了简化和统一结构力学教材中杆件体系计算自由度$W$的算法,本文提出了“直接法”。该方法以相邻节点间的杆件和结点为分析对象,对于含$m$根杆件、$g$ 个单刚结点和$h$个单铰结点的平面杆件体系,直接法给出计算自由度公式$W=3m-(3g+2h$)。相比于已有方法,直接法研究对象清晰,数学运算统一,适合于编程计算,便于初学者准确而快速计算复杂体系的$W$;也为结构超静定次数的确定提供了一种简单有效的数值算法。     

THE MODIFIED TRIPLES ALGORITHM FOR FLUSH AIR DATA SENSING SYSTEM APPLIED TO THE VEHICLE WITH BLUNT FORE-BODIES1)

针对传统的用于钝头体飞行器的嵌入式大气数据传感系统的经典三点式算法对测压孔配置约束性严格的特点,对经典三点式算法进行了改进及验证。首先,对于经典三点式算法及改进算法进行了论述;其次,针对不同测压孔配置对算法精度的影响进行了系统的评估;最后,对于传统的经典三点式算法与改进三点式算法的优劣进行了比较。结论为：(1)改进的三点式算法对于测压孔的配置敏感性变差,即对测压孔约束很宽松,可用测压孔数增加,从而使得算法的适用性更强;(2)改进的三点式算法的精度与三点式算法相当,但是需要对测压孔进行系统选取及对比验证。     

Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.     

The spectral analysis and exponential stability of a bi‐directional coupled wave‐ODE system

In this paper, an unstable linear time invariant (LTI) ODE system is stabilized exponentially by the PDE compensato—a wave equation with Kelvin‐Voigt (K‐V) damping. Direct feedback connections between the ODE system and wave equation are established: The velocity of the wave equation enters the ODE through the variable v_t(1,t); meanwhile, the output of the ODE is fluxed into the wave equation. It is found that the spectrum of the system operator is composed of two parts: point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point , and there are two branches of asymptotic eigenvalues: the first branch approaches to , and the other branch tends to ?∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum‐determined growth condition and exponential stability of the system are concluded.     

求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析

本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法，分析当矩阵A，B，C，D均是Hermite正（负）定矩阵时，迭代矩阵的特征值表达式，给出了最优参数的确定方法，并提出了相应的加速算法.     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.