非协调数值流形方法的稳定性和收敛性分析

在流形元的基础上，提出了非协调数值流形方法，非协调数值流形方法的优点是在不增加广义节点自由度的前提下，大大提高数值流形方法的计算精度和计算效率.利用内部自由度静力凝聚处理，推导了消除内参后的单元应变矩阵和单元刚度矩阵.在Hilbert空间内，从最小势能原理出发对非协调数值流形方法的稳定性和收敛性进行了分析和讨论，得到了保证非协调流形元解唯一存在和收敛的基本条件，完善了非协调数值流形方法的理论基础.数值试验表明，新单元构造过程简单，有较高的精度，从而证明了本方法的可行性.     

Stokes问题的非协调广义差分法

本文提出解Stokes问题的非协调广义差分法,速度用不连续分片线性函数逼近,压力用分片常数函数逼近。速度近似按‖.‖_h模,压力近似按L²模都具有最优的逼近阶误差估计。本文还给出了数值计算结果。     

90°束转动环形非稳腔模场数值分析

用矩阵方法导出了ＵＲ９０（ｕｎｓｔａｂｌｅｒｉｎｇｒｅｓｏｎａｔｏｒｗｉｔｈ９００１６７ｂｅａｍｒｏｔａｔｉｏｎ）环形非稳腔的衍射积分方程，获得了腔的等价菲涅耳数Ｎｅｑ的关系公式，分析了反向模的抑制方法并给出反向模抑制镜的曲率半径，通过数值计算的方法阐明了腔模本征值与放大因子Ｍ的变化关系，当腔的放大因子Ｍ＝１．２时，得到了腔的模场分布曲线。     

非守恒型粘性流方程的展开方法和数值模拟

在曲线坐标系中，给出了非守恒粘性流矢量方程一种新的展开方法，应用此展开方法使方程的展开式得到简化。对扩压管和二维平面叶栅进行了数值计算，计算结果表明，所给出的新展开式具有实用价值。     

岩石Hopkinson层裂的流形元法模拟

 利用二阶流形元法,通过引入裂纹产生及扩展判据,对冲击载荷作用下岩石Hopkinson动态层裂过程进行了数值模拟,再现了拉伸波作用下Hopkinson层裂过程,计算得到的层裂片厚度和速度等与理论值符合较好,验证了流形元法在模拟冲击载荷作用下材料动态破坏过程方面的有效性和优越性。     

非结构网格上大涡模拟数值方法研究

随着计算能力的飞速发展,在非结构网格上进行大涡模拟是研究叶轮机械真实几何结构下复杂流动问题的有效途径。本文针对非结构网格上数值格式人工黏性过大的缺点,利用湍流中动能级联特性,发展了适用于大涡模拟的低耗散数值格式,并结合亚格子模型,考察了其在基础湍流算例中的有效性。通过与传统迎风格式的对比,说明本文发展的低耗散格式可以显著提高非结构网格上大涡模拟的精度和可靠性。     

一种非稳腔计算机辅助装调方法的数值模拟

谐振腔的自动准直技术是高功率激光器工程实践中的关键技术之一.针对这一问题,对非稳腔的计算机辅助装调方法进行了研究,并对该过程进行了数值模拟.在失调参量和像差系数小范围内线性近似的前提下,获取到一系列表征系统失调的像差值之后,通过求解线性方程组来计算系统的失调量.根据求解结果对失调系统进行修正.数值模拟结果表明单结构参量失调可以很快求出,多结构参量失调情况通过几次迭代求解后也能得到比较理想的结果.目前已经可以确定多个同时存在的失调量(包含倾斜和偏心).倾斜量的求解范围约为10～104 μrad,偏心量的求解范围约为10-2～1 mm.这种辅助装调方法能够有效地指导谐振腔的精装调过程,为今后实际的激光器谐振腔系统的自动调节提供了一种方法.     

共焦腔稳定性突变的分析

光学谐振腔是现代光学的基础性器件.本文从最常见的共焦腔出发,分别从代数解析和几何拓扑的角度解释了其稳定性随参数变化而发生突变的现象,给出了突变的数学原因和物理原因.从数学的角度看,共焦腔稳定性突变是因为反三角余弦函数的函数值在传统的定义域以外由复数向实数的突变;从几何拓扑的角度看,根据光线在腔内的传播路径定义拓扑荷,由于只有拓扑荷为零的腔是稳定的,且拓扑荷的变化是量子化的,因此共焦腔的稳定性发生突变.并根据其突变原因设计由双非稳腔组合的耦合腔,重新构建拓扑荷,实现了新的稳定腔,并且在其中发现了单腔中没有的新模式.     

非均匀三腔谐振腔高频特性的数值分析

 用SUPERFISH程序对非均匀三腔谐振腔的高频特性进行了数值分析。分析了各腔长度的变化对类TM₀₁₀ 2π/3模式及其频率、各腔纵向场分量Ez大小及Ez径向分布的影响。结果表明：当各腔长度变化时，该模式只在一定范围内存在，且频率变化不大，频率的最大值和最小值相差小于4%；当该模式存在时，第一腔长度越小，则第一腔的纵向场分量越大；当第一腔长度不变时，第三腔的纵向场分量随着第二腔长度的增大而增大，而第一，二腔纵向场分量则随之变小；各腔长度变化对纵向场分量的径向分布影响很小。     

基于子结构技术的光机装置反射镜组件的稳定性分析

反射镜组件是光机装置的重要组成部分,反射镜片的转角稳定性对光路的传输有着直接影响。为了分析获得在地脉动载荷作用下反射镜片的转角响应,分别基于整体结构建模技术和子结构技术建立了某光机装置简化结构的有限元模型,并分析获得了装置中两个反射镜片的转角响应。两种方法得到的反射镜片的转角响应差别分别为3.99%,11.84%,说明基于子结构技术开展光机装置反射镜架组件的稳定性分析是可行的。     

Stability for the equilibrium state manifold of relativistic Birkhoffian systems

In this paper, the stability of equilibrium state manifold for relativistic Birkhoffian systems in studied. The equilibrium state equations, the disturbance equations and their first approximation are presented. The criteria of stability for the equilibrium state manifold are obtained. The relationship between the stability of the equilibrium-state manifold of relativistic Birkhoffian systems and that of classical Birkhoffian systems is discussed. An example is given to illustrate the results.     

Boundary element numerical method for the electric field generated by oblique multi-needle electrodes

According to the electric potential of oblique multi-needle electrodes (OMNE) in biological tissue, the discrete equations based on the indetermination linear current density were established by the boundary element integral equations (BEIE). The non-uniform distribution of the current flowing from multi-needle electrodes to conductive biological tissues was imaged by solving a set of linear equations. Then, the electric field and potential generated by OMNE in biological tissues at any point may be determined through the boundary element method (BEM). The time of program running and stability of computing method are examined by an example. It demonstrates that the algorithm possesses a quick speed and the steady computed results. It means that this method has an important referenced significance for computing the field and the potential generated by OMNE in bio-tissue, which is a fast, effective and accurate computing method. Supported by the Natural Science Foundation of Beijing (Grant No. 1083011), the National Natural Science Foundation of China (Grant No. 10705049), and the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality     

动态断裂力学的无网格流形方法

运用无网格流形方法求解动态断裂力学问题.该方法利用单位分解法和有限覆盖技术建立形函数，形函数的建立不受域内不连续的影响，可较好地求解裂纹问题.对于局部化问题，该方法的形函数构造较其他方法更为有效，避免了其他方法在建立试函数时没有考虑不连续尖端的缺点.由于采用有限覆盖技术建立试函数，该方法克服了不连续对试函数的影响，尤其当不连续变得复杂时，更能显示该方法在处理不连续方面的优点.在求解动态断裂力学问题时，弹性动力学积分弱形式的推导采用加权残数法，空间离散采用基于单位分解法的无网格流形方法，时间离散主要采用Newmark法.最后给出两个数值算例，将计算结果与解析解对比，说明该方法的正确性和可行性. 关键词： 有限覆盖 无网格流形方法 动态断裂力学 动态应力强度因子     

基于有限元分析的大型固体激光器稳定性指标重分配

在大型固体激光器结构稳定性设计中,使用等概率分配方法的分配值作为光学元件稳定性设计指标常常会增加结构设计的难度,造成结构建造的巨大浪费。为此,提出了基于结构有限元分析的稳定性指标重分配方法,即将同一光路中光学元件振动响应引起靶点光束的定位误差作为各自的权重系数,采用线性加权和法对稳定性指标进行重新分配。稳定性指标重分配后,所得到的同一光路中各光学元件的安全系数相等。利用此方法对某大型固体激光装置主机装置靶区一条光路中光学元件的稳定性指标进行了重分配,得到每条光路上光学元件稳定性的安全系数均为1.229,满足结构稳定性设计要求。     

Numerical Stability Analysis of FDLBM

We analyze the numerical stability of Finite Difference Lattice Boltzmann Method (FDLBM) by means of von Neumann stability analysis. The stability boundary of the FDLBM depends on the BGK relaxation time, the CFL number, the mean flow velocity, and the wavenumber. As the BGK relaxation time is increased at constant CFL number, the stability of the central difference LB scheme may not be ensured. The limits of maximum stable velocity are obtained around 0.39, 0.43, and 0.43 for the central difference, for the explicit upwind difference, and for the semi-implicit upwind difference schemes, respectively. We derive artificial viscosities for every difference scheme and investigate their influence on numerical stability. The requirements for artificial viscosity is consistent with the conditions derived from von Neumann stability analysis. This analysis elucidates that the upwind difference schemes are suitable for simulation of high Reynolds number flows.     

A three-dimensional Eulerian method for the numerical simulation of high-velocity impact problems

In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.     

On the rate of convergence of the Legendre spectral collocation method for multi-dimensional nonlinear Volterra-Fredholm integral equations

While the approximate solutions of one-dimensional nonlinear Volterra-Fredholm integral equations with smooth kermels are now well understood,no systematic studies of the numerical solutions of their multi-dimensional counterparts exist.In this paper,we provide an efficient numerical approach for the multi-dimensional nonlinear Volterra-Fredholm integral equations based on the multi-variate Legendre-collocation approach.Spectral collocation methods for multi-dimensional nonlinear integral equations are known to cause major difficulties from a convergence analysis point of view.Consequently,rigorous error estimates are provided in the weighted Sobolev space showing the exponential decay of the numerical errors.The existence and uniqueness of the numerical solution are established.Numerical experiments are provided to support the theoretical convergence analysis.The results indicate that our spectral collocation method is more flexible with better accuracy than the existing ones.