谱元法数值模拟约束结构内炸药中应力波的传播

针对高速侵彻类战斗部在侵彻过程中的装药安定性以及在意外事故中的安全性问题,对约束结构内炸药在冲击加载下的应力波传播规律进行了模拟研究。计算了不同侵彻速度下弹体的冲击响应函数,并将具有高精度和低耗散特点的谱元法应用于约束结构内凝聚炸药中的应力波传播模拟;考虑炸药-金属界面的动摩擦特性,计算了冲击加载下由动摩擦引起的装药-壳体界面温升,以及装药内部的塑性功积累。成功地将谱元法应用于凝聚炸药中应力波传播过程的模拟,模拟结果对更准确地评估热点生成机制,以及进行装药安定性分析具有参考意义。     

线性与非线性波的Chebyshev广义有限谱模拟

给出求解二维线性与非线性波的Chebyshev广义有限谱模拟方法.结合时间层次的高精度预报-校正方法，模拟了二维线性浅水驻波和波在浅滩的非线性变形.方法能够准确模拟水波的物理特征. 关键词： Chebyshev广义有限谱 线性波 非线性波     

谱有限元模拟正交各向异性黏弹性材料中导波传播特性

研究了导波在正交各向异性黏弹性复合板中传播的色散特性、波结构及功率流密度。基于二维平面运动方程,采用谱有限元方法得到了导波色散的特征方程。分析了正交各向异性黏弹性板中各向异性和黏性对能量速度和波结构的影响,以及基底对导波功率流密度的影响。数值研究结果表明:导波沿纤维方向传播的能量速度大,材料的黏性对速度影响较小,但会减小波结构的幅度;在高频时,基底的存在使两个基本模态的功率流密度分别集中到波导的上下表面,形成弱色散、高衰减及无色散、零衰减的表面波。数值模拟结果为导波用于复合材料定量无损检测和性能评价提供理论依据。      

对声波和弹性波传播模拟的Hamilton系统方法

建立了离散化网格上的准粒子体系，引入此体系的Hamilton系统描述，用来模拟声波和弹性波的传播.介绍了准粒子间相互作用的九点模型并给出互作用系数.证明了Hamilton系统方法 和声波、弹性波方程的关系，并给出两个方法中所使用物理量的关系.使用辛算法对给定的 介质模型进行数值模拟. 关键词： Hamilton系统方法 九点互作用模型 声波方程 弹性波方程 辛算法     

正交异性钢桥面板声发射波三维谱元法模拟及损伤定位*

针对大跨度桥梁正交异性钢桥面板的疲劳损伤评估与结构健康监测需求,开展基于声发射波场谱元法模拟的大型复杂板类结构损伤定位研究。采用Legendre高阶插值三维时域谱元法模拟声发射波在正交异性钢桥面板中的传播过程,验证了其内部显著的反射、衍射和频散现象,并代替人工预断铅实测试验获得大量声发射数据。然后,利用赤池信息准则判定声发射波到达各传感器的时间,通过高斯过程回归建立到达时差与声发射源位置的关系模型,用于未知损伤的定位监测。数值模型实验结果表明,赤池信息准则和高斯过程回归改进的时差图法在正交异性钢桥面板中的平均定位误差为37.3 mm(25 dB信噪比工况),平板的定位精度高于U肋。谱元法模拟有望代替繁琐的预断铅实测试验,提升声发射时差图系列损伤定位方法的实用性。     

各向异性渗流条件下弹性波的传播特征

研究了弹性波在非均匀裂纹孔隙介质中的传播特性,建立了各向异性喷射流模型.当弹性波通过裂纹孔隙介质时,由于波的扰动及裂纹和孔隙几何结构的不一致,导致在裂纹内部及裂纹与周边孔隙之间同时存在着流体压力梯度.此时的弹性波波动响应中包含着裂纹内连通性特征和背景孔隙渗透率信息.流体的动态流动过程使得介质的等效弹性参数为复数(非完全弹性),并且具有频率依赖性.当弹性波为低频和高频极限时,介质为完全弹性;当处于中间频段时,波有衰减和频率依赖.裂纹孔隙介质的各向异性连通性(渗透率)对应着各向异性特征频率(当渗流长度等于非均匀尺度时的弹性波频率),波的传播受到裂纹内连通性的影响.在一定频段内,随着裂纹厚度的增加,将出现第二峰值,峰值大小同时受到裂纹厚度和半径的影响.     

3维Mortar谱元法模拟Kelvin-Helmhtz不稳定性混合层

采用Mortar谱元法和多处理器并行计算技术模拟了Kelvin-Helmhtz界面不稳定性湍流的混合发展过程,通过对混合层动量厚度、能谱和总动能的计算,评估了Kelvin-Helmhtz混合层的演化机理。计算结果表明：3维Mortar谱元法具有高计算精度和光滑区域的指数收敛特性,可以有效模拟混合层流动的湍流混合和演化,能够捕捉到涡的合并现象和大涡到小涡的级联过程;初期的混合层层流运动发展成具有连续谱结构的湍流运动过程,实现了Kelvin-Helmhtz界面不稳定性混合层流动从2维发展到3维的转捩特征,总湍流统计动能的变化反映了粘性耗散过程的作用。通过对Kelvin-Helmhtz 3维界面不稳定性混合层流动和3维层流向湍流转捩过程的数值模拟,程序的有效性得到了验算,表明谱元法应用于湍流混合模拟是可行的。     

3维Mortar谱元法模拟Kelvin-Helmhtz不稳定性混合层

采用Mortar谱元法和多处理器并行计算技术模拟了Kelvin-Helmhtz界面不稳定性湍流的混合发展过程,通过对混合层动量厚度、能谱和总动能的计算,评估了Kelvin-Helmhtz混合层的演化机理。计算结果表明:3维Mortar谱元法具有高计算精度和光滑区域的指数收敛特性,可以有效模拟混合层流动的湍流混合和演化,能够捕捉到涡的合并现象和大涡到小涡的级联过程;初期的混合层层流运动发展成具有连续谱结构的湍流运动过程,实现了Kelvin-Helmhtz界面不稳定性混合层流动从2维发展到3维的转捩特征,总湍流统计动能的变化反映了粘性耗散过程的作用。通过对Kelvin-Helmhtz 3维界面不稳定性混合层流动和3维层流向湍流转捩过程的数值模拟,程序的有效性得到了验算,表明谱元法应用于湍流混合模拟是可行的。     

井间地震波场数值模拟和弹性波逆时偏移

该文利用时域有限差分法数值模拟了井间地震波场,探讨了井间地震弹性波逆时偏移成像的若干问题.基于多层地层模型,根据数值模拟的人工合成阵列信号,对比了3种不同成像条件下井间地震逆时偏移的结果,并对不同倾角的狭缝模型进行逆时偏移成像.通过对不同成像条件的对比,发现震源归一化成像条件能够对检波器一端的地质结构成像进行增强.由于...     

Some theoretical aspects of elastic wave modeling with a recently developed spectral element method

A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media, based on the Galerkin approach applied to a partition, in small subdomains, of the original physical domain. In this work, some mathematical aspects of the method and the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobatto collocation points are introduced. The related integration formulas are obtained. The standard error estimations and expansion convergence are discussed. An element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence, neither the global matrices nor the effective force vector is assembled. When analytical formulas are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without losing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes this method much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The first part mainly focuses on theoretical studies with a simple numerical result for the Che-byshev spectral element, and the second part, mainly with the Legendre spectral element, will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the detailed modeling example comparisons of the proposed spectral element method with a pseudo-spectral method, which will be seen in another work by Lin, Wang and Zhang.     

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.     

The research of space-time coupled spectral element method for acoustic wave equations

A space-time coupled spectral element method based on Chebyshev polynomials is presented for solving time-dependent wave equations.Acoustic propagation problems in1+1,2+1,3+1 dimensions with the Dirichlet boundary conditions are simulated via space-time coupled spectral element method using quadrilateral,hexahedral and tesseractic elements respectively.Space-time coupled spectral element method can obtain high-order precision over time.With the same total number of nodes,higher numerical precision is obtained if the higher-order Chebyshev polynomials in space directions and lower-order Chebyshev polynomials in time direction are adopted.Numerical illustrations have indicated that the space-time algorithm provides higher precision than the semi-discretization.When space-time coupled spectral element method is used,time subdomain-by-subdomain approach is more economical than time domain approach.     

Galerkin时空耦合谱元法求解声波动方程

提出了时空耦合谱元方法,并将其用于带第一类边界条件的非齐次一维、二维、三维波动方程的求解。分别采用四边形、六面体和超六面体作为计算单元,在每个单元内采用Chebyshev多项式的极值点作为Lagrange插值节点,并且探讨了区域剖分方式对计算精度的影响。时空耦合谱元法能够得到精度很高的数值结果,并且其色散随时间推移是稳定的;当总网格节点数相同时,不同的网格剖分方式所得数值误差不同,当空间方向Chebyshev多项式的阶数较高和时间方向Chebyshev多项式的阶数较低时,得到的数值精度较高;在总节点数相同的情况下,与时间全域方式相比,逐时间子区域方式计算所需要的时间更经济,两种方式可以得到相同的精度。结果表明:时空耦合谱元方法使时空方向精度相匹配,可以提高整体精度;空间方向的Chebyshev多项式对数值精度起主要影响作用;时间子区域方式的采用可以扩大问题的计算区域。      

Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals

A boundary element method (BEM) is presented to compute the transmission spectra of two-dimensional (2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction. The cross sections of the scatterers may be circular or square. For a periodic cell, the boundary integral equations of the matrix and the scatterers are formulated. Substituting the periodic boundary conditions and the interface continuity conditions, a linear equation set is formed, from which the elastic wave transmission can be obtained. From the transmission spectra, the band gaps can be identified, which are compared with the band structures of the corresponding infinite systems. It is shown that generally the transmission spectra completely correspond to the band structures. In addition, the accuracy and the efficiency of the boundary element method are analyzed and discussed.     

A spectral finite element for analysis of wave propagation in uniform composite tubes

A spectral finite element model (SFEM) for analysis of coupled broadband wave propagation in composite tubular structure is presented. Wave motions in terms of three translational and three rotational degrees of freedom at tube cross-section are considered based on first order shear flexible cylindrical bending, torsion and secondary warping. Solutions are obtained in wavenumber space by solving the coupled wave equation in 3-D. An efficient and fully automated computational strategy is developed to obtain the wavenumbers of coupled wave modes, spectral element shape function, strain-displacement matrix and the exact dynamic stiffness matrix. The formulation emphasizes on a compact matrix methodology to handle large-scale computational model of built-up network of such cylindrical waveguides. Thickness and frequency limits for application of the element is discussed. Performance of the element is compared with analytical solution based on membrane shell kinematics. A map of the distribution of vibrational modes in wavelength and time scales is presented. Effect of fiber angle on natural frequencies, phase and group dispersions are also discussed. Numerical simulations show the ease with which dynamic responses can be obtained efficiently. Parametric studies on a clamped-free graphite-epoxy composite tube under short-impulse load are carried out to obtain the effect of various composite configurations and tube geometries on the response.     

Local spectral time-domain method for electromagnetic wave propagation

We explore the feasibility of using a local spectral time-domain (LSTD) method to solve Maxwell's equations that arise in optical and electromagnetic applications. The discrete singular convolution (DSC) algorithm is implemented in the LSTD method for spatial derivatives. Fourier analysis of the dispersive error of the DSC algorithm indicates that its grid density requirement for accurate simulations can be as low as approximately two grid points per wavelength. The analysis is further confirmed by numerical experiments. Our study reveals that the LSTD method has the potential to yield high resolution for solving large-scale electromagnetic problems.     

Multidomain spectral method for the helically reduced wave equation

We consider the 2+1 and 3+1 scalar wave equations reduced via a helical Killing field, respectively referred to as the 2-dimensional and 3-dimensional helically reduced wave equation (HRWE). The HRWE serves as the fundamental model for the mixed-type PDE arising in the periodic standing wave (PSW) approximation to binary inspiral. We present a method for solving the equation based on domain decomposition and spectral approximation. Beyond describing such a numerical method for solving strictly linear HRWE, we also present results for a nonlinear scalar model of binary inspiral. The PSW approximation has already been theoretically and numerically studied in the context of the post-Minkowskian gravitational field, with numerical simulations carried out via the “eigenspectral method.” Despite its name, the eigenspectral technique does feature a finite-difference component, and is lower-order accurate. We intend to apply the numerical method described here to the theoretically well-developed post-Minkowski PSW formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation.