APPLICATION OF VARIABLE-FIDELITY MODELS TO AERODYNAMIC OPTIMIZATION

For aerodynamic shape optimization, the approximation management framework (AMF) method is used to organize and manage the variable-fidelity models. The method can take full advantage of the low-fidelity, cheaper models to concentrate the main workload on the low-fidelity models in optimization iterative procedure. Furthermore, it can take high-fidelity, more expensive models to monitor the procedure to make the method globally convergent to a solution of high-fidelity problem. Finally, zero order variable-fidelity aerodynamic optimization management framework and search algorithm are demonstrated on an airfoil optimization of UAV with a flying wing. Compared to the original shape, the aerodynamic performance of the optimal shape is improved. The results show the method has good feasibility and applicability.     

改进的移动最小二乘法

近年来发展的无网格方法大多采用移动员小二乘法来构造试函数，而应用移动最小二乘法形成的方程组有时会是病态的甚至奇异的，从而限制了它的发展和应用。本文采用带权正交函数作为基函数对移动最小二乘法做了改进，避免出现病态方程组，且在计算过程中不需要进行短阵求逆运算，提高了计算速度。之后，借鉴牛顿法、平衡法和摄动法对由移动最小二乘法得到的非线性代数方程组提出了新的求解方法。     

Twist Character of the Fourth Order Resonant Periodic Solution

In this paper, we will give, for the periodic solution of the scalar Newtonian equation, some twist criteria which can deal with the fourth order resonant case. These are established by developing some new estimates for the periodic solution of the Ermakov–Pinney equation, for which the associated Hill equation may across the fourth order resonances. As a concrete example, the least amplitude periodic solution of the forced pendulum is proved to be twist even when the frequency acroses the fourth order resonances. This improves the results in Lei et al. (2003). Twist character of the least amplitude periodic solution of the forced pendulm. SIAM J. Math. Anal. 35, 844–867.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

化学反应流中分子扩散的二点封闭MCA模型

在化学反应流的概率密度函数(PDF)方法中,对流项和化学反应项都是封闭的,但分子扩散项必须模拟。现有的分子扩散模型都是唯象的,需要引入外加参数,并难以通过一些基本物理过程的检验。本文发展了随机映射逼近(mapping closure approximation,MCA)方法,解析地从控制方程导出一个封闭的分子扩散模型。该方法考虑两点联合概率密度函数方程,引入空间特征尺度,因此解决了以往映射封闭方法中分子扩散速率无法确定的问题。数值模拟表明该方法能用于预测标量扩散的速度,以及概率密度函数和条件平均扩散等统计量。     

盒形结构在碰撞下的能量吸收能力

用盒形结构保护产品是最常见的包装方式之一。本文对盒形结构在碰撞载何作用下的大挠度变形模式和能量吸收能力进行了实验研究;在同时考虑弯曲和膜力消耗塑性功的基础上,用能量平衡法给出了一个近似理论分析。理论与实验结果基本一致,可望用于盒形结构的耐撞性设计。     

The crumbling of a viscous prism with an inclined free surface

Summary We study the two-dimensional instantaneous Stokes flow driven by gravity in a viscous triangular prism supported by a horizontal rigid substrate and a vertical wall. The oblique side of the prism, inclined at an angle α with respect to the substrate, is a fluid-air interface, where the stresses are zero and surface tension is neglected. We develop the stream function ψ in polar coordinates (r,θ) centered at the vertex of α and split it into an inhomogeneous part, which accounts for gravity effects, and a homogeneous part, which is expressed as a series expansion. The inhomogeneous part and the first term of the expansion may be envisioned, respectively, as self-similar solutions of the first kind and of the second kind for r→0, each one holding in complementary α domains with a crossover at α _c =21.47^∘, which we study in some detail. The coefficients of the series are calculated by truncating the expansion and using the method of direct collocation with a suitable set of points at the wall. The solution strictly holds for t=0, because later the free surface ceases to be a plane; nevertheless, it provides a good approximation for the early time evolution of the fluid profile, as shown by the comparison with numerical simulations. For 0<α<45^∘, the vertex angle remains constant and the edge remains strictly at rest; the transition at α _c manifests itself through a change in the rate of growth of the curvature. The time at which the edge starts to move (waiting time) cannot be calculated since the instantaneous solution ceases to be valid. For α>45^∘, the instantaneous local solution indicates that the surface near the vertex is launched against the substrate so that the edge starts to move immediately with a power law dependence on time t. However, due to the high value of the exponent, the vertex may seem to be at rest for some finite time even in this case. Received 29 August 1997; accepted for publication 21 January 1998     

二维介质参数的大扰动反演方法

对非均匀介质参数反演问题进行了研究，并提出了用于反演二维介质参数的广义射线近似方法．利用参考场量和扰动变量对声波方程中的介质参数进行处理，并利用Ｇｒｅｅｎ函数理论得到扰动参数比的积分方程．基于非均匀介质中波函数的局部理论和射线理论，引入了全波场的广义射线近似形式，通过定义介质参数函数，把反演目标归结为其第一类Ｆｒｅｄｈｏｌｍ积分方程．利用积分变换方法得到二维介质的介质参数函数，从而得到介质参数，在Ｂｏｒｎ近似方法中，反演的介质参数扰动不能超过２０％，但是在本文中介绍的方法能够有效地反演其扰动比不超过５０％的变化情况     

完全变换法在无网格伽辽金方法中的应用

由于移动最小二乘形函数一般不具有常规有限元或边界元形函数所具有的插值特征，本质边界条件的处理成为无网格伽辽金法实施中的一个难点。本文通过建立节点位移和广义位移之间的关系对移动最小二乘形函数进行修正，给出了修正的移动最小二乘形函数；以二维问题为例，对完全交换法在无网格伽辽金方法中的应用进行了研究，实现了本质边界条件在节点处的精确施加。数值计算结果表明该方法不仅简单合理，而且具有较高的精度、收敛性和稳定性。     

Zur Strömung viskoser Flüssigkeiten durch gewellte Rohre

Zusammenfassung Die Strömung zäher nicht-newtonscher Flüssigkeiten durch gewellte kreisförmige Rohre unter Wirkung eines axialen Druckgefälles wurde theoretisch und experimentell untersucht. Das besondere Interesse galt dabei der durch die Wellung veränderten Druck-Durchsatz-Charakteristik. Die theoretischen Betrachtungen beziehen sich auf den Grenzfall hinreichend langer Wellen, wo sich der Querschnitt des Flüssigkeitsfadens in Strömungsrichtung nur langsam ändert und sowohl die Trägheit als auch die Elastizität der Flüssigkeit eine untergeordnete Rolle spielen. In dieser Näherung konnte der Durchsatz in Abhängigkeit vom Druckgefälle und den nichtlinearen Fließeigenschaften der Flüssigkeit für beliebige Wellenamplituden analytisch bestimmt werden. Die theoretischen Ergebnisse sind in Einklang mit experimentellen Befunden.

---

The flow of a non-Newtonian fluid driven by an axial pressure gradient through a corrugated pipe of circular cross-section is analysed theoretically and realized experimentally. Particular attention is directed toward the pressure-discharge characteristics of the pipe which change due to the corrugation. A theory is developed for the limiting case of corrugations with long wave-length, where the cross-section of the pipe varies gradually in the flow direction and the effects of inertia and elasticity of the fluid are of minor importance. Within such a long-wave approximation the flow rate, in dependence on the applied pressure drop and on the non-linear viscous properties of the fluid, is determined analytically for arbitrary wave amplitudes. The theoretical results are in agreement with experimental findings.

Korrespondenz bitte an diese Adresse richten     

NUMERICAL SIMULATION OF FLOW OF HIGHLY VISCOELASTIC FLOW IN THREE－DIMENSIONAL VARYING THICK SLIT CHANNEL

（杨伯源）（李勇）ＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＦＬＯＷＯＦＨＩＧＨＬＹＶＩＳＣＯＥＬＡＳＴＩＣＦＬＯＷＩＮＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＶＡＲＹＩＮＧＴＨＩＣＫＳＬＩＴＣＨＡＮＮＥＬ￥ＹａｎｇＢｏｙｕａｎ；ＬｉＹｏｎｇ（Ｄｅｐａｒｔ...