应用隐式SMAC格式计算射流放水阀内部非定常不可压粘性流场

为了分析射流放水阀内部的非定常不可压粘性流场,在一般曲线坐标系下求解了以逆变速度为参数的不可压Ｎ－Ｓ方程和压力椭圆方程。计算采用了基于隐式ＳＭＡＣ格式的有限差分格式。在这种格式中,非定常流场的速度是通过使用Ｃｒａｎｋ－Ｎｉｃｈｏｌｓｏｎ格式,并在每一时间步处以牛顿迭代的方法得到的;而压力椭圆方程是通过使用Ｔｓｃｈｅｂｙｓｃｈｅｆｆ ＳＬＯＲ格式并交替改变计算方向而求解。通过使用交错网格和迎风差分,诸如改进的ＱＵＩＣＫ格式;计算过程中的误差和数值不稳定能够得到有效地控制。计算结果和实验观察得到的流动图谱对比表明,二者十分吻合。     

基于中心差分的对流扩散方程四阶紧凑格式

在经典中心差分格式的基础上,提出对流扩散方程的四阶紧凑差分格式。具体方法是,先就一维情形,将中心差分格式改造为不受网格Reynolds数限制的恒稳二阶格式,再在不增加相关网格点的前提下,通过格式中对流系数和源项的摄动处理,使稳格式的精度提高至四阶。本文并作一、二、三维流动模型方程及高Rayleigh数自然对流传热问题的数值求解,例示本文格式的优良性态。     

一维非线性对流占优扩散方程的变网格特征差分方法

针对一维非线性对流占优扩散方程,提出了一类变网格特征差分格式,该格式能够根据解的梯度变化及时对计算网格进行调整.与均匀网格格式相比,给出的变网格特征差分格式对于对流占优扩散问题有着更好的计算效果.     

三维对流扩散方程非等距网格上的四阶紧致格式及其多重网格方法

提出了数值求解三维变系数对流扩散方程非等距网格上的四阶精度19点紧致差分格式,为了提高求解效率,采用多重网格方法求解高精度格式所形成的大型代数方程组。数值实验结果表明本文方法对于不同的网格雷诺数问题,在精确性、稳定性和减少计算工作量方面均明显优于7点中心差分格式。     

一类迎风紧致差分格式全离散特性分析

采用Ｆｏｕｒｉｅｒ分析方法，通过显式多步Ｒｕｎｇｅ－Ｋｕｔｔａ时间离攻一维线性对流方程，导出了一类高精度迎风紧致格式全离散色散关系式，详细分析了不同ＣＦＬ数下所研究差分格式的耗散、色散及相应的相速度、群速度等特性。以数值实验显示了格式较高的计算精度和分辨率。     

双相各向同性介质BISQ模型弹性波方程数值模拟方法

本文从Taylor级数展开式出发,推导出了交错网格一阶空间导数的任意偶数阶精度展开式和相应差分系数计算式;从本构方程和运动方程推导出了BISQ模型双相介质一阶双曲型应力-速度弹性波方程交错网格任意偶数阶精度差分格式以及推导出二维双相各向同性介质完全吸收层边界条件公式和相应的高阶交错网格差分格式。通过数值模拟研究表明,该方法边界吸收效果好,稳定性好,能够高精度模拟双相介质中地震弹性波场,且计算效率也高。     

自然对流换热的高精度非结构网格有限体积法

用非结构网格有限体积法求解自然对流换热时,传统的对流项离散格式难以兼顾数值精度与计算效率,我们发展了一种耦合高精度格式的延迟修正方法,用于对流项的离散.高Re数下方腔驱动流数值计算验证了该方法具有较高的计算精度和较好的稳定性.Boussinesq流体的自然对流换热数值模拟,表明该方法能有效克服高Ra数时数值计算发散,可准确捕捉自然对流换热问题中不同偏心率下的等温线和流线分布特征.     

高精度有限差分法模拟Kelvin-Helmholtz不稳定性

 WENO有限差分格式有较高的分辨精度,适合复杂流场的计算,在国际上被广泛采用。本文利用WENO有限差分格式求解2维守恒型欧拉方程,实现了对无粘流体中Kelvin-Helmholtz不稳定性的数值模拟。速度剪切方向采用周期边界条件;扰动增长方向采用嵌边出流边界条件,一个不稳定波长分布64个网格。数值模拟给出的扰动幅值线性增长率与线性稳定性分析给出的结果很好符合,显示了该格式的有效性和精度。数值模拟给出了清晰的密度等值线,表明该方法还具有较好的界面变形捕捉能力。     

Klein-Gordon方程初边值问题的一种新的差分方法

对非线性Kiein-Gordon方程的初边值问题提出了一种能量守恒差分格式。证明了该格式的收敛性和稳定性。并给出数值计算结果。     

对流扩散方程的一些单调性差分格式

本文分析了逆风格式、格式和修正Dennis格式随网格Reynolds数变化的性质,构造了相应的半隐差分格式,它们具有无条件稳定性和无条件单调性。数值例子说明这些格式可以计算高Reynolds的定态流动问题。     

SOME OBSERVATIONS ON THE CHARACTERIZATION OF STRUCTURAL DAMPING

This paper deals with the characterization of damping in dynamical structural systems. In particular, the problem of how the modal damping ratios change with different boundary conditions is addressed. It is shown that only Rayleigh-type damping is actually independent of boundary conditions and modal damping ratios can be easily converted from one boundary condition to another. This condition applies independently to continuous, discrete and discretized systems.     

边界条件与一维高分子系统的稳定性

讨论了SSH模型在一维有限系统上的稳定性，提出了几种稳定边界的办法，并对边界条件的作用进行了分析讨论 关键词：     

Excess Diffusion of a Driven Colloidal Particle in a Convection Array

We numerically investigate the transport of a passive colloidal particle in a periodic array of planar counterrotating convection rolls,at high Peclet numbers.It is shown that an external bias,oriented parallel to the array,produces a huge excess diffusion peak,in cases where bias and advection drag become comparable.This effect is not restricted to one-dimensional convection geometries,and occurs independently of the array's boundary conditions.     

A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation

This paper considers the one-dimensional dissipative cubic nonlinear Schrödinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.     

Some mathematical aspects of Anderson localization: boundary effect,multimodality, and bifurcation

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary conditions using a probabilistic approach, and further investigate some mathematical aspects of Anderson localization that are rarely discussed before. First, we observe that under the Neumann boundary condition, the low energy quantum states are localized on the boundary of the domain with high probability. We provide a detailed explanation of this phenomenon using the concept of extended subregions and obtain an analytical expression of this probability in the one-dimensional case. Second, we find that the quantum states may be localized in multiple different subregions with high probability in the one-dimensional case and we derive an explicit expression of this probability for various boundary conditions. Finally, we examine a bifurcation phenomenon of the localization subregion as the strength of disorder varies. The critical threshold of bifurcation is analytically computed based on a toy model and the dependence of the critical threshold on model parameters is analyzed.     

Transverse Vibration and Stability Analysis of Circular Plate Subjected to Follower Force and Thermal Load

Transverse vibration and stability analysis of circular plate subjected to follower force and thermal load are analyzed . B ased on the thin plate theory in involving the variable temperature, the differential equation of transverse vibration for the axisymmetric circular plate subjected to follower force and thermal load is established. Then, the differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Meanwhile, the generalized eigenvalue under three different boundary conditions are calculated. In this case, the change curve of the first order dimensionless complex frequency of the circular plate subjected to the follower force in the different conditions with the variable temperature coefficient and temperature load is analyzed. The stability and corresponding critical loads of the circular plate subjected to follower force and thermal load with simply supported edge, clamped edge and free edge are discussed. The results provide theoretical basis for improving the dynamic stability of the circular plate.     

Direct assessment of lattice Boltzmann hydrodynamics and boundary conditions for recirculating flows

A hydrodynamic boundary condition is developed for lattice Boltzmann hydrodynamics using a square, orthogonal grid. A constraint based on energy considerations is developed to provide closure for the equations which govern the particle distribution at the boundaries. This boundary condition is applied to the two-dimensional, steady flow of an incompressible fluid behind a grid, known as Kovasznay flow. The results are compared to those using alternate boundary conditions using the known exact solution. The hydrodynamic boundary condition produces quadratic spatial convergence, while alternate techniques fail to maintain this second-order accuracy.     

用统计力学方法讨论平衡稳定条件

一.引言 1876年吉布斯(J.W.Gibbs)首先论述了物体系的平衡稳定条件,普朗克(M.Planck)也曾用孤立系熵增加原理讨论了单元系与二元系的稳定条件,1948年王竹溪先生用吉布斯的能量最小判据法系统地全面地研究了物体系的平衡稳定条件问题,其结果为对于任一具有l种分子的均匀系统,平衡稳定条件为l 1个独立的不等式:     

多缝衍射反演光谱学的计算机实验研究

本文根据计算机模拟实验给出了当Q为任意(大于1的)数值时提高多缝衍射反演光谱学抗噪音能力的具体条件和方法,在适当的条件下,其抗噪音能力可达到一个实用化的水平10^-2.此外,我们发现在稳定条件下,衍射反演光谱学的光谱范围可以提高到传统光栅光谱仪自由光谱范围的3倍。