任意精度的三点紧致显格式及其在CFD中的应用

通过在泰勒级数展开中运用逐阶迭代的方法,推导出了空间任意精度的三点紧致显格式的表达式,又由Fourier分析法得到了格式的数值弥散和耗散特性．与以往的高精度紧致差分格式不同,提出的格式不用隐式求解代数方程组并且可以达到任意精度．通过方波问题和顶盖方腔流的算例表明,格式在稀疏网格下可以得到很高的精度,不仅能节省计算量,而且易于编程,有很高的计算效率．     

激波捕捉差分方法研究

在迎风型格式和矢通量分裂技术的基础之上,对捕捉激波方法进行一种新的尝试．该方法首先对原始格式在特征方向上进行投影,然后用限制器对这些特征分量的变化幅值进行限制以抑止非物理波动,最后再把它转换成守恒形式,得到了基本上无振荡的激波捕捉格式．用该方法对两种迎风显示格式(二阶和三阶)和3种迎风紧致格式(三阶、五阶和七阶)进行处理,并在一维和二维的情况下进行了应用测试．通过与高阶WENO、MP、Compact-WENO等格式的比较,表明该方法在光滑捕捉激波的前提下仍有较高精度和分辨率．     

Uniform attractors for non-autonomous Klein-Gordon-Schrödinger lattice systems

The existence of a compact uniform attractor for a family of processes corresponding to the dissipative non-autonomous Klein-Gordon-Schrödinger lattice dynamical system is proved. An upper bound of the Kolmogorov entropy of the compact uniform attractor is obtained, and an upper semicontinuity of the compact uniform attractor is established.     

Small-signal analysis of a rectangular helix structure traveling-wave-tube

This paper investigates the properties of traveling wave-beam interaction in a rectangular helix traveling-wave-tube (TWT) for a solid sheet electron beam. The `hot' dispersion equation is obtained by means of the self-consistent field theory. The small signal analysis, which includes the effects of the beam parameters and slow-wave structure (SWS) parameters, is carried out by theoretical computation. The numerical results show that the bandwidth and the small-signal gain of the rectangular helix TWT increase as the beam current increases; and the beam voltage not obviously influences the small signal gain. Among different rectangular helix structures, the small-signal gain increases as the width of the rectangular helix SWS increases, however, the bandwidth decreases whether structure parameters a and L or ψ and L are fixed or not. In addition, a comparison of the small-signal gain of this structure with a conventional round helix is made. The presented analysis will be useful for the design of the TWT with a rectangular helix circuit.     

求解Navier-Stokes方程组的组合紧致迎风格式

给出一种新的至少有四阶精度的组合紧致迎风(CCU)格式,该格式有较高的逼近解率,利用该组合迎风格式,提出一种新的适合于在交错网格系统下求解Navier-Stokes方程组的高精度紧致差分投影算法.用组合紧致迎风格式离散对流项,粘性项、压力梯度项以及压力Poisson方程均采用四阶对称型紧致差分格式逼近,算法的整体精度不低于四阶.通过对Taylor涡列、对流占优扩散问题和双周期双剪切层流动问题的计算表明,该算法适合于对复杂流体流动问题的数值模拟.     

反应扩散方程的紧交替方向差分格式

本文研究二维常系数反应扩散方程的紧交替方向隐式差分格式．首先综合应用降阶法和降维法导出了紧差分格式,并给出了差分格式截断误差的表达式．其次引进过渡层变量,给出了紧交替方向隐式差分格式算法．接着用能量分析方法给出了紧交替方向隐式差分格式的解在离散H^1范数下的先验估计式,证明了差分格式的可解性、稳定性和收敛性,在离散H^1范数下收敛阶为O(r^2 H^4)．然后将Rechardson外推法应用于紧交替方向隐式差分格式,外推一次得到具有O(r^4 H^6)阶精度的近似解．最后给出了数值例子,数值结果和理论结果是吻合的．     

群速度控制格式及二维Riemann解

强激波和强接触间断的数值模拟一直是计算流体力学里一个富有挑战性的课题,它们是很多实际流动的基础。三阶迎风紧致格式是一种具有较高分辨率的高精度方法,但是在计算激波时仍有数值振荡产生。本文根据数值解的群速度特性,在三阶迎风紧致格式的基础上提出了一种群速度控制格式,使得能够正确模拟含有强激波和强接触间断的复杂流动。在此基础上构造了求解包含大压力比和密度比的二维界面问题的数值方法。计算结果表明,方法对激波和接触间断的分辨效果是令人满意的。     

Totally geodesic submanifolds in compact Riemannian symmetric spaces and their stability

In this paper, we determine a large class of totally geodesic submanifolds of a compact Riemannian symmetric space. The stability of these submanifolds in their ambient space is also determined.     

两个凸多面体的差及几种次微分之间的关系

给出两种两个凸多面体差的表达式,利用这些表达式,可以具体计算这两种凸多面体的差,做为应用讨论了利用拟微分计算Penot微分和Clarke广义梯度,特别讨论了一类非光滑函数,极大值函数的光滑复合。     

Gaussian Fluctuation for the Number of Particles in Airy, Bessel, Sine, and Other Determinantal Random Point Fields

We prove the Central Limit Theorem (CLT) for the number of eigenvalues near the spectrum edge for certain Hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the Gaussian fluctuation of the number of particles in random point fields with determinantal correlation functions. As another corollary of the Costin–Lebowitz Theorem we prove the CLT for the empirical distribution function of the eigenvalues of random matrices from classical compact groups.