三维PTT黏弹性液滴撞击固壁面问题的改进SPH模拟

基于光滑粒子动力学(smoothed particle hydrodynamics, SPH)方法,对三维Phan-Thien Tanner(PTT)黏弹性液滴撞击固壁面问题进行了数值模拟.为了有效地防止粒子穿透固壁,且缩减三维数值模拟所消耗的计算时间,提出了一种适合三维数值模拟的改进固壁边界处理方法.为了消除张力不稳定性问题,采用一种简化的人工应力技术.应用改进SPH方法对三维PTT黏弹性液滴撞击固壁面问题进行了数值模拟,精细地捕捉了液滴在不同时刻的自由面,讨论了PTT黏弹性液滴不同于Newton(牛顿)液滴的流动特征,分析了PTT拉伸参数对液滴宽度、高度和弹性收缩比等的影响.模拟结果表明,改进SPH方法能够有效而准确地描述三维PTT黏弹性液滴撞击固壁面问题的复杂流变特性和自由面变化特征.     

尖劈吸波体的研究和微波暗室的模拟

对尖劈形状吸波体的吸波性能进行了研究,并对导弹导引仿真实验用的微波暗室的性能进行分析和仿真.首先对尖劈体的二维反射性能进行了研究,从单条波线反射的原理出发,得到波束平面反射的统计模型.单条波线的反射通过数值模拟得到;波束反射模型则通过对数值模拟的结果进行统计和拟合得到,最终用多项式表示.对于一些简单或特殊的情况,也给出了解析解.通过分析发现,三维反射和二维反射之间有明确的关系.这种关系可以由三维入射角和反射次数决定,而反射次数可以通过二维模型得到.据此将平面反射模型扩展为三维反射模型,从而得到尖劈形状吸波体的三维反射模型.无回波暗室用于模拟没有背景微波辐射的环境,其关键在于选择合适的吸波材料.基于微波反射通量平衡原理,建立了考虑暗室墙面各点之间的相互影响的耦合模型,从而可以求解出在指定的发射源照射之下墙面各点的辐射强度分布.对模型的求解精度和收敛性进行了验证.基于此模型,对一个导弹引导试验进行了数值模拟,推算出了使用两种不同吸波材料时静区接收到的微波信号的信噪比.     

轴对称弹性动力学问题的重构核插值法

重构核插值法是近年来提出的一种新型无网格方法.该方法的形函数具有点插值性和高阶光滑性,不仅能够直接施加本质边界条件,而且能保证较高的计算精度.为了更有效地求解三维轴对称弹性动力学问题,对重构核插值法(reproducing kernel interpolation method, RKIM)应用于此类问题进行了研究,并发展了相应的数值模拟方法.由于几何形状和边界条件的轴对称性,计算时只需要横截面上离散节点的信息,因而前处理变得简单.采用Newmark-β法进行了时域积分.数值算例表明,轴对称弹性动力学分析的重构核插值法既有无网格方法的优势,又有较高的计算精度.     

热弹性波在偶应力固体界面上的反射和透射

基于广义热弹性无能量耗散的G-N理论,研究了两种不同偶应力固体界面上弹性波的反射和透射.首先,建立偶应力弹性固体中的运动方程和边界条件.然后,根据非传统界面条件推导出弹性波反射和透射的振幅比.最后,用法向能量守恒验证了数值计算结果,根据数值计算结果,讨论了微结构参数和热力学参数对弹性波反射和透射的影响.结果显示,偶应力热弹性固体界面处存在三种体波和一种表面波;微结构参数对所有波的传播都有影响,而热力学参数只对热波的影响显著.     

极坐标系下非分裂PML及时域有限元实现

在弹性波传播的数值模拟中,吸收边界被广泛应用于截取有限空间进行无限空间问题的分析.完全匹配层（perfect matched layer, PML）吸收边界较其他吸收边界条件具有更优越的吸收性能,已被成功应用于直角坐标系下的弹性波方程正演模拟.考虑极坐标系下二阶弹性波动方程,通过采用辅助函数的方法,提出了一种非分裂格式的完全匹配层吸收边界条件.并且基于Galerkin近似技术,给出了非对称以及轴对称条件下的时域有限元计算格式.通过数值算例分析了该极坐标系下分裂格式的完全匹配层吸收边界的有效性.     

CH-γ方程的两类新有界波

用动力系统分支方法和微分方程数值方法研究CH-γ方程.发现了两类新的有界波, 一类称为紧孤立子, 另一类称为广义扭波.文中模拟了它们的平面图形, 并给出了其隐函数表达式, 最后展示了理论推导和数值模拟的一致性.     

CH-r方程的尖波解

用动力系统的定性分析理论和数值模拟方法, 对CH-r方程的尖波解进行研究, 获得了孤立尖波和周期尖波的解析表达式, 揭示了这两种尖波解之间的一些关系, 还指出了产生尖点的原因.     

任意形状凸起地形对平面SH波的散射

将具有任意形状的凸起地形对称态SH波散射问题转换为契合问题加以研究,利用求解弹性波动问题的复变函数与保角映射方法,在包括任意形状凸起边界在内的一个区域中,构造一个在凸起边界上应力自由,其他部分位移和应力均为任意的驻波解,然后再将这个驻波解与其余下的区域中的散射波解在两个区域结合面上完成契合过程,由此决定出这两个区域中的驻波和散射波解答,最后对圆弧形和半椭圆形凸起进行了数值计算,并将计算结果与有限元法的数值解进行了比较。     

压电固体中弹性波传播的数学模型

依据动量定理、电荷守恒定律建立了弹性波在压电固体中传播的数学模型.不仅考虑了压电效应,也同时考虑了电流效应.在压电固体中同时存在机械位移场、极化电势场和电流场.求解波动方程,发现不考虑电流效应时,弹性波是非色散的;考虑电流效应后,弹性波是色散的.不仅如此,电流效应还导致弹性波的衰减.通过数值模拟,揭示了平衡载流子浓度对色散和衰减的影响规律.     

非线性薛定谔方程的平均向量场方法

利用平均向量场方法(AVF)对非线性薛定谔方程进行求解, 在理论上得到了一个保非线性薛定谔方程描述的系统能量守恒的AVF格式, 再分别用非线性薛定谔方程的AVF格式和辛格式数值模拟孤立波的演化行为, 并比较两个格式是否保系统能量守恒特性. 数值结果表明, AVF格式也能很好地模拟孤立波的演化行为,并且比辛格式更能保持系统的能量守恒.     

Three methods for two‐sided bounds of eigenvalues—A comparison

We compare three finite element‐based methods designed for two‐sided bounds of eigenvalues of symmetric elliptic second order operators. The first method is known as the Lehmann–Goerisch method. The second method is based on Crouzeix–Raviart nonconforming finite element method. The third one is a combination of generalized Weinstein and Kato bounds with complementarity‐based estimators. We concisely describe these methods and use them to solve three numerical examples. We compare their accuracy, computational performance, and generality in both the lowest and higher order case.     

Spectral element method for acoustic wave simulation in heterogeneous media

In this paper, we present a spectral element method for studying acoustic wave propagation in complex geological structures. Due to complexity (both lithological and stratigraphical), the use of numerical methods of higher accuracy and flexibility is needed to achieve the correct results. The spectral element method shows more accurate results compared to the low-order finite element, the conventional finite difference and the pseudospectral methods. High accuracy is reached even for rather long wave propagation times and dispersion errors are essentially eliminated; pirregular interfaces between different media can be well described so that numerical artifacts or noises are not at all introduced. The method is tested against analytical solutions both in the two-dimensional homogenous and heterogeneous media. The results of different simulations are presented.     

Complex conjugate gradient methods

Linear systems with complex coefficients arise from various physical problems. Examples are the Helmholtz equation and Maxwell equations approximated by finite difference or finite element methods, that lead to large sparse linear systems. When the continuous problem is reduced to integral equations, after discretization, one obtains a dense linear system. The resulting matrices are generally non-Hermitian but, most of the time, symmetric and consequently the classical conjugate gradient method cannot be directly applied. Usually, these linear systems have to be solved with a large number of unknowns because, for instance, in electromagnetic scattering problems the mesh size must be related to the wave length of the incoming wave. The higher the frequency of the incoming wave, the smaller the mesh size must be. When one wants to solve 3D-problems, it is no longer practical to use direct method solvers, because of the huge memory they need. So iterative methods are attractive for this kind of problems, even though their convergence cannot be always guaranteed with theoretical results. In this paper we derive several methods from a unified framework and we numerically compare these algorithms on some test problems.     

A GLOBAL-LOCAL FINITE ELEMENT METHOD IN SPACE-TIME FOR A HYPERBOLIC PROBLEM

ABSTRACT

A finite element method for solving the wave equation with couples boundary conditions is presented. In this approach finite elements are applied globally with respect to space and simultaneously but locally with respect to time. This gives rise to a single-step method in time. The method is a practical and economic one and the numerical results obtained compare favourably with the available analytic solution.     

High‐order energy‐preserving schemes for the improved Boussinesq equation

This article proposes a class of high‐order energy‐preserving schemes for the improved Boussinesq equation. To derive the energy‐preserving schemes, we first discretize the improved Boussinesq equation by Fourier pseudospectral method, which leads to a finite‐dimensional Hamiltonian system. Then, the obtained semidiscrete system is solved by Hamiltonian boundary value methods, which is a newly developed class of energy‐preserving methods. The proposed schemes can reach spectral precision in space, and in time can reach second‐order, fourth‐order, and sixth‐order accuracy, respectively. Moreover, the proposed schemes can conserve the discrete mass and energy to within machine precision. Furthermore, to show the efficiency and accuracy of the proposed methods, the proposed methods are compared with the finite difference methods and the finite volume element method. The results of several numerical experiments are given for the propagation of the single solitary wave, the interaction of two solitary waves and the wave break‐up.     

Modeling and computation of metal powder compaction processes

In this short communication the numerical treatment of a thermomechanical consistent finite strain viscoplasticity model for metal powder compaction is discussed. The convex single surface yield function evolves according to two evolution equations and remains convex under all loading conditions. The very challenging numerical treatment on local level for integrating the constitutive model requires particular globally convergent Newton-like method with inequality constraints so that a stable solution scheme results. This is embedded into a time-adaptive finite element program which makes use of diagonally-implicit Runge-Kutta methods combined with a Multilevel-Newton algorithm. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

特征值问题的自适应反迭代有限元算法

1引言设Ω∈R~2为Lipschitz单连通的有界闭区域,X为定义在Ω的Sobolev空间,a(·,·)和b(·,·)为X×X→C的有界双线性或半双线性泛函,考虑变分特征值问题:求(λ,u≠0)∈C×X使得a(u,v)=λb(u,u),(?)u∈X,其中a(·,·)满足X上的"V-强制性"条件或者连续的inf-sup条件,设M_h为Q区域上的正则三角形剖分,X_h∈X为定义在M_h有限元子空间,上述变分问题对应的有限元离散问题为:求(λ_h,u_h)∈R×X,u_h≠0使得     

A symplectic analytical wave propagation model for damping and steady state forced vibration of orthotropic composite plate structure

An analytical wave propagation model is proposed in this paper for damping and steady state forced vibration of orthotropic composite plate structure by using the symplectic method. By solving an eigen-problem derived in the symplectic dual system of free bending vibration of orthotropic rectangular thin plates, the wave shape of plate is obtained in symplectic analytical form for any combination of simple boundary conditions along the plate edges. And then the specific damping capacity of wave mode is obtained symplectic analytically by using the strain energy theory. The steady state forced vibration of built-up plates structure is calculated by combining the wave propagation model and the finite element method. The vibration of the uniform plate domain of the built-up plates structure is described using symplectic analytical waves and the connector with discontinuous geometry or material is modeled using finite elements. In the numerical examples, the specific damping capacity of orthotropic rectangular thin plate with three different combinations of boundary condition is first calculated and analyzed. Comparisons of the present method results with respect to the results from the finite element method and from the Rayleigh–Ritz method validate the effectiveness of the present method. The relationship between the specific damping capacity of wave mode and that of modal mode is expounded. At last, the damped steady state forced vibration of a two plates system with a connector is calculated using the hybrid solution technique. The availability of the symplectic analytical wave propagation model is further validated by comparing the forced response from the present method with the results obtained using the finite element method.     

Three-dimensional simulation of flat rolling through a combined finite element–boundary element approach

This paper presents an innovative approach for analysing three-dimensional flat rolling. The proposed approach is based on a solution resulting from the combination of the finite element method with the boundary element method. The finite element method is used to perform the rigid–plastic numerical modelling of the workpiece allowing the estimation of the roll separating force, rolling torque and contact pressure along the surface of the rolls. The boundary element method is applied for computing the elastic deformation of the rolls. The combination of the two numerical methods is made using the finite element solution of the contact pressure along the surface of the rolls to define the boundary conditions to be applied on the elastic analysis of the rolls. The validity of the proposed approach is discussed by comparing the theoretical predictions with experimental data found in the literature.     

A space‐time mixed‐hybrid finite element method for the damped wave equation

A space‐time finite element method is introduced to solve the linear damped wave equation. The scheme is constructed in the framework of the mixed‐hybrid finite element methods, and where an original conforming approximation of H(div;Ω) is used, the latter permits us to obtain an upwind scheme in time. We establish the link between the nonstandard finite difference scheme recently introduced by Mickens and Jordan and the scheme proposed. In this regard, two approaches are considered and in particular we employ a formulation allowing the solution to be marched in time, i.e., one only needs to consider one time increment at a time. Numerical results are presented and compared with the analytical solution illustrating good performance of the present method. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008