线性传输方程的几种数值格式的比较

本文研究了线性传输方程的数值计算问题.利用Godunov格式、Entropy格式、Ultra-bee格式和Entropy-Ultra-bee格式对线性传输方程进行了数值计算,获得了相应的数值结果.数值实验结果表明Entropy-Ultra-bee格式结合了Entropy格式和Ultra-bee格式的优点,在整个计算区域都有比较高的分辨率,而且没有出现非物理振荡.     

粘性流动有限差分计算的新策略 *

对粘性流动计算 ,提出有限离散单元流动的流体分析 (理论 )和耦合离散流体理论(CDFT)的差分格式 .利用CDFT差分格式计算Burgers方程和计算激波边界层干扰流动的数值实验表明 :对计算精度和计算效率的提高 ,CDFT格式比提高常用差分格式 (即离散流体力学方程得到的格式 )精度和改进常用格式形式等更有效 ,且运算量小 .     

三阶WENO-Z格式精度分析及其改进格式

首先通过理论推导给出了三阶WENO格式(WENO-JS3格式)满足收敛精度的充分条件.采用Taylor(泰勒)级数展开的方法,分析发现传统的三阶WENO-Z格式(WENO-Z3格式)在光滑流场极值点处精度降低.为了提高WENO-Z3格式在极值点处的计算精度,根据收敛精度的充分条件构造一种改进的三阶WENO-Z格式(WENO-NZ3格式),并综合权衡计算精度和计算稳定性确定所构造格式的参数.通过两个典型的精度测试,验证了WENO-NZ3格式在光滑流场极值点区域逼近三阶精度.选用Sod激波管、激波与熵波相互作用、Rayleigh-Taylor不稳定性、二维Riemann(黎曼)问题经典算例,进一步证实了本文提出的WENO-NZ3格式相较其他格式(WENO-JS3、WENOZ3、WENO-N3),不仅提高了计算精度,而且提高了对复杂流场结构的分辨率.     

一类非自共轭非线性Schrodinger方程的三层差分格式

本文对一类非自共轭非线性Schrodinger方程提出了一种三层差分格式,并证明了该格式的收敛性与稳定性.这种格式不需叠代,故计算速度比C-N格式快,数值计算结果表明,该格式是有效的和可靠的.     

一类非自共轭非线性Schrödinger方程的三层差分格式

本文对一类非自共轭非线性Schrodinger方程提出了一种三层差分格式,并证明了该格式的收敛性与稳定性.这种格式不需叠代,故计算速度比C-N格式快,数值计算结果表明,该格式是有效的和可靠的.     

线性传输方程带二次多项式重构的熵格式（英文）

最近几年来,茅德康等发展了一类有限体积格式计算偏微分方程[1,3-4,6-9].该类格式得到比较好的计算结果.在文[8]中王和茅提出一个满足两个守恒律和三个守恒律的熵格式计算线性发展方程,但是该格式是基于线性多项式重构.本文发展了一个基于二次多项式重构满足两个守恒律的熵格式.数值试验表明本文的格式在长时间计算方面优于文[8].     

基于AUSM分裂的二维通量分裂格式

基于对流迎风分裂思想构造的AUSM类格式具有简单、高效、分辨率高等优点,在计算流体力学中得到了广泛的应用.传统的AUSM类格式在计算界面数值通量时只考虑网格界面法向的波系,忽略了网格界面横向波系的影响.使用Liou-Steffen通量分裂方法将二维Euler方程的通量分裂成对流通量和压力通量,采用AUSM格式来分别计算对流数值通量和压力数值通量.通过求解考虑了横向波系影响的角点数值通量来构造一种真正二维的AUSM通量分裂格式.在计算一维算例时,该格式保留了精确捕捉激波和接触间断的优点.在计算二维算例时,该格式不仅具有更高的分辨率而且表现出更好的鲁棒性,可以消除强激波波后的不稳定现象.此外,在多维问题的数值模拟中,该格式大大地提高了稳定性CFL数,具有更高的计算效率.因此,它是一种精确、高效并且强鲁棒性的数值方法.     

一类非自共轭非线性Schrdinger方程的三层差分格式

本文对一类非自共轭非线性Schr(?)dinger方程提出了一种三层差分格式,井证明了该格式的收敛性与稳定性.这种格式不需叠代,故计算速度比C-N格式快,数值计算结果表明,该格式是有效的和可靠的.     

求解Klein-Gordon-Schrdinger方程组的一个新型守恒差分算法的收敛性分析

对复Schrdinger场和实Klein-Gordon场相互作用下一类耦合方程组的初边值问题进行了数值研究,提出了一个高效差分格式,该格式非耦合且为半显格式,因此比隐格式具有更快的计算速度,而且便于并行计算;同时,该格式很好地模拟了初边值问题的守恒性质,保证了格式计算的可靠性,从而便于长时间计算.细致讨论了格式的守恒性质,并在先验估计的基础上运用能量方法分析了差分格式的收敛性.     

时间分数阶期权定价模型的一类有效差分方法

时间分数阶期权定价模型(时间分数阶Black-Scholes方程)数值解法的研究具有重要的理论意义和实际应用价值.对时间分数阶Black-Scholes方程构造了显-隐格式和隐-显差分格式,讨论了两类格式解的存在唯一性,稳定性和收敛性.理论分析证实,显-隐格式和隐-显格式均为无条件稳定和收敛的,两种格式具有相同的计算量.数值试验表明:显-隐和隐-显格式的计算精度与经典Crank-Nicolson(C-N)格式的计算精度相当,其计算效率(计算时间)比C-N格式提高30%.数值试验验证了理论分析,表明本文的显-隐和隐-显差分方法对求解时间分数阶期权定价模型是高效的,证实了时间分数阶Black-Scholes方程更符合实际金融市场.     

考虑损伤效应的正交各向异性板的弹塑性后屈曲分析

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,进而建立了混合硬化正交各向异性材料的增量型弹塑性损伤本构方程和损伤演化方程．基于经典非线性板理论,得到了考虑损伤效应的正交各向异性板的增量型非线性平衡方程,且采用有限差分法和迭代法进行求解．数值算例中,讨论了损伤演化、初始缺陷对正交各向异性板弹塑性后屈曲行为的影响．数值结果显示了弹塑性后屈曲与弹性后屈曲的不同,并且损伤和损伤演化对板的弹塑性后屈曲的影响不可忽略．     

Hamilton体系下含弱粘接复合材料层合板的灵敏度分析研究

基于径向基点插值函数(RPIM),在Hamilton体系下研究了含弱粘接复合材料层合板的灵敏度分析问题．利用弹簧层模型和修正H-R(Hellinger-Reissner)变分原理,推导了可用于含弱粘接复合材料层合板响应和灵敏度分析的混合控制方程,给出了基于该混合控制方程进行灵敏度分析的解析法(AM)、半解析法(SA)和有限差分法(FD)．该混合控制方程的主要优点是可以在进行灵敏度分析过程中避免卷积运算．另外,利用该混合控制方程进行灵敏度分析不仅能够同时得到响应结果和灵敏度系数,而且还考虑了层合板的层间弱粘接问题．     

损伤对粘弹性矩形板非线性动力特性的影响

研究了考虑损伤效应的粘弹性矩形板在横向周期载荷作用下的非线性动力学问题．基于Von Karman方程、Boltzmann叠加原理和连续损伤力学理论,建立了以中面位移表示的考虑损伤效应的粘弹性薄板的非线性动力学方程,然后,应用有限差分法和Newmark法进行求解,并与相应的文献作出了比较．具体讨论了外载荷参数和板的几何尺寸对含损伤效应的粘弹性板非线性动力响应的影响．数值结果表明,考虑损伤效应时,结构的非线性动力响应会发生显著的变化．     

Mindlin板条中弹性波传播问题的分析

基于Mindlin弹性厚板理论，采用Hamilton状态空间求解方法，研究了板条横向两侧为自由边界条件下的弹性：波传播问题，给出了问题的分析解，以及各种振动模态和波传播模的存在性．采用本征函数展开法给出了条形板中导波模的频散方程，并与直接根据Mindlin提出的解获得的频散关系进行了比较，通过比较发现：在短波时，频散曲线相差较大，即前几阶低频模式有一定差别。根据Hamilton体系得到的截止频率高一些，长波时频散曲线几乎相同，即高频模式无差别。     

Nonlinear free vibration analysis of simply supported piezo-laminated plates with random actuation electric potential difference and material properties

Studies are made on nonlinear free vibrations of simply supported piezo-laminated rectangular plates with immovable edges utilizing Kirchoff’s hypothesis and von Kármán strain–displacement relations. The effect of random material properties of the base structure and actuation electric potential difference on the nonlinear free vibration of the plate is examined. The study is confined to linear-induced strain in the piezoelectric layer applicable to low electric fields. The von Kármán’s large deflection equations for generally laminated elastic plates are derived in terms of stress function and transverse deflection function. A deflection function satisfying the simply supported boundary conditions is assumed and a stress function is then obtained after solving the compatibility equation. Applying the modified Galerkin’s method to the governing nonlinear partial differential equations, a modal equation of Duffing’s type is obtained. It is solved by exact integration. Monte Carlo simulation has been carried out to examine the response statistics considering the material properties and actuation electric potential difference of the piezoelectric layer as random variables. The extremal values of response are also evaluated utilizing the Convex model as well as the Multivariate method. Results obtained through the different statistical approaches are found to be in good agreement with each other.     

Modified mixed Ritz-DQ formulation for free vibration of thick rectangular and skew plates with general boundary conditions

Recently, the present authors proposed a simple mixed Ritz-differential quadrature (DQ) methodology for free and forced vibration, and buckling analysis of rectangular plates. In this technique, the Ritz method is first used to discretize the spatial partial derivatives with respect to a coordinate direction of the plate. The DQ method is then employed to analogize the resulting system of ordinary or partial differential equations. The mixed method was shown to work well for vibration and buckling problems of rectangular plates with simple boundary conditions. But, due to the use of conventional Ritz method in one coordinate direction of the plate, the geometric boundary conditions of the problem can only be satisfied in that direction. Therefore, the conventional mixed Ritz-DQ methodology may encounter difficulties when dealing with rectangular plates involving adjacent free edges and skew plates. To overcome this difficulty, this paper presents a modified mixed Ritz-DQ formulation in which all the natural boundary conditions are exactly implemented. The versatility, accuracy and efficiency of the proposed method for free vibration analysis of thick rectangular and skew plates are tested against other solution procedures. It is revealed that the proposed method can produce highly accurate solutions for the natural frequencies of thick rectangular plates involving adjacent free edges and skew plates using a small number Ritz terms and DQ sampling points.     

Unsteady MHD two-phase Couette flow of fluid–particle suspension

The problem of two-phase unsteady MHD Couette flow between two parallel infinite plates has been studied taking the viscosity effect of the two phases into consideration. Unified closed form expressions are obtained for the velocities and the skin frictions for both cases of the applied magnetic field being fixed to either the fluid or the moving plate. The novelty of this study is that we have obtained the solution of the unsteady flow using the Laplace transform technique, D’Alemberts method and the Riemann-sum approximation method. The solution obtained is validated by assenting comparisons with the closed form solutions obtained for the steady states which have been derived separately and also by the implicit finite difference method. Graphical result for the velocity of both phases based on the semi-analytical solutions are presented and discussed. A parametric study of some of the physical parameters involved in the problem is conducted. The skin friction for both the fluid and the particle phases decreases with time on both plates until a steady state is reached, it is also observed to decrease with increase in the particle viscosity on the moving plate while an opposite behaviour has been noticed on the stationary plate.     

Inelastic buckling of skew and rhombic thin thickness-tapered plates with and without intermediate supports using the element-free Galerkin method

In this paper, skew and rhombic isotropic plates subjected to in-plane loadings are analyzed using the element-free Galerkin method. Inelasticity effect is included in the buckling analysis while plates are thin thickness-tapered type. The governing differential equation for a plate in plastic range of response is numerically solved using the Galerkin method. The shape functions are constructed using the moving least squares (MLS) approximation and the essential boundary conditions are introduced into the formulation through the use of the Lagrange multiplier method and the orthogonal transformation techniques. The Stowell theory for the plastic buckling of flat skew plates with variable thicknesses is used. The inelastic analysis is based on the Ramberg–Osgood representation of the stress–strain curve which is used in the deformation theory of plasticity. Using this method the initial inelastic local buckling of skew plates with or without intermediate line supports is studied. Stiffness and geometric matrices are formulated by weak form of the Galerkin method. Finally, the inelastic local buckling loads of these plates are obtained and the results are compared with known solutions in the literature.     

弹性矩形薄板受迫振动的功的互等定理法(Ⅰ)——四边固定的矩形板和三边固定的矩形板

本文将功的互等定理法(MRT)推广于求解在简谐干扰力作用下矩形板的稳态响应.给出了各种边界条件矩形板的一系列封闭解并提供了一些有实用价值的图表.功的互等定理法(MRT)是求解在各种简谐干扰力作用下的矩形板稳态响应的一个简便、通用的方法.本文包括三部分:(Ⅰ)四边固定的矩形板和三边固定的矩形板;(Ⅱ)二邻边固定的矩形板;(Ⅲ)悬臂矩形板.我们准备分三次陆续发表它们.     

轴对称圆板(含叠层板)的三维非线性分析

本文提出了轴对称固支圆板(含叠层板)受均布横向载荷作用下的三维非线性摄动解答.文中所考虑的是一种中等大挠度的几何非线性,并采用一种发展的摄动方法对复杂的三维非线性平衡微分方程进行求解.该方法的基本思想是以二维解答为基础,对板的厚度参数进行摄动而求得相应的三维解答.文中给出了一般板及叠层板的三维非线性理论结果及数值结果,并图示出了各个应力的分布情况.而且,该三维非线性结果能退化为完全一致的相应的二维板理论非线性结果.结果表明,该方法对板的三维非线性分析是一种行之有效的方法.