求解流固耦合问题的一种四步分裂有限元算法

基于arbitrary Lagrangian Eulerian (ALE) 有限元方法,发展了一种求解流固耦合问题的弱耦合算法．将半隐式四步分裂有限元格式推广至求解ALE描述下的Navier-Stokes（N-S）方程,并在动量方程中引入迎风流线（streamline upwind/Petrov-Galerkin, SUPG）稳定项以消除对流引发的速度场数值振荡;采用Newmark-β法对结构方程进行时间离散;运用经典的Galerkin有限元法求解修正的Laplace方程以实现网格更新,每个计算步施加网格总变形量防止结构长时间、大位移运动时的网格质量恶化．运用上述算法对弹性支撑刚性圆柱体的流致振动问题进行了数值模拟,计算结果与已有结果相吻合,初步验证了该算法的正确性和有效性．     

直管束流固耦合振动的数值模拟

为了研究反应堆结构中的诸如燃料棒、蒸汽发生器和其它换热器传热管束等的流体-结构交互作用问题,利用有限体积法离散大涡模拟(large eddy simulation, LES)的流体控制方程,用有限元方法求解结构动力学方程,并结合动网格技术,建立三维流体诱发振动的数值模型,模拟直管束中流体的流动及结构振动,实现计算结构动力学(computational structure dynamics, CSD)与计算流体力学(computational fluid dynamics, CFD)之间的联合仿真．首先,基于流固耦合方法对单管的流致振动特性进行了详细分析,得到了其动力学响应与流场特性;其次基于建立的传热管束流致振动计算模型,研究了两并列管、两串列管以及3×3正方形排列管束的流致振动行为．     

微曲输流管道振动固有频率分析与仿真北大核心CSCD

首次建立了基于Timoshenko梁理论的微曲输流管道横向振动的动力学模型,并分析了流体流动影响下微曲管道横向自由振动的固有特征.采用广义Hamilton原理,导出了考虑流体影响的微曲管道横向振动的控制方程,通过Galerkin截断对控制方程离散化,再由广义本征值问题得到管道横向振动的固有频率,并研究了液体流速和弯曲幅度对管道横向固有振动特征的影响.发展了基于等效刚度和等效阻尼方法的考虑流体影响的微曲管道振动分析的有限元仿真计算方法,并通过有限元软件实现数值仿真,验证了Galerkin截断的分析结果以及所建立的Timoshenko微曲管道动力学模型的有效性.研究表明,流体的流速以及管道的弯曲幅度对管道横向振动固有频率均有显著影响.     

一类非线性传输问题的区域分解方法（英文）

针对一类非线性传输问题提出了有限元与边界元的耦合方法并设计了基于耦合法的区域分解算法.该算法避免了求解边界积分方程,从而计算量大大减少.算法的收敛性分析和数值算例验证了该算法的合理和有效性.     

饱和多孔弹性杆流固耦合动力响应的保结构算法

研究了不可压饱和多孔弹性杆的流固耦合动力响应问题.基于多孔介质理论,根据多孔介质流固混合物动量方程、孔隙流体动量方程及体积分数方程,建立流固耦合不可压饱和多孔弹性杆的轴向振动方程;引入正则变量,构造饱和多孔弹性杆轴向振动方程的广义多辛保结构形式、广义多辛守恒律及广义多辛局部动量误差;采用中点Box离散方法得到轴向振动方程的广义多辛离散格式、广义多辛守恒律数值误差及局部动量数值误差;数值模拟不可压饱和多孔弹性杆的轴向振动过程及流相渗流速度分布,考察了流固两相耦合系数对轴向振动过程及广义多辛守恒律误差和局部动量误差的影响.结果表明,已构造的广义多辛保结构算法具有很高的精确性和长时间的数值稳定性.     

广义神经传播方程的A.D.I.有限元分析

广义神经传播方程是神经传播方程的更一般形式，是一类非常重要的非线性发展方程，在生物、力学诸领域有实际背景．有关其解的性质，已有许多讨论I‘－‘］，但数值计算和数值分析方面，还没有研究．而实际当中，研究模型的数值方法和定量计算，往往是非常重要的．本文着重讨论一类具有非线性边值条件的广义神经传播方程的交替方向有限元方法及其数值分析．算法上，采用交替方向有限元，化高维问题为低维问题，在缩减计算量的同时，保持高精确度．分析上，采用Sobolev投影，简化论证，得到理想的稳定性和收敛性结果．1方程模型及有限元数值…     

论理想流体与线弹性结构的耦联振动

本文对理想流体与线弹性结构的耦联振动问题作理论分析和数值分析.文中证明了耦联振动的固有频率存在并且均为正实数.将流-固耦合系统分析转化为单一结构物在真空中的自由振动分析后,频率方程中不再含有流体变元.使问题得以大大简化.给出了数值解的收敛性证明,以保证解的可靠性.文中还综合里兹法、边界元和有限元方法,提出一种分析转化后结构的混合算法.利用该算法,只需对现有结构分析程序稍作改进,就可分析那些理想流场与结构的耦合问题.一些数例说明了算法的有效性.     

一种有限元-边界元耦合分域算法

提出了一种有限元-边界元耦合分域算法．该算法将所分析问题的区域分解成有限元和边界元子域,在满足两子域界面上位移和面力协调连续的条件下,通过迭代求解得到问题的解．在迭代求解过程中,引入动态松弛系数,使收敛得以加速．该方法在两子域界面上有限单元结点和边界单元结点的位置相互独立,无需协调一致,对诸如裂纹扩展过程的模拟具有独特的优势．用所提出的耦合算法分析算例,得到的结果与有限元法、边界元法和另一种耦合算法的数值计算结果一致,验证了这种算法的正确性和可行性．     

扁球壳和扁锥壳的轴对称非线性热弹耦合振动

假设温度场与应变场相互耦合,研究了旋转扁薄球壳和锥壳的轴对称非线性热弹振动问题．基于von Krmn理论和热弹性理论,导出了本问题的全部控制方程及其简化形式．应用Galerkin技术进行时空变量分离后,得到了一个关于时间的非线性常微分方程组．根据方程的特点,分别用多尺度法和正则摄动法求得了壳体振动的频率与振幅间特征关系和振幅衰减规律的一次近似解析解,并讨论了壳体几何参数、热弹耦合参数以及边界条件等因素对其非线性热弹耦合振动特性的影响．     

基于改进位移模式的二维有限元线法超收敛算法

提出了基于改进位移模式的二维有限元线法超收敛算法．利用单元内部需满足平衡方程的条件,推导了超收敛计算的解析公式的显式,即将高阶有限元线法解的位移模式用常规有限元线法解的位移模式表示．用常规有限元线法解的位移模式与高阶有限元线法解的位移模式之和构造新的位移模式,基于线性形函数,采用变分形式推导了有限元线法求解的修正的常微分方程组．该算法在前和后处理同时使用超收敛计算公式,在原有试函数的基础上,增加了高阶试函数．使得单元内平衡方程的残差减少,从而达到提高精度的目标．对于二维Poisson方程问题,给出了有代表性的算例,结点和单元内的位移、导数的收敛精度得到了极大的提高．     

Dynamic responses of shear flows over a deformable porous surface layer in a cylindrical tube

This paper investigates dynamic responses of a viscous fluid flow introduced under a time dependent pressure gradient in a rigid cylindrical tube that is lined with a deformable porous surface layer. With the Darcy’s law and a linear elasticity assumption, we have solved the coupling effect of the fluid movement and the deformation of the porous medium in the Laplace transform space. Governing equations are deduced for the solid displacement and the fluid velocity in the porous layer. Analytical solutions in the transformed domain are derived and the time dependent variables are inverted numerically using Durbin’s algorithm. Interaction between the solid and the fluid phases in the porous layer and its effects on fluid flow in tube are investigated under steady and unsteady flow conditions when the solid phase is either rigid or deformable. Examples are presented for flows driven by a Heaviside or a sinusoid pressure gradient. Significant effects of the porous surface layer on the flow in the tube are observed. The analytical solutions can be used to test more complicated numerical schemes.     

On the convergence behavior of the restarted GMRES algorithm for solving nonsymmetric linear systems

The solution of nonsymmetric systems of linear equations continues to be a difficult problem. A main algorithm for solving nonsymmetric problems is restarted GMRES. The algorithm is based on restarting full GMRES every s iterations, for some integer s>0. This paper considers the impact of the restart frequency s on the convergence and work requirements of the method. It is shown that a good choice of this parameter can lead to reduced solution time, while an improper choice may hinder or preclude convergence. An adaptive procedure is also presented for determining automatically when to restart. The results of numerical experiments are presented.     

基于GMRES的多项式预处理广义极小残差法

求解大型稀疏线性方程组一般采用迭代法,其中GMRES(m)算法是一种非常有效的算法,然而该算法在解方程组时,可能发生停滞．为了克服算法GMRES(m)解线性系统Ax=b过程中可能出现的收敛缓慢或不收敛,本文利用GMRES本身构造出一种有效的多项式预处理因子pk(z),该多项式预处理因子非常简单且易于实现．数值试验表明,新算法POLYGMRES(m)较好地克服了GMRES(m)的缺陷．     

A simpler GMRES

The generalized minimal residual (GMRES) method is widely used for solving very large, nonsymmetric linear systems, particularly those that arise through discretization of continuous mathematical models in science and engineering. By shifting the Arnoldi process to begin with Ar₀ instead of r₀, we obtain simpler Gram–Schmidt and Householder implementations of the GMRES method that do not require upper Hessenberg factorization. The Gram–Schmidt implementation also maintains the residual vector at each iteration, which allows cheaper restarts of GMRES(m) and may otherwise be useful.     

Stability and free vibration analyses of double-bonded micro composite sandwich cylindrical shells conveying fluid flow

In this study, based on Reddy cylindrical double-shell theory, the free vibration and stability analyses of double-bonded micro composite sandwich cylindrical shells reinforced by carbon nanotubes conveying fluid flow under magneto-thermo-mechanical loadings using modified couple stress theory are investigated. It is assumed that the cylindrical shells with foam core rested in an orthotropic elastic medium and the face sheets are made of composites with temperature-dependent material properties. Also, the Lorentz functions are applied to simulation of magnetic field in the thickness direction of each face sheets. Then, the governing equations of motions are obtained using Hamilton's principle. Moreover, the generalized differential quadrature method is used to discretize the equations of motions and solve them. There are a good agreement between the obtained results from this method and the previous studies. Numerical results are presented to predict the effects of size-dependent length scale parameter, third order shear deformation theory, magnetic intensity, length-to-radius and thickness ratios, Knudsen number, orthotropic foundation, temperature changes and carbon nanotubes volume fraction on the natural frequencies and critical flow velocity of cylindrical shells. Also, it is demonstrated that the magnetic intensity, temperature changes and carbon nanotubes volume fraction have important effects on the behavior of micro composite sandwich cylindrical shells. So that, increasing the magnetic intensity, volume fraction and Winkler spring constant lead to increase the dimensionless natural frequency and stability of micro shells, while this parameter reduce by increasing the temperature changes. It is noted that sandwich structures conveying fluid flow are used as sensors and actuators in smart devices and aerospace industries. Moreover, carotid arteries play an important role to high blood rate control that they have a similar structure with flow conveying cylindrical shells. In fact, the present study can be provided a valuable background for more research and further experimental investigation.     

一种新型压缩预处理CGS算法

CGS算法是求解大型非对称线性方程组的常用算法，然而该算法无极小残差性质，因此它常因出现较大的中间剩余向量而出现典型的不规则收敛行为．本根据IRA方法提出了一种压缩预处理CGS方法，数值实验表明这种算法在一定程度上减小了迭代算法在收敛过程中的剩余问题，从而使得算法具有更好的稳定性，该法构造简单，减少了收敛次数，加快了收敛速度．     

A higher-order Godunov method for modeling finite deformation in elastic-plastic solids

In this paper we develop a first-order system of conservation laws for finite deformation in solids, describe its characteristic structure, and use this analysis to develop a second-order numerical method for problems involving finite deformation and plasticity. The equations of mass, momentum, and energy conservation in Lagrangian and Eulerian frames of reference are combined with kinetic equations of state for the stress and with caloric equations of state for the internal energy, as well as with auxiliary equations representing equality of mixed partial derivatives of the deformation gradient. Particular attention is paid to the influence of a curl constraint on the deformation gradient, so that the characteristic speeds transform properly between the two frames of reference. Next, we consider models in rate-form for isotropic elastic-plastic materials with work-hardening, and examine the circumstances under which these models lead to hyperbolic systems for the equations of motion. In spite of the fact that these models violate thermodynamic principles in such a way that the acoustic tensor becomes nonsymmetric, we still find that the characteristic speeds are always real for elastic behavior, and essentially always real for plastic response. These results allow us to construct a second-order Godunov method for the computation of three-dimensional displacement in a one-dimensional material viewed in the Lagrangian frame of reference. We also describe a technique for the approximate solution of Riemann problems in order to determine numerical fluxes in this algorithm. Finally, we present numerical examples of the results of the algorithm.     

An analysis of the finite element method for natural convection problems

We derive stability properties and error estimates for the finite element method when used to approximate heat flow in a fluid enclosed by a solid medium. The coupled Navier Stokes system involves the Boussinesq equations in the fluid-filled cavity linked through an interface with heat conduction in the solid enclosing the fluid. As we assume no extra regularity then can be shown to hold under mild restriction on the data (at least over a small time interval in R ³), we focus primarily on low order finite element spaces.     

A coupled NMM-SPH method for fluid-structure interaction problems

The main challenges in the numerical simulation of fluid–structure interaction (FSI) problems include the solid fracture, the free surface fluid flow, and the interactions between the solid and the fluid. Aiming to improve the treatment of these issues, a new coupled scheme is developed in this paper. For the solid structure, the Numerical Manifold Method (NMM) is adopted, in which the solid is allowed to change from continuum to discontinuum. The Smoothed Particle Hydrodynamics (SPH) method, which is suitable for free interface flow problem, is used to model the motion of fluids. A contact algorithm is then developed to handle the interaction between NMM elements and SPH particles. Three numerical examples are tested to validate the coupled NMM-SPH method, including the hydrostatic pressure test, dam-break simulation and crack propagation of a gravity dam under hydraulic pressure. Numerical modeling results indicate that the coupled NMM-SPH method can not only simulate the interaction of the solid structure and the fluid as in conventional methods, but also can predict the failure of the solid structure.     

Simulation of a membrane flow interaction by an iteration based on a panel method

A flow structure interaction of a membrane and a fluid is investigated. A conventional segregated numerical algorithm, where the membrane deformation and the flow dynamics are calculated alternately has to fail due to the artificial added mass instability. Thus, a new iteration scheme is proposed. In order to get a good prediction for the deformation of the membrane, the equations describing the membrane are coupled to a potential flow solver (panel method). Then a CFD solver can be used to determine the corrections of the flow field due viscosity and turbulence. An example is presented that this procedure seems to be numerically stable. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)