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. 关键词： 数值流形方法 非协调元 稳定性分析 收敛性分析     

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.     

高超声速可压缩流中粗糙壁热流研究

用计算流体力学（CFD）数值模拟和理论方法对高超声速可压缩湍流中粗糙壁面热增量进行研究. 着重考虑粗糙单元密度和粗糙单元形状对粗糙表面热流的影响. 结果表明： ①粗糙单元密度变化时, CFD数值方法计算所得的粗糙单元等效热流随着粗糙单元密度的降低而增加, 理论方法预测结果的规律随方法不同而不同;②在相同粗糙单元密度和高度时,如果粗糙单元形状改变,CFD计算结果也随之发生改变. 理论预测方法所得结果不发生变化.     

变饱和渗流数值模拟的有限元方法

本文研究时间相关变饱和渗流数值模拟的有限单元法,提出了两种计算系数矩阵的简便方法(影响系数法)。新算法避免了大量的数值积分,极大地减少了数值计算量。两个典型的物理模型被用来检验和阐明本文方法的计算特性。     

非均质低渗透油藏非线性流动数值模拟

提出一种适用于非均质低渗透油藏非线性流动数值模拟的方法.通过引入单元边界压力和速度两组物理量,在单个网格单元中构造数值计算格式,可精确地获取每个网格单元的压力梯度.以单相非线性渗流问题为出发点,详细阐述该方法的基本原理;通过数值算例验证方法的正确性和适用性.     

声学时域边界元法的时间卷积计算方法研究

核函数中保留Dirac函数的原型,形成关于时间的卷积积分,是声学时域边界元法中一种稳定、有效的时间数值积分计算方法 (CQ-BEM)。然而,传统CQ-BEM中卷积积分系数的获取有计算量大、耗时长,且对不同单元需要重新计算的问题,极大地降低了CQ-BEM法计算时域声场的效率。针对传统CQ-BEM积分系数计算效率低的问题,本文利用多项式展开定理给出了待求函数泰勒系数的解析表达与数值计算方法,建立了不同单元间待求系数的转换理论,可以在一次循环迭代内完成不同单元的积分系数的计算,大幅降低了计算量,提高了CQ-BEM方法的声场计算效率。脉动球源数值算例结果表明,在相同要求下,本文方法计算时间较传统方法减少50%以上,相对误差小5个数量级以上,且计算时间随单元数的增长率仅为传统方法的2.34%。因此,本文提出的系数计算方法能够有效提高CQ-BEM方法的时域声场计算效率,拓展了CQ-BEM在大型机电设备时域声场模拟的计算规模。     

双曲型守恒律的一种高精度TVD差分格式

构造了一维双曲型守恒律方程的一个高精度高分辨率的守恒型TVD差分格式.其主要思想是:首先将计算区域划分为互不重叠的小单元,且每个小单元再根据希望的精度阶数分为细小单元;其次,根据流动方向将通量分裂为正、负通量,并通过小单元上的高阶插值逼近得到了细小单元边界上的正、负数值通量,为避免由高阶插值产生的数值振荡,进一步根据流向对其进行TVD校正;再利用高阶Runge KuttaTVD离散方法对时间进行离散,得到了高阶全离散方法.进一步推广到一维方程组情形.最后对一维欧拉方程组计算了几个算例.     

EBE技术在结构分析中的应用(Ⅲ)-EBE-PCG法

在建立单元向量、伪单元向量等概念的基础上,提出了当不形成总刚度矩阵时,预处理共轭梯度法(PCG)的一种高度并行的EBE计算方法,其基本思想是把PCG法各步的计算都单元化。文[3]中的数值试验结果表明了它的有效性。     

局部时间步长间断有限元方法求解三维欧拉方程

使用间断有限元方法求解三维流体力学方程.空间剖分采用非结构四面体网格,为了克服显格式在单元网格尺寸差别较大时计算效率低下的问题,在格式中采用局部时间步长技术(LTS),即控制方程在空间、时间上积分得到一种单步格式,既可以局部计算每个单元又避免了Runge-Kutta高精度格式处理三维问题时存储量过大的问题.为了提高流体力学方程计算精度,在计算单元边界的数值流通量时使用任意高阶精度方法(ADER).数值算例表明格式稳定有效.     

基于自适应单元细分法的高效高精度近奇异域积分计算

本文针对边界元法在计算薄型结构力学、裂纹扩展等物理问题时存在的积分难题,提出一种基于自适应单元细分法的高效高精度近奇异域积分计算方法,该方法基于二叉树数据结构的单元细分技术对体单元进行自适应细分,消除单元几何形状所引起的近奇异性,能直接用于计算连续核函数的近奇异域积分。针对间断核函数的近奇异域积分,在细分单元的基础上采用腔面重建算法和投影算法,重新构建源点附近的积分子单元。数值算例表明：本方法可采用较少的积分点得到准确结果,是处理近奇异域积分的一种有效方法。     

无限长圆管中任意轴对称体绕中心轴旋转的小Re数问题

本文以Sampson旋转子在圆管中反演得到的无穷级数作为基本奇点,对分布函数采用离散奇点线分布法和分段二次抛物分布法,解决了任意轴对称体在无限长圆管中绕中心轴旋转的Stokes流动问題。通过对长球的数值计算,比较了两种方法,结果表明分段二次抛物分布法各方面都优于离散法。此外,本文还研究球串在无穷长圆管中绕中心轴旋转的小Re数问题,第一次给出了每个球所受的阻力矩系数。     

库特（Couette）剪切流准确解的一般形式

 从N-S方程出发,得到了轴对称异型断面管纯剪切流动速度分布的一般解,进而推出了纯剪切流动有限宽度矩形断面管的速度分布和流量计算公式,证明了库特剪切流是有限宽度矩形断面管当宽度趋向无穷大时的一种特例。并对库特剪切流流量的计算误差进行了分析,给出了该公式的适用范围,同时对有限宽度矩形断面管剪切流公式进行了曲线拟合,得到了便于工程使用的流量计算公式。     

波导短程透镜的优化理论设计研究

本文给出了非球面短程透镜的优化理论设计。卷边与平面波导连接处的曲率半径为无限大,卷边与实际透镜连接处的曲率半径为较大的有限值。完善了短程透镜的一般解析法。     

LINE FORCE RECEPTANCE OF AN ELASTIC CYLINDRICAL SHELL WITH HEAVY EXTERIOR FLUID LOADING

A time-harmonic line force is applied to an infinite elastic cylindrical shell immersed in compressible fluid. The force may also have axial harmonic dependence. The formal solution for the shell displacement is obtained as the sum of circumferential harmonics and evaluated in the asymptotic limit of heavy exterior fluid-loading. The resulting asymptotic expressions for the elements of the receptance matrix, either at the line of application of the force, or elsewhere on the shell surface, are simple trigonometric functions of the shell and fluid parameters, and show excellent agreement with numerical evaluation of the circumferential harmonic series over a wide frequency range.     

椭圆截面的无限长金属棒对任意平面电磁波在有损耗的均匀各向同性无限媒质中的散射

本文利用椭圆柱形坐标系,严格地分析了具有任意偏心度的椭圆截面的无限长理想导电的金属棒,放在有损耗的均匀各向同性的无限介质中,对从任意方向入射的均匀平面波的散射问题;并将散射场表示为马许函数。     

Long-range coulomb interaction in ionic crystals

Expressions have been proposed for calculating the matrix elements of the Coulomb interaction of p and d electrons in a chosen ion of a crystal with an infinite crystal lattice. The matrix elements have been calculated at Gaussian-type orbitals. The Coulomb interaction energy per molecular unit of the ????-NaV₂O₅ crystal has been calculated in the ionic approximation for homogeneous and chain orderings. It has been shown that the more correct determination of the energetic favorability of one or other ordering requires calculation of the Coulomb interaction energy with an infinite crystal lattice of electrons that are at different orbitals of the ion under consideration.     

Diffraction of electromagnetic plane wave by an infinitely long conducting strip on dielectric slab

Diffraction of electromagnetic plane wave by an infinitely long conducting strip which is placed on a dielectric slab of finite thickness is formulated rigorously. Both the principal polarizations have been considered. The method of analysis is Kobayashi potential. Imposition of boundary conditions result in dual integral equations. These dual integral equations are reduced to matrix equations with infinite number of unknowns. The elements of the matrix equations are given in terms of infinite integrals. These integrals are hard to solve analytically, so computed numerically. Diffracted far field patterns for different angle of incidence have been computed. Current distributions on the strip are also presented. We have compared our field patterns with those of obtained through physical optics. The agreement is good.     

关于无限薄平板中圆孔的线性声阻

本文提出至今尚未圆满解决的无限薄平板中一个圆孔的线性声阻的理论分析方法,得到了线性声阻率的高频(或大孔径)近似式及低频(或小孔径)极限值;理论计算和实测值符合良好;最后给出了在全频率范围适用的声阻率近似公式。 关键词：     

Computational simulation of wave propagation problems in infinite domains

This paper deals with the computational simulation of both scalar wave and vector wave propagation problems in infinite domains. Due to its advantages in simulating complicated geometry and complex material properties, the finite element method is used to simulate the near field of a wave propagation problem involving an infinite domain. To avoid wave reflection and refraction at the common boundary between the near field and the far field of an infinite domain, we have to use some special treatments to this boundary. For a wave radiation problem, a wave absorbing boundary can be applied to the common boundary between the near field and the far field of an infinite domain, while for a wave scattering problem, the dynamic infinite element can be used to propagate the incident wave from the near field to the far field of the infinite domain. For the sake of illustrating how these two different approaches are used to simulate the effect of the far field, a mathematical expression for a wave absorbing boundary of high-order accuracy is derived from a two-dimensional scalar wave radiation problem in an infinite domain, while the detailed mathematical formulation of the dynamic infinite element is derived from a two-dimensional vector wave scattering problem in an infinite domain. Finally, the coupled method of finite elements and dynamic infinite elements is used to investigate the effects of topographical conditions on the free field motion along the surface of a canyon.     

Direct numerical simulation of transitional flow in a finite length curved pipe

Transition to turbulent flow in a curved pipe has been well studied through experiments and numerical simulations. Numerical simulations often use a helical pipe with an infinite length such that the inlet and outlet boundary conditions can be modelled as periodic which greatly reduces computational time. In this study, we examined a finite length curved pipe with Poiseuille flow imposed at the inlet and a stress-free boundary condition at the outlet. Direct numerical simulation of the Navier-Stokes equations for rigid walls and a Newtonian fluid was performed using nek5000. Straight extensions were added to the inlet and outlet such to diminish the impact of boundary conditions on the flow field in the region with curvature. The examined model has a pipe radius of curvature that is three times the pipe radius. The model has ～355 million nodes and required an order of magnitude greater computational time when compared with an infinite length curved pipe. Results show that the critical Reynolds number, the lowest value with instabilities present in the flow, is much greater than that of a straight pipe and occurs near Re=5000–5200. This is larger than the critical Reynolds number typically reported for an infinite length curved pipe (Re=4200–4300).