基于对偶混合变分原理的Signorini问题的数值模拟

基于Signorini问题的对偶混合变分形式,提出了一种非协调有限元逼近格式,证明了离散的B-B条件,获得了Raviart-Thomas(k=0)有限元逼近的误差界O(h^3/4),并且Uzawa型算法对协调与非协调有限元逼近格式进行了数值求解.根据数值结果的分析和比较,表明应用非协调有限元逼近格式求解更有效.     

Least-squares finite element method for radiation heat transfer in graded index medium

To avoid the complicated and time-consuming computation of curved ray trajectories, a least-squares finite element method based on discrete ordinate equation is extended to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Four cases of radiative heat transfer are examined to verify this least-squares finite element method. Linear and nonlinear graded index are considered. The predicted dimensionless net radiative heat fluxes are determined by the least-squares finite element method and compared with the results obtained by other methods. The results show that the least-squares finite element method is stable and has a good accuracy in solving the multi-dimensional radiative transfer problem in a semitransparent graded index medium, while the Galerkin finite element method sometimes suffers from nonphysical oscillations.     

Finite element method for radiation heat transfer in multi-dimensional graded index medium

In graded index medium, ray goes along a curved path determined by Fermat principle, and curved ray-tracing is very difficult and complex. To avoid the complicated and time-consuming computation of curved ray trajectories, a finite element method based on discrete ordinate equation is developed to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Two particular test problems of radiative transfer are taken as examples to verify this finite element method. The predicted dimensionless net radiative heat fluxes are determined by the proposed method and compared with the results obtained by finite volume method. The results show that the finite element method presented in this paper has a good accuracy in solving the multi-dimensional radiative transfer problem in semitransparent graded index medium.     

Free vibration of formed sandwich panel

In this paper, the free vibration of prefabricated architectural sandwich panels is studied. The core of the sandwich panel is approximated by finite prisms and the thin faces are modelled by finite strips. The finite prism-strip method is simple to program and saves considerable computing effort when compared with the finite element method. In this paper, only the dynamic characteristics of flat faced homogeneous sandwich panels are compared with results obtained by other methods, and also with the analytical solutions. Several examples are also presented for the free vibration of prefabricated architectural sandwich panels.     

Discontinuous finite element method for radiative heat transfer in semitransparent graded index medium

To avoid the complicated and time-consuming computation of curved ray trajectories, a discontinuous finite element method based on discrete ordinate equation is extended to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Two cases of radiative heat transfer in two-dimensional rectangular gray semitransparent graded index medium enclosed by opaque boundary are examined to verify this discontinuous finite element method. Special layered and radial graded index distributions are considered. The predicted dimensionless net radiative heat fluxes and dimensionless temperature distributions are determined by the discontinuous finite element method and compared with the results obtained by the curved Monte Carlo method in references. The results show that the discontinuous finite element method has a good accuracy in solving the multi-dimensional radiative transfer problem in a semitransparent graded index medium.     

Impact on short length bars

A finite element method for the solution of an axisymmetric wave propagation problem of a bar of finite length is proposed. The results are obtained for a uniform bar with (i) a displacement input and (ii) a stress input. Also results are obtained for a discontinuous bar with stress input. They are compared with the existing finite difference solutions and experimental results. It is observed that the results are in close agreement. The study is then extended to the case of bars with an hemispherical end. The advantage of using the finite element method for such problems is indicated. Finally the results for a composite bar comprising a hallow cylinder and hemisphere are obtained by using the finite element method. Experiments are conducted to verify these results.     

Developing a time-domain finite-element method for modeling of electromagnetic cylindrical cloaks

In this paper we propose a time-domain finite element method for modeling of electromagnetic cloaks. The permittivity and permeability of the cloak model are described by the Drude dispersion model. The model to be solved is quite challenging in that we have to solve a coupled problem with different partial differential equations given in different regions. Our method is based on a mixed finite element method using edge elements with different types of meshes in different regions. Numerical results demonstrate that our algorithm is quite effective for simulating cloaks in time-domain. To our knowledge, this is the first cloak simulation carried out by the time-domain finite element method.     

用拉普拉斯变换差分法求解试井分析中的一维渗流问题

结合拉普拉斯变换和有限差分法给出求解试井分析中一维渗流问题的拉普拉斯变换差分法:首先对渗流方程采用拉普拉斯变换消去时间变量得到拉普拉斯空间数学模型,采用有限差分法求解拉普拉斯空间数学模型,最后通过拉普拉斯反演算法得到井底压力或产量.通过与有限差分法结果和解析解对比,拉普拉斯变换差分法比有限差分法计算误差小.虽然单步计算耗时长,但计算任意时刻结果时对空间网格的适应性和不依赖其它时刻计算结果的特性使得拉普拉斯变换差分法在试井分析中有非常好的应用前景.     

Pseudo-spectral methods and linear instabilities in reaction-diffusion fronts

We explore the application of a pseudo-spectral Fourier method to a set of reaction-diffusion equations and compare it with a second-order finite difference method. The prototype cubic autocatalytic reaction-diffusion model as discussed by Gray and Scott [Chem. Eng. Sci. 42, 307 (1987)] with a nonequilibrium constraint is adopted. In a spatial resolution study we find that the phase speeds of one-dimensional finite amplitude waves converge more rapidly for the spectral method than for the finite difference method. Furthermore, in two dimensions the symmetry preserving properties of the spectral method are shown to be superior to those of the finite difference method. In studies of plane/axisymmetric nonlinear waves a symmetry breaking linear instability is shown to occur and is one possible route for the formation of patterns from infinitesimal perturbations to finite amplitude waves in this set of reaction-diffusion equations. (c) 1996 American Institute of Physics.     

求解对流-扩散-反应问题的改进有限积分法

将求解偏微分方程的有限积分法应用于对流-扩散-反应问题,发现对于非对流占优的对流扩散问题,有限积分法的精度比QUICK法高一个数量级,比传统的有限体积法高两个数量级.处理对流占优的对流-扩散-反应问题时,对流项的离散时引进加权参数,通过调节该参数反映输运的方向性.结果表明这种改进的有限积分法的精度比传统的有限体积法至少高四个数量级,同时明显改进了原来的有限积分法的精度和稳定性.对于对流占优的对流-扩散-反应问题,即使采用粗网格,计算结果也未出现非物理振荡现象,表明改进的有限积分法具有很好的稳定性.     

声表面波在厚金属栅阵中的耦合模参数

提出了一种研究声表面波在压电晶体厚金属栅阵中传播特性的理论方法。将有限元和声表面波在周期栅阵中的变分原理分析方法相结合,在陈东培和H.A.Haus理论基础上、用有限元分析金属短路栅对声表面波传输特性的影响,将力学负载贡献的耦合模参数用有限元矩阵表示,使其适用于声表面波在厚金属或任意形状栅条中传输情况,给出了具体理论分析方法和相应的理论表达式。最后,具体研究了几种压电晶体上金、铝或银栅阵中声表面波的传输特性,通过数值计算给出了声表面波的耦合模参数。      

有限体积法求解圆柱形散射介质内辐射与导热耦合换热

将谱带模型与有限体积解法相结合;求吸收、发射、散射性非灰介质圆柱体内辐射传递方程。考虑辐射强度场与热扩散温度场的耦合,将控制容积法与有限体积法结合,求解辐射与导热耦合换热。经与光线踪迹法、离散传递法的计算结果比较表明,谱带模型与有限体积解法相结合能处理多场耦合下非灰介质内的辐射换热。     

水位骤变时的饱和-不饱和渗流数值计算

本文应用全隐式交替方向迭代法对水位骤变时的饱和-不饱和渗流问题求出了数值解。对于赤井模型,计算结果与实验结果十分接近,比有限元法的计算结果好。对于大尺度的驹田蓄水池模型,计算结果与有限元法的结果基本一致。     

基于SNGR方法的后缘噪声数值模拟

采用随机噪声产生和传播(SNGR)方法对后缘噪声进行数值模拟.SNGR方法结合随机方法和计算流体力学,耗费较少的计算资源就可以预测噪声水平.数值模拟时采用有限体积法求解雷诺平均Navier-Stokes(RANS)方程;采用有限差分法求解声学扰动方程,数值格式采用色散关系保持(DRP)格式,远场边界条件采用无反射边界条件.以二维平板和NACA0012翼型为例,编制程序,与参考结果对比表明,程序可以预测后缘噪声.     

Transient torsional vibration responses of finite, semi-infinite and infinite hollow cylinders

Torsional guided waves are often used to detect the defects in a hollow cylinder. To realize the excitation of the torsional guided waves with high efficiency, the transient vibration responses of finite, semi-infinite and infinite hollow cylinders to external torsional forces must be clarified theoretically. In this study, the method of eigenfunction expansion is employed to solve the above problems. The exact analytical solutions derived by this method are not only explicit but also concise. Furthermore, the analytical solution of the transient torsional vibration of the finite hollow cylinder is numerically evaluated. The results obtained agree well with those simulated by the finite element method.     

悬线式力矩器磁路设计中的有限元分析应用

光学头力矩器的空间磁场分布直接决定了力矩器的动态性能,对磁场进行准确分析是力矩器设计的前提。分析了悬线式力矩器的空间磁场产生机理,并采用有限元分析法进行了理论推导。以一款动线圈式二维对称型只读悬线式力矩器为例,采用有限元仿真软件（ANSYS）分析并设计了其空间磁场分布,对影响力矩器空间磁场分布的相关因素进行了分析。将采用有限元法对悬线式力矩器空间磁场仿真计算得出的力矩器动态特性参数与实测力矩器动态特性参数相比,其结果均符合力矩器的设计要求,证明基于有限元分析法的悬线式力矩器空间磁场设计是可行的。     

An element-free Galerkin(EFG) method for numerical solution of the coupled Schrdinger-KdV equations

The present paper deals with the numerical solution of the coupled Schrdinger-KdV equations using the elementfree Galerkin(EFG) method which is based on the moving least-square approximation.Instead of traditional mesh oriented methods such as the finite difference method(FDM) and the finite element method(FEM),this method needs only scattered nodes in the domain.For this scheme,a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method.In numerical experiments,the results are presented and compared with the findings of the finite element method,the radial basis functions method,and an analytical solution to confirm the good accuracy of the presented scheme.     

A microscopic theory of the lambda transition,II

The previously proposed finite temperature field theory of the lambda transition based on the Schwinger functional method is investigated further. A systematic method for calculating the higher-order loop terms is presented by introducing the one-loop Green's functions, which are found to be a natural finite temperature extension of the Beliaev-Hugenholtz-Pines-Gavoret-Nozières zero-temperature Green's functions. The application of the finite temperature loop expansion to the dynamical properties is presented by calculating the retarded density correlation functions at the one-loop level. The result gives a microscopic basis for the form of the dynamical structure factor recently proposed by Woods and Svensson. From a general point of view, without using any approximations or model interactions, Goldstone's theorem for the lambda transition at finite temperature is presented.     

静态电磁场边值问题计算方法

介绍常用的电磁场分析方法——解析法、有限差分法、有限元法.以静态电磁场边值问题为例,分别用自己编写的MATLAB有限差分程序及大型有限元分析软件ANSYS求出了数值解,并与解析法得到的精确解进行比较,得出了用数值法求解电磁场问题基本满足工程需要的结论.采用数值计算时,对如何减小计算机内存,取消冗余数据,也做了进一步的讨论.     

The finite difference time domain calculation of one-dimensional photonic crystals composed of repetitive metallic and dielectric layers

The frequency dependence on the reflectance of a one-dimensional (1D) photonic crystal composed of repetitive metallic and dielectric layers was simulated by the finite difference in the time domain (FDTD) method, and with results compared to the conventional transfer matrix (TM) method. The simulation from the FDTD method with an impedance-matched boundary of finite dimensions yields results similar to the calculation from the TM method with unbounded planes. The FDTD method is prominent in dealing with films of finite area including defects at some locations. The reflectivity increases and the rejection bandwidth decreases as the number of layers increases. PACS 42.70.Qs; 47.11.Bc; 78.20.-e; 78.67.-n