第二类边界积分方程Nystrom解的高精度组合方法

第二类边界积分方程常用配置法或Ｇａｌｅｒｋｉｎ法计算，主要困难有：计算积分耗去大量机时；离散方程是满阵且不对称，计算量随剖分精细而急剧增加。本文提出Ｎｙｓｔｒｏｍ近似解的高精度组合法能有效克服上述困难。组合方法是并行地解ｍ个具有ｎ个不同结点的方程组，对得到的ｍ个内点值取算术平均就得到了组合近似，本文证明组合近似精度几乎与解ｍｎ个结点近似方程达到精度同阶，数值结果表明本文方法简单、有效、并且算法高度     

圆柱绕流问题的初期流动数值模拟

本文继Zheng-huan Teng[1]中介绍的解Navier-stokes方程的椭圆涡团法,研究了一种新的变形涡团法,用以模拟不可压粘性流体绕圆柱的不定常流动。圆柱在静止流体中突然起动并做匀速直线运动。对整个流动区域构造完全Navier-Stokes方程的解并不容易,近十年出现很多数值研究,本文对算法有所推进。把本文的方法称作变形涡团法是因为圆柱边界附近的流体中用椭圆涡团,远离边界时用圆形涡团。计算圆柱绕流比平板绕流在满足附着条件上更为困难,本文分析了怎样在圆柱边界上给出适当的附着条件的数值方法。在算例中雷诺数分别取200、550、3000,得到了不定常边界层分离,二次涡等复杂的物理现象,这些数值结果与近年实验结果[2]是一致的。     

坐标变换在波导管涡流计算中的应用

在脉冲引导磁场涡流的计算中，为克服不规则计算区域给网格划分带来的麻烦，可进行坐标变换，将不规则的区域转换成新的规则计算区域。     

一种改进的高效稳定内嵌边界算法

在气固多相流数值计算中,内嵌边界方法用于处理固体颗粒和流体之间的相互作用问题。本文将程玉民等改进的移动最小二乘法应用于内嵌边界方法中,克服了移动最小二乘逼近法需要求解逆矩阵的弊端,提高了计算效率和精度。通过直接数值模拟具有精确解的Taylor-Green涡、均匀来流绕过固定圆柱和NACA-0012机翼,验证了本算法可以取得很好的模拟结果。     

解深穿透问题的小区域蒙特卡罗方法

对于深穿透问题则一般蒙特卡罗方法存在一定的困难。本文提出了一个新的蒙特卡罗计算深穿透问题的小区域方法。在此基础上给出了两个小区域方法,即平几何小区域方法和球几何小区域方法,通过例子的实际计算表明,小区域方法是比较好的和可行的,克服了一般蒙特卡罗方法解深穿透问题的缺点。     

移动边界问题的时空域正则区域迭代配点法

考虑热传导方程的移动边界问题,其定解区域随着时间而变化.构造一种时空域上的高精度数值算法求解1+1维移动边界问题.在时空域上假设一个初始移动边界位置,构成移动边界问题的不规则计算区域,选择一个适当的正则区域(矩形区域)完全覆盖所计算的不规则区域,在正则区域上利用移动边界约束条件和固定边界条件,采用时空域重心插值配点法求...     

离散坐标SRAP_N法及其与T_N法的比较

提出了一种新的坐标离散方法-球带等差数列微元等分法。并经双动量理论检验,与较精确的区域法数值解进行了比较计算。     

数值模拟输运问题的一种破开算子方法

本文通过破开算子方法,把二维输运问题的控制方程破开为对流问题和扩散问题。在任意四边形网格的离散下,用特征线法解对流问题,并采用伽辽金加权余量法,从而有效地减少插值所引起的数值阻尼,提高计算精度。用有限单元法和迭代计算格式解扩散问题。由于采用了辛普生积分公式,在每个时间步长都不需要求逆矩律,节省了计算时间。算例表明,本文数值模拟结果与精确的理论解吻合较好。     

等离子体在均匀强磁场中的横向输运系数

本文利用Kubo型线性输运系数公式和Landau表象计算了等离子体在强磁场中的扩散系数、热导率和粘滞系数。和以往解Boltzmann方程的方法相比,本文所用方法有如下优点:在处理强磁场、多体长程相互作用体系时没有原则上的困难;物理图象简单、清晰;在准确到相互作用的二次项时,不用解输运方程就能得到上述的横向输运系数的解析表达式。本文结果和用Chapman-Enskog法解线性Boltzlmann方程时得到的数值结果基本相符而略有不同,在对离子电荷数Z的依赖关系上则有较明显的不同。     

改进的半空间频率均方声压法计算结构频带振动声辐射

为计算中高频半空间结构频带振动下声辐射问题,推导了基于能量源的半空间频率均方声压法(Frequency Averaged Quadratic Pressure,FAQP),并提出了改进的半空间FAQP法,克服了半空间FAQP法在失效频率下解不唯一的问题。频率带宽为4 Hz的刚性壁面作用下的脉动球和与自由表面相接触的脉动半球的声辐射数值计算,验证了改进的半空间FAQP法对解决失效频率下解不唯一问题的有效性。同时,刚性壁面作用下的脉动球和与自由表面相接触的脉动半球声辐射数值计算结果均表明,在1/3倍频程下,改进的半空间FAQP法与常规边界元方法相比,具有更高的计算精度,更适用于中高频计算。      

A conjugated infinite element method for half-space acoustic problems

Many acoustic problems (especially in environmental acoustics) involve half-space domains bounded by a plane subjected to normal admittance boundary conditions. In the "low" frequency domain, the numerical treatment of such problems usually relies on boundary element methods based on a particular Green's function suited for the half-(admittance) plane. In the present paper, an alternative hybrid finite/infinite element scheme is proposed. The method relies on a direct treatment of nonhomogeneous boundary conditions along infinite element edges (or faces). The procedure is validated through comparisons with an available reference solution.     

Finite element formulations for acoustical radiation

Finite and infinite element techniques are applied to linear acoustical problems involving infinite anechoic boundaries. Theory is presented for a simple one dimensional model based on Webster's horn equation. Results are then presented both for the one dimensional model and for two axisymmetric test cases. Comparisons with exact solutions indicate that both the infinite element and wave envelope schemes are effective in correctly predicting the near field. The wave envelope scheme is also shown to be capable of resolving the far field radiation pattern.     

(2+1)维改进的Zakharov-Kuznetsov方程的无穷序列复合型类孤子新解

对(G′/G)展开法做了进一步的研究,利用两次函数变换将二阶非线性辅助方程的求解问题转化为一元二次代数方程与Riccati方程的求解问题.借助Riccati方程的B?cklund变换及解的非线性叠加公式获得了辅助方程的无穷序列解.这样,利用(G′/G)展开法可以获得非线性发展方程的无穷序列解,这一方法是对已有方法的扩展,与已有方法相比可获得更丰富的无穷序列解.以(2+1)维改进的Zakharov-Kuznetsov方程为例得到了它的无穷序列新精确解.这一方法可以用来构造其他非线性发展方程的无穷序列解.     

A finite element method for analysis of vibration induced by maglev trains

This paper developed a finite element method to perform the maglev train–bridge–soil interaction analysis with rail irregularities. An efficient proportional integral (PI) scheme with only a simple equation is used to control the force of the maglev wheel, which is modeled as a contact node moving along a number of target nodes. The moving maglev vehicles are modeled as a combination of spring-damper elements, lumped mass and rigid links. The Newmark method with the Newton–Raphson method is then used to solve the nonlinear dynamic equation. The major advantage is that all the proposed procedures are standard in the finite element method. The analytic solution of maglev vehicles passing a Timoshenko beam was used to validate the current finite element method with good agreements. Moreover, a very large-scale finite element analysis using the proposed scheme was also tested in this paper.     

A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation

A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb's problem and plane wave nonlinear propagation.     

非饱和水流问题的迎风有限体积元方法及数值模拟

考察非饱和水流问题的模型方程,利用线性迎风有限体积元方法建立非饱和流动的守恒形式,并获得该方法形式为O(Δt+h)的误差估计,最后给出数值模拟.     

A Modified Helmholtz Equation with Impedance Boundary Conditions

Here considered is the problem of transient electromagnetic scattering from overfilled cavities embedded in an impedance ground plane. An artificial boundary condition is introduced on a semicircle enclosing the cavity that couples the fields from the infinite exterior domain to those fields inside. A Green's function solution is obtained for the exterior domain, while the interior problem is solved using finite element method. Well-posedness of the associated variational formulation is achieved and convergence and stability of the numerical scheme are confirmed. Numerical experiments show the accuracy and robustness of the method.     

A New Numerical Method for Solving the Acoustic Radiation Problem

A numerical method of solving the problem of acoustic wave radiation in the presence of a rigid scatterer is described. It combines the finite element method and the boundary algebraic equation one. In the proposed method, the exterior domain around the scatterer is discretized, so that there appear an infinite domain with regular discretization and a relatively small layer with irregular mesh. For the infinite regular mesh, the boundary algebraic equation method is used with spurious resonance suppression according to Burton and Miller. In the thin layer with irregular mesh, the finite element method is used. The proposed method is characterized by simple implementation, fair accuracy, and absence of spurious resonances.     

On the vibration of an elastic plate on an elastic foundation

The forced vibration of an elastic plate under a time harmonic point force is studied. The plate is infinite in extent and supported by an elastic foundation. This study is made on the basis of the improved (Timoshenko) plate theory. The mathematical problem is to seek a fundamental solution (the Green's function) of the time-reduced plate equation of the improved plate theory. Such a fundamental solution is constructed by the distributional Fourier transform method. From the explicit expressions of the fundamental solution, the behavior of the fundamental singularity as a function of the vibration frequency and the foundation stiffness is examined. Conditions under which plate resonance occurs are also determined.     

Energy law preserving continuous finite element schemes for a gas metal arc welding system

In this paper a modifed continuous energy law was explored to investigate transport behavior in a gas metal arc welding(GMAW)system.The energy law equality at a discrete level for the GMAW system was derived by using the finite element scheme.The mass conservation and current density continuous equation with the penalty scheme was applied 10 improve the stability.According to the phase-field model coupled with the energy law preserving method,the GMAW model was discretized and a metal transfer process with a pulse current was simulated.It was found that the numerical solution agrees well with the data of the metal transfer process obtained by high-speed photography.Compared with the numerical solution of the volume of fuid model,which was widely studied in the GMAW system based on the finite element method Euler scheme,the energy law preserving method can provide better accuracy in predicting the shape evolution of the droplet and with a greater computing efficiency.