基于3D连续壳理论和无网格法的任意壳受迫振动分析

板壳结构是航空航天和建筑水利等工程领域中最常见的基本构件,研究板壳受迫振动问题对工程应用具有重要意义.本文基于3D连续壳理论和移动最小二乘近似建立了任意壳的无网格模型,其中移动最小二乘近似不仅用于几何曲面插值,还用于位移场近似.利用Hamilton原理导出描述任意壳受迫振动的无网格控制方程,并采用时域隐式Newmark方法求解该方程,采用完全转换法来施加本质边界条件.最后,通过MATLAB编制无网格程序计算了几个具有代表性的壳体算例,并将计算结果和ABAQUS有限元解进行比对,验证了本文方法求解任意壳受迫振动的有效性及准确性.结果表明,无网格法不依赖网格划分,适应性较强,所提方法可以有效地求解各种不同形状的板壳结构受迫振动问题,具有广阔的应用前景.     

不可压缩流动的移动粒子半隐式法数值模拟

介绍了一种新的移动粒子半隐式方法。该方法采用Lagrange描述,用一系列离散粒子代替流体,通过半隐式求解和时间推进法来进行计算,弥补了传统网格法对复杂形状、大变形、高速撞击等情况下网格划分和重构过于繁琐的缺点,在模拟不可压缩流动问题中得到了较好的效果。     

高雷诺数下求解NS方程的无网格算法

提出了一种适合高雷诺数NS方程求解的隐式无网格算法。针对高雷诺数粘性流动的特点,在附面层内的粘性影响区域采用法向层次推进布点的方法形成离散点云,在附面层外的计算区域内实行填充式布点的方法形成离散点云。根据附面层内外点云的不同构造特点,推导出运用格林公式和最小二乘曲面拟合方法求取空间导数的统一形式,在此基础上运用AUSM _up格式求得数值通量,并引入BL湍流模型对雷诺平均NS方程的湍流应力项进行封闭。时间推进格式方面,采用了计算效率较高的隐式高斯-赛德尔迭代算法。为了验证本文方法的计算精度和鲁棒性,对NACA0012翼型低速流动、RAE2822翼型跨音速绕流和二维圆柱的分离流动进行了数值模拟。     

一种基于块雅可比迭代的高阶FR格式隐式方法

最近, 基于非结构网格的高阶通量重构格式(flux reconstruction, FR)因其构造简单且通用性强而受到越来越多人的关注. 但将FR格式应用于大规模复杂流动的模拟时仍面临计算开销大、求解时间长等问题. 因此, 亟需发展与之相适应的高效隐式求解方法和并行计算技术. 本文提出了一种基于块Jacobi迭代的高阶FR格式求解定常二维欧拉方程的单GPU隐式时间推进方法. 由于直接求解FR格式空间和隐式时间离散后的全局线性方程组效率低下并且内存占用很大. 而通过块雅可比迭代的方式, 能够改变全局线性方程组左端矩阵的特征, 克服影响求解并行性的相邻单元依赖问题, 使得只需要存储和计算对角块矩阵. 最终将求解全局线性方程组转化为求解一系列局部单元线性方程组, 进而又可利用LU分解法在GPU上并行求解这些小型局部线性方程组. 通过二维无黏Bump流动和NACA0012无黏绕流两个数值实验表明, 该隐式方法计算收敛所用的迭代步数和计算时间均远小于使用多重网格加速的显式Runge-Kutta格式, 且在计算效率方面至少有一个量级的提升.      

RTM充模过程数值模拟的隐式有限元算法

建立了基于欧拉方法描述树脂传递模塑(RTM)工艺充模过程的基本数学方程,并采用有限元隐式时间积分方法对基本方程进行了数值求解．编制了基于隐式有限元算法及传统有限元控制体算法的程序,通过具体算例比较了这两种算法的优缺点．与传统的有限元控制体法相比,该文提出的隐式有限元算法能节省计算时间,特别适合于单元、节点数目多的情况．隐式有限元算法是一种纯有限元方法,不需要使用控制体积技术,采用该算法计算出的流动前沿与时间步长无关。     

高阶紧致格式求解二维粘性不可压缩复杂流场

提出了一种求解二维不可压缩复杂流场的高精度算法．控制方程为原始变量、压力Ｐｏｉｓｓｏｎ方程提法．在任意曲线坐标下，采用四阶紧致格式求解Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组，时间推进采用交替方向隐式（ＡＤＩ）格式，在非交错网格上用松弛法求解压力Ｐｏｉｓｓｏｎ方程．对于复杂的流场，采用了区域分解方法，并在每一时间步对各子域实施松弛迭代使之能精确地反映非定常流场．利用该算法计算了二维受驱空腔流动，弯管流动和垂直平板的突然起动问题．计算结果与实验结果和其他研究者的计算结果相比较吻合良好．对于平板起动流动，成功地模拟了流场中旋涡的生成以及Ｋａｒｍａｎ涡街的形成     

三维弹性动力学的改进的无单元Galerkin方法

基于改进的移动最小二乘法建立三维弹性动力学问题的形函数,结合三维弹性动力学的Galerkin积分弱形式,采用罚函数法施加位移边界条件,并引入隐式时间积分,建立了三维弹性动力学的改进的无单元Galerkin方法。该方法由于引入了改进的移动最小二乘法,避免了病态或奇异方程,在保证计算精度的同时提高了传统的无单元Galerkin方法的计算效率。最后通过数值算例对收敛性进行了分析,并证明了该方法比传统的无单元Galerkin方法计算效率提高了15%。     

正交各向异性稳态热传导问题的ICVEFG方法

本文将改进的复变量无单元Galerkin方法（Improved Complex Variable Element-free Galerkin method,ICVEFG）应用于求解正交各向异性介质中的稳态热传导问题,提出了正交各向异性稳态热传导问题的ICVEFG方法。采用罚函数法引入本质边界条件,推导了正交各向异性介质中的稳态热传导问题的Galerkin积分弱形式。采用改进的复变量移动最小二乘近似（Improved Complex Variable Moving least-squares approximation,ICVMLS）建立二维温度场问题的逼近函数,推导了相应的计算公式。编制了计算程序,对三个正交各向异性介质中的热传导问题进行了分析,说明了本文方法的有效性。     

配置点谱方法-人工压缩法(SCM-ACM)求解同心圆筒内流体流动

发展了配置点谱方法SCM(Spectral collocation method)和人工压缩法ACM(Artificial compressibility method)相结合的SCM-ACM数值方法,计算了柱坐标系下稳态不可压缩流动N-S方程组。选取典型的同心圆筒间旋转流动Taylor-Couette流作为测试对象,首先,采用人工压缩法获得人工压缩格式的非稳态可压缩流动控制方程;再将控制方程中的空间偏微分项用配置点谱方法进行离散,得到矩阵形式的代数方程;编写了SCM-ACM求解不可压缩流动问题的程序;最后,通过与公开发表的Taylor-Couette流的计算结果对比,验证了求解程序的有效性。结果证明,本文发展的SCM-ACM数值方法能够用于求解圆筒内不可压缩流体流动问题,该方法既保留了谱方法指数收敛的特性,也具有ACM形式简单和易于实施的特点。本文发展的SCM-ACM数值方法为求解柱坐标下不可压缩流体流动问题提供了一种新的选择。     

求解定常势流正命题的全时-空变分有限元法

非定常流动变分原理的建立使得用有限元法来求解多工况点的设计问题成为可能。本文在刘高联的非定常变分理论的基础上，对定常变分问题进行时间相关有限元求解。但由于可压缩非定常位势流动的控制方程是双曲型的，简单地把时间当作同空间一样的物理维来求解是不可行的。而现有的时-空有限元法极其复杂，增加了计算复杂度，使其很难用于工程设计中。为此，文[2、3]提出了求解一维非定常问题的新型时-空有限元法。本文把该方法推广到二维流动，用它求解二维弯管内的流动和翼型绕流问题。计算结果与用定常方法求得的结果几乎重合，说明该方法可以用于多维时间相关求解。     

Time marching integral equation method for unsteady transonic flows

In this paper, we have proposed a time marching intregral equation method which does not have the limitation of the time linearized integral equation method in that the latter method can not satisfactorily simulate the shock-wave motions. Firstly, a model problem—one dimensional initial and boundary value wave problem is treated to clarify the basic idea of the new method. Then the method is implemented for 2-D and 3-D unsteady transonic flow problems. The introduction of the concept of a quasi-velocity-potential simplifies the time marching integral equations and the treatment of trailing vortex sheet condition. The numerical calculations show that the method is reasonable and reliable.     

A momentum coupling method for the unsteady incompressible Navier–Stokes equations on the staggered grid

A new numerical method is developed to efficiently solve the unsteady incompressible Navier–Stokes equations with second-order accuracy in time and space. In contrast to the SIMPLE algorithms, the present formulation directly solves the discrete x- and y-momentum equations in a coupled form. It is found that the present implicit formulation retrieves some cross convection terms overlooked by the conventional iterative methods, which contribute to accuracy and fast convergence. The finite volume method is applied on the fully staggered grid to solve the vector-form momentum equations. The preconditioned conjugate gradient squared method (PCGS) has proved very efficient in solving the associate linearized large, sparse block-matrix system. Comparison with the SIMPLE algorithm has indicated that the present momentum coupling method is fast and robust in solving unsteady as well as steady viscous flow problems. © 1998 John Wiley & Sons, Ltd.     

Linearized and non‐linear acoustic/viscous splitting techniques for low Mach number flows

Computation of the acoustic disturbances generated by unsteady low‐speed flow fields including vortices and shear layers is considered. The equations governing the generation and propagation of acoustic fluctuations are derived from a two‐step acoustic/viscous splitting technique. An optimized high order dispersion–relation–preserving scheme is used for the solution of the acoustic field. The acoustic field generated by a corotating vortex pair is obtained using the above technique. The computed sound field is compared with the existing analytic solution. Results are in good agreement with the analytic solution except near the centre of the vortices where the acoustic pressure becomes singular. The governing equations for acoustic fluctuations are then linearized and solved for the same model problem. The difference between non‐linear and linearized solutions falls below the numerical error of the simulation. However, a considerable saving in CPU time usage is achieved in solving the linearized equations. The results indicate that the linearized acoustic/viscous splitting technique for the simulation of acoustic fluctuations generation and propagation by low Mach number flow fields seems to be very promising for three‐dimensional problems involving complex geometries. Copyright © 2003 John Wiley & Sons, Ltd.     

基于气动力降阶模型的跨音速气动弹性稳定性分析

基于离散型输入输出差分模型,运用非定常CFD方法训练信号,然后运用最小二乘方法进行参数辨识,得到降阶的非定常气动力模型,再将该离散差分模型转换为连续时间域内的状态方程。耦合气动状态方程和结构状态方程,得到耦合系统的气动弹性状态方程。求解不同动压下状态矩阵的特征值,根据根轨迹图分析系统的稳定性特性。分析结果与直接耦合CFD/CSD方法结果相吻合,可以计算跨音速非线性气动弹性问题。其计算效率比直接耦合CFD/CSD方法提高1~2个数量级。针对Isogai wing在跨音速出现的S型颤振边界进行了较为细致的分析,阐述了该现象是由于系统诱发颤振的分支随着速度(来流动压)的提高而发生转移所导致的。     

A Helmholtz pressure equation method for the calculation of unsteady incompressibl eviscous flows

A time-implicit numerical method for solving unsteady incompressible viscous flow problems is introduced. The method is based on introducing intermediate compressibility into a projection scheme to obtain a Helmholtz equation for a pressure-type variable. The intermediate compressibility increases the diagonal dominance of the discretized pressure equation so that the Helmholtz pressure equation is relatively easy to solve numerically. The Helmholtz pressure equation provides an iterative method for satisfying the continuity equation for time-implicit Navier–Stokes algorithms. An iterative scheme is used to simultaneously satisfy, within a given tolerance, the velocity divergence-free condition and momentum equations at each time step. Collocated primitive variables on a non-staggered finite difference mesh are used. The method is applied to an unsteady Taylor problem and unsteady laminar flow past a circular cylinder.     

On the incremental singular value decomposition method to support unsteady adjoint-based optimization

This paper proposes and evaluates an approximation model based on an incremental Singular Value Decomposition (iSVD) algorithm, for unsteady flow field reconstructions, needed for integrating the unsteady adjoint equations backward in time, within a gradient-based optimization loop. Due to the iSVD algorithm, the computational cost of solving the unsteady adjoint equations is reduced considerably, without practically affecting the accuracy of the computed gradient. Approximations to the unsteady flow fields are constructed while solving the time-varying flow equations (moving forward in time) and used to reconstruct these fields during the backward-in-time integration of the continuous adjoint equations. Optimization results obtained using the proposed method are compared to those computed using the binomial checkpointing technique, which acts as the reference method. Test cases for both flow control and shape optimization problems are presented.     

A study of gridless method with dynamic clouds of points for solving unsteady CFD problems in aerodynamics

When solving unsteady computational fluid dynamics problems in aerodynamics with a gridless method, a cloud of points is usually required to be regenerated due to its accommodation to moving boundaries. In order to handle this problem conveniently, a fast dynamic cloud method based on Delaunay graph mapping strategy is proposed in this paper. A dynamic cloud method makes use of algebraic mapping principles and therefore points can be accurately redistributed in the flow field without any iteration. In this way, the structure of the gridless clouds is not necessarily changed so that the clouds regeneration can be avoided successfully. The spatial derivatives of the mathematical modeling of the flow are directly determined by using weighted least‐squares method in each cloud of points, and then numerical fluxes can be obtained. A dual time‐stepping method is further implemented to advance the two‐dimensional Euler equations in arbitrary Lagarangian–Eulerian formulation in time. Finally, unsteady transonic flows over two different oscillating airfoils are simulated with the above method and results obtained are in good agreement with the experimental data. Copyright © 2009 John Wiley & Sons, Ltd.     

裂隙岩体非稳态渗流数值模型及其应用

为解决裂隙岩体非稳态渗流问题, 发展了一种新的数值模型. 对于单裂隙渗 流求解, 其控制方程是基于一定假设的简化Navier-Stokes方程, 数值方法采用有限差分法 和流体体积法. 在裂隙网络中, 交界处渗流可以由专门的控制方程求解. 计算结果表明, 该 数值模型既可以大幅提高非稳态渗流的计算效率, 还可以避免孤立裂隙所带来的影响. 最后, 通过两个工程算例验证该数值模型的适用性.     

Least‐squares meshfree method for incompressible Navier–Stokes problems

A least‐squares meshfree method based on the first‐order velocity–pressure–vorticity formulation for two‐dimensional incompressible Navier–Stokes problem is presented. The convective term is linearized by successive substitution or Newton's method. The discretization of all governing equations is implemented by the least‐squares method. Equal‐order moving least‐squares approximation is employed with Gauss quadrature in the background cells. The boundary conditions are enforced by the penalty method. The matrix‐free element‐by‐element Jacobi preconditioned conjugate method is applied to solve the discretized linear systems. Cavity flow for steady Navier–Stokes problem and the flow over a square obstacle for time‐dependent Navier–Stokes problem are investigated for the presented least‐squares meshfree method. The effects of inaccurate integration on the accuracy of the solution are investigated. Copyright © 2004 John Wiley & Sons, Ltd.