平面Poisenille流动的二维Hopf分叉

本文用直接数值模拟的方法计算了二维Ｐｏｉｓｅｕｉｌｌｅ流动中扰动波的演化问题。得到了二维平衡态，在一定的波数下，Ｒｅ３９５０时，这种平衡态，将变得不稳定，模拟发现出现第二周期解，即二次分叉。     

用格子Boltzmann方程模拟浅水波问题

提出了用格子Ｂｏｌｔｚｍａｎｎ方程（ＬＢＥ）模拟浅水波问题的方法．通过无粘气体运动方程与浅水波方程的比较，确定了ＬＢＥ方法中平衡态的形式，使宏观方程与浅水波方程一致．计算了二维浅水波的一个问题，数值结果与精确解做了比较．     

Blasius边界层的二次稳定性

采用人为中性方法使二维基本流达到有限幅值的平衡态,用小参数展开法求解二次稳定性方程.同时按 Floquet 理论研究了空间模式三维亚谐扰动的二次稳定性及幅值沿流向的演化.数值结果与实验结果一致.     

对二维分离流涡黏性系数非线性分布的新认识

以弱非线性涡黏性模型为出发点,对Delery分离流动实验结果进行分析并获得了非平衡态分离区涡黏性系数与形状因子J之间的非线性关系. 该非线性关系显示在分离起始阶段,涡黏性系数较平衡态先减小,后增大;再附阶段,涡黏性系数较平衡态数值逐渐增大,并在再附点位置接近最大,而后又逐渐减小,恢复到平衡态水平. 总结涡黏性系数的这种非线性发展数学关系式,并将它应用于BL模型,在不添加微分方程的情况下发展出一种适用于分离流动的改进代数湍流模型. 对低速平板流动,跨声速,超声速以及高超声速分离流动的计算结果表明,该改进湍流模型可以较准确地模拟各类复杂分离流动,计算精度明显优于传统代数模型以及一些两方程模型,而计算工作量仍与BL模型相当. 这表明所提出的涡黏性系数非线性发展规律是正确的,且应用在二维分离流动中具有一定的普适性.      

龙山门断裂带活动特征与工程区域地壳稳定性评价理论

以弱非线性涡黏性模型为出发点,对Delery分离流动实验结果进行分析并获得了非平 衡态分离区涡黏性系数与形状因子J之间的非线性关系. 该非线性关系显示在分离起始阶段, 涡黏性系数较平衡态先减小,后增大;再附阶段,涡黏性系数较平衡态数值逐渐增大,并在 再附点位置接近最大,而后又逐渐减小,恢复到平衡态水平. 总结涡黏性系数的 这种非线性发展数学关系式,并将它应用于BL模型,在不添加微分方程的情况下发展出一种 适用于分离流动的改进代数湍流模型. 对低速平板流动,跨声速,超声速以及高超声速分离 流动的计算结果表明,该改进湍流模型可以较准确地模拟各类复杂分离流动,计算精度明显 优于传统代数模型以及一些两方程模型,而计算工作量仍与BL模型相当. 这表明所提出的 涡黏性系数非线性发展规律是正确的,且应用在二维分离流动中具有一定的普适性.     

点引爆圆板装药驱动飞板的实验及二维数值模拟

本文报导点引爆圆板装药驱动飞板的实验及二维数值模拟研究结果。实验测定了有机玻璃、铝、钢和铜四种飞板在爆轰产物驱动下的碰靶时间及碰靶波形,并将二维数值模拟结果与测量结果进行了比较,二者符合较好。文中还就数值模拟中存在的一些问题进行了简要分析、讨论。     

二维数值模拟爆轰中化学反应率的应用

续定常爆轰数值模拟中化学反应率与人为粘性的相关性,本文对体积起爆函数进行了一维、二维系统考查,并与Cochran反应率做了二维对比计算给出数值结果。数值模拟爆轰的复杂相互作用,应用体积起爆函数为好。     

二维材料曲面生长:力学与化学的邂逅

理解二维材料在曲面上的生长形态和机制具有重要的理论和应用价值,但现有关于二维材料曲面生长的力学行为及形貌演化规律的研究极为缺乏.二维材料曲面生长会导致薄膜变形及其相关的应力/应变.这类应力可引发二维材料的滑移、屈曲、褶皱、断裂和离面运动等二次力学行为,并直接与生长反应耦合,进而改变材料的生长过程.与化学能和表面扩散主导的平面生长不同,曲面生长二维材料的形貌受曲面几何形状和材料力学行为的共同影响,会产生更为复杂多样的生长形貌.通过总结国际上相关研究进展,剖析了模拟曲面生长二维材料所面临的科学问题,并论述了如何结合原子模拟(如分子动力学和蒙特卡罗模拟)与唯象理论(如相场方法)开展多尺度计算研究,再辅以实验揭示二维材料曲面生长规律.     

二维磁流体力学ALE数值模拟

介绍采用ALE方法进行的电磁内爆二维磁流体（MHD）力学模拟。二维MHD力学模拟的ALE方法分成拉格朗日、网格重分、对流输运三步。拉格朗日步采用文献[4]的时间分裂法,分成辐射冷却、热扩散、磁扩散、Lagrangian流动四步求解,并对Lagrangian流动步的方法进行了改进,消除了其拉氏计算的质量损失等。编制了二维计算程序并通过验证,获得的二维电磁内爆不稳定性发展与文献[2,5,11]吻合。     

爆炸作用数值模拟

采用简单的炸药化学反应率方程，利用二维流体弹塑性流动程序，对一个变直径铜壳中装药的爆炸作用做了数值模拟。     

Occurrence of multiple attractor bifurcations in the two-dimensional piecewise linear normal form map

Multiple attractor bifurcations occurring in piecewise smooth dynamical systems may lead to potentially damaging situations. In order to avoid these in physical systems, it is necessary to know their conditions of occurrence. Using the piecewise-linear 2D normal form, we investigate which types of multiple attractor bifurcations may occur and where in the parameter space they can be expected. For piecewise smooth maps, multiple attractor bifurcations will be expected to occur if the condition we identified for the piecewise-linear 2D normal form are satisfied in the close neighborhood of the border.     

Border collision bifurcations in 3D piecewise smooth chaotic circuit

A variety of border collision bifurcations in a three-dimensional (3D) piecewise smooth chaotic electrical circuit are investigated. The existence and stability of the equilibrium points are analyzed. It is found that there are two kinds of non-smooth fold bifurcations. The existence of periodic orbits is also proved to show the occurrence of non-smooth Hopf bifurcations. As a composite of non-smooth fold and Hopf bifurcations, the multiple crossing bifurcation is studied by the generalized Jacobian matrix. Some interesting phenomena which cannot occur in smooth bifurcations are also considered.     

Flow dynamics in the short asymmetric Taylor-Couette cavities at low Reynolds numbers

This paper reports on the numerical investigations of Taylor-Couette flow of radius ratio η = 0.25–0.6 performed at low Reynolds numbers Re = 100–200. The inner cylinder and the bottom end-wall rotate, while the outer cylinder and the top end-wall are held fixed. A fully 3D DNS code based on the spectral Chebyshev – Fourier approximation is used. This study is complementary to those of Mullin and Blohm (Phys. of Fluids 2001, vol 13, 136–140) and Lopez et al. (J. Fluid Mech. 2004, vol 501, 327–354) where investigations have been performed for radius ratio 0.5. The 1-cell and 3-cell structures found by these authors are shown to exist for a wide range of radius ratios, and the transition processes between them are qualitatively similar. These structures show hysteresis, disappearing at saddle-node bifurcations which connect at a cusp point in the (Re, Γ) plane. This cusp exists for the entire range of 0.1 < η < 0.75, and it traces out a parabolic curve in the (Re, Γ) plane, reaching a minimum Re at η = 0.375. The detailed 3D DNS computations provide a lot of new information about such phenomena as the modulated rotating wave, the period doubling cascade and homoclinic collision. The results show that the period doubling bifurcation is important in the flow when the radius ratio is close to η = 0.375.     

黏弹性流体纯弹性不稳定现象研究综述

近年来粘弹性流体流动的弹性不稳定性现象引起了越来越多学者的关注与研究,与牛顿流体惯性不稳定现象不同,这种现象是由粘弹性流体流动中的弹性应力和粘性力之间相互作用,使得在较低的雷诺数下即可产生复杂的流动分岔不稳定现象。当流动中的弹性数（表现为 Deborah 数 De 与Reynolds 数Re 的比值,其中 De 数定义为粘弹性流体的松弛时间和流动的特征时间的比值,Re 数表征流动中惯性力与粘性力之比）较大时,在 Re<相似文献   

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分析了机械通风房间气流分岔的原因和主要影响参数. 首先根据射流理论,结 合数值模拟结果,通过分析Coanda效应在平面射流和集中射流中的作用,解释了平面射流相 对出射时可能出现分岔、而集中射流一般不出现分岔的原因,得出Coanda效应是引起分岔的 主要机理. 然后采用正交试验理论和方差分析法分析了影响分岔的参数,找到显著性因子, 并得出分岔强度和主要影响因子之间的关系.     

Homoclinic-Doubling Cascades

Cascades of period-doubling bifurcations have attracted much interest from researchers of dynamical systems in the past two decades as they are one of the routes to onset of chaos. In this paper we consider routes to onset of chaos involving homoclinic-doubling bifurcations. We show the existence of cascades of homoclinic-doubling bifurcations which occur persistently in two-parameter families of vector fields on ?³. The cascades are found in an unfolding of a codimension-three homoclinic bifurcation which occur an orbit-flip at resonant eigenvalues. We develop a continuation theory for homoclinic orbits in order to follow homoclinic orbits through infinitely many homoclinic-doubling bifurcations.     

Bifurcations of travelling waves in the thermo-diffusive model for flame propagation

The main topic of this paper is the study of steady-state bifurcations occurring in the two-dimensional thermo-diffusive model in the framework of large activation energies.The physical situation is well established, due to the classical work of Sivashinsky. He derived a dispersion relation and observed that the planar waves bifurcated into stable multidimensional waves as the Lewis number crossed a critical value.The purpose of this paper is to give a mathematical basis to this theory, furthering a study of D. Terman. We then investigate the bifurcation in detail. Finally, we investigate the three-dimensional case, where a different bifurcation pattern may occur.     

Elastoplastic buckling and post-buckling analysis of sandwich columns

Sandwich structures are widely used in many industrial applications thanks to their interesting compromise between lightweight and high mechanical properties. This compromise is realized thanks to the presence of different parts in the composite material, namely the skins which are particularly thin and stiff relative to the homogeneous core material and possibly core reinforcements. Owing to these geometric and material features, sandwich structures are subject to global but also local buckling phenomena which are mainly responsible for their collapse. The buckling analysis of sandwich materials is therefore an important issue for their mechanical design. In this respect, this paper is devoted to the theoretical study of the local/global buckling and post-buckling behavior of sandwich columns under axial compression. Only symmetric sandwich materials are considered with homogeneous and isotropic core/skin layers. First, the buckling problem is analytically addressed, by solving the so-called bifurcation equation in a 3D framework. The bifurcation analysis is performed using an hybrid model (the two faces are represented by Euler–Bernoulli beams, whereas the core material is considered as a 2D continuous solid), considering both an elastic and elastoplastic core material. Closed-form expressions are derived for the critical loadings and the associated bifurcation modes. Then, the post-buckling response is numerically investigated using a 2D finite element bespoke program, including finite plasticity, arc-length methods and branch-switching procedures. The numerical computations enable us to validate the previous analytical solutions and describe several kinds of post-critical responses up to advanced states, depending on geometric and material parameters. In most cases, secondary bifurcations occur during the post-critical stage. These secondary modes are mainly due to the modal interaction phenomenon and give rise to unstable post-buckled solutions which lead to final collapse.     

Direct numerical simulation of driven cavity flows

Direct numerical simulations of 2D driven cavity flows have been performed. The simulations exhibit that the flow converges to a periodically oscillating state at Re=11,000, and reveal that the dynamics is chaotic at Re=22,000. The dimension of the attractor and the Kolmogorov entropy have been computed. Explicit time-integration techniques are discussed.