集成单元边界元法及其在主动冷却热防护系统分析中的应用

随着高超声速飞行器的快速发展,飞行器及发动机所面临的热防护压力越来越大. 传统的被动热防护系统已很难满足设计要求,因此主动冷却热防护系统受到了越来越多的关注. 主动冷却热防护系统因为管道密布、结构复杂,传统的分析方法需要花费大量的精力和时间来建模和计算分析. 针对管道阵列排布的主动冷却系统,提出了一种用边界元法求解空间周期性结构的集成单元法,并将其用来分析具有冷却通道的热防护系统的传热与受力变形问题. 此方法求解空间周期性结构问题,仅需要针对一个胞元建立边界元胞元方程,并由其形成由指定胞元数组成的集成单元,然后由集成单元组集成总体系统方程组. 提出的集成单元法既有常规子结构法的消元思想,又有传统有限单元、边界单元易于组集的特征,便于大型空间周期性结构的快速分析. 由于集成单元的系数矩阵只需形成一次,且最终方程只含边界节点未知量,计算效率显著提高. 论文最后用功能梯度平板和主动冷却燃烧室算例验证了本文所述算法的正确性和计算效率.      

用子域边界元法研究各向异性材料中的界面裂纹

用子域边界元法研究各向异性材料中的界面裂纹，在边界元公式中，采用了带特征根的基本解，以增量形式的边界积分方程为基础，通过二次等参元及国分之一面力奇异远离散化处理，可以得到各子域的代数方程组，依据凝集技术，可得到仅含有子域公共边界及裂纹边界未知量的求解方程组，通过迭代法，可以寻求到每种载荷作用下的裂纹所处的真实状态，然后，由文献「２」中的方法求解界面裂纹的应力强度因子。结果表明，子域边界方法是正确的     

基于边界元法的弹性动力问题并行求解

为了扩大结构弹性动力分析的规模和提高分析速度,在微机机群环境下给出了两种基于边界元法的瞬态问题并行求解算法,即并行拉普拉斯变换求解算法和并行时域求解算法.并行拉氏变换法通过拉氏变换隐去时间变量,由各结点机独立求解各自负责的变换边界元问题.并行时域法采用与时间有关的基本解,使得边界元系统矩阵可以实现时间域上的并行形成.系数矩阵采用卷帘存储,以保持负载平衡.通过矩阵向量运算的并行化实现时间步进算法的并行化.理论分析和数值试验结果表明:两种算法都具有较好的并行性能.可以用于大型问题的高效求解.     

大规模边界元模态分析的高效数值方法

随着大规模快速边界元计算技术的发展,在复杂结构的动态设计、振动与噪声分析中愈来愈多地采用边界元法,因此求解大规模边界元特征值问题、进行复杂结构和声场模态分析,成为工程应用中一个十分重要,但却极具挑战性的课题,目前国际上还没有十分有效的数值方法.本文针对边界元法中典型的非线性特征值问题,提出了一种通用、高效的数值解法,称为基于预解矩阵采样的Rayleigh-Ritz投影法,记为RSRR.首先,通过求解一系列频域边界元问题来构造特征向量搜索空间,进而可以采用Rayleigh-Ritz投影,将原问题转化为一个可以采用现有方法求解的小规模缩减特征值问题;其次,为了降低Rayleigh-Ritz投影过程的计算量,基于解析函数的Cauchy积分公式,构造了边界元系数矩阵的插值近似方法,以及缩减特征值问题系数矩阵的快速计算方法,给出了插值项数的估计策略;最后,将RSRR与声学快速边界元法结合,应用于大规模吸声结构的复模态分析.数值算例表明,RSRR方法能够可靠地求出给定频段内的全部特征值和特征向量,具有计算效率高、精度高、通用等优点.     

直接边界元法三维自由面兴波时域模拟

应用直接边界元法在时域中求解稳定航速运动的三维自由面兴波问题.基于格林定理,在所有边界面上划分网格,对边界积分方程进行数值离散,采用线性自由面边界条件,随时间步进更新自由面势.由于物体空间位置移动辐射条件不需要单独表述,迭代过程中自由面计算域保持不变.以割划水面NACA0024为例,计算模拟了自由面兴波稳定波形;提出了求解矩阵方程组奇异性的处理方法和解决割划问题的动网格技术.本文计算结果和有限体积法及有关试验结果对比表明,该方法是可靠的.     

三维边界元法求解浮体水动力系数及与试验结果的比较

简要介绍了三维边界元法求解浮体水动力系数的方法；着重介绍了用三维边界元法求解程序的编制方程，给出了比较具体的程序框图，同时给出了理论计算曲线和试验结果的比较。     

薄板结构的边界元优化设计

完成了一种用边界元法对弹性薄板结构进行优化设计的计算机分析及彩色绘图系统.本文论述了平板弯曲问题的边界元法及其优化设计.系统采用本文作者提出的三方程协调方案,并精确计算分布荷载的域内积分.本文完成了多个平板弯曲问题的边界元分析算例及板结构边界元优化设计的工程算例.结果表明,本系统方法先进、结果精确可靠,具有十分明显的工程实用价值.     

一种改进的边界元法在弹性扭转问题中的应用

本文用一种改进的边界元法分析与计算了椭圆截面等直杆的扭转问题,并与正规的边界元法的解进行比较,其结果完全一致.然而,改进边界元法较正规边界元法需要准备的数据大大减少,计算时间更加缩短.因此,本文方法对求解 Poisson 方程问题是一种经济而行之有效的数值计算方法.     

一种求解瑞利波散射问题的修正边界元方法

边界元法的一大优势是用于求解半空间等无限域问题,然而对于弹性波的传播问题,传统边界元法在采用全平面或全空间格林函数时,在截断边界处仍会产生虚假的反射回波,直接影响到散射场的求解准确性。因此,本文在传统边界元法基础上提出一种修正边界元法,用于计算无限大半平面中的弹性波场问题。该方法以瑞利波形式的远端散射场代替原本因截断而舍去的部分,通过互易定理建立单位瑞利波和全平面格林函数的积分方程,求得修正系数,并代入修正边界元矩阵,计算出瑞利波的散射场。为验证本文所提方法,文中将多个算例的结果与解析解对比,并用该方法计算了不同缺陷的散射场。这些对比结果表明,本文所提修正边界元法可准确求解瑞利波散射场,为基于表面波的缺陷反演问题研究提供了有效的正演途径。     

基于自适应交叉近似边界元法的快速声学灵敏度分析

基于自适应交叉近似边界元法构造一组快速声学灵敏度分析方法,其中,声学灵敏度分析分别采用直接微分法和伴随变量法;而自适应交叉近似算法被用以克服常规边界元法的高计算量和高存储量的固有缺点。自适应交叉近似算法在迭代求解之前对边界元系数矩阵进行压缩存储,可以在降低存储量的同时提高求解效率。在声学灵敏度分析中,通过直接使用求解未知边界状态值时保存的压缩系数矩阵,可以进一步提高求解效率。数值算例验证了所构造的方法的计算精度和求解效率,以及在大规模声场问题的最优化分析中的应用潜力。     

弹性力学的一种边界无单元法

首先对移动最小二乘副近法进行了研究，针对其容易形成病态方程的缺点，提出了以带权的正交函数作为基函数的方法－改进的移动最小二乘副近法，改进的移动最小二乘逼近法比原方法计算量小，精度高，且不会形成病态方程组，然后，将弹性力学的边界积分方程方法与改进的移动最小二乘逼近法结合，提出了弹性力学的一种边界无单元法，这种边界无单元法法是边界积分方程的无网格方法，与原有的边界积分方程的无网格方法相比，该方法直接采用节点变量的真实解为基本未知量，是边界积分方程无网格方法的直接解法，更容易引入界条件，且具有更高的精度，最后给出了弹性力学的边界无单元法的数值算例，并与原有的边界积分方程的无网格方法进行了较为详细的比较和讨论。     

非均质问题中的无网格边界单元法

介绍了一种不需要内部网格计算非均匀介质问题的边界元算法.该算法是建立在一种能将任何区域积分转换成边界积分的径向积分转换法基础上,首先用对应各向同性问题的基本解来建立以正规化位移表示的非均质问题的积分方程,然后用径向积分转换法将出现在积分方程中的区域积分转换成边界积分,从而形成不需要使用内部网格来计算区域积分的纯边界元算法.与其它无网格法相比,此方法需要很少的内部点,有些问题甚至不需要内部点都能得到满意的结果,因此,可以计算大型的三维非均匀介质工程问题.由于此方法继承了边界元和无网格算法的优点,因而具有广阔的发展前景.     

势问题的重构核粒子边界无单元法

将重构核粒子法和势问题的边界积分方程方法结合,提出了势问题的重构核粒子边界无单元法. 推导了势问题的重构核粒子边界无单元法的公式,研究其数值积分方案,建立了重构核粒子边界无单元法的离散化边界积分方程,并推导了重构核粒子边界无单元法的内点位势的积分公式. 重构核粒子法形成的形函数具有重构核函数的光滑性,且能再现多项式在插值点的精确值,所以该方法具有更高的精度. 最后给出了数值算例,验证了所提方法的有效性和正确性. }      

Computation of unsteady viscous incompressible flows in generalized non‐inertial co‐ordinate system using Godunov‐projection method and overlapping meshes

Time‐dependent incompressible Navier–Stokes equations are formulated in generalized non‐inertial co‐ordinate system and numerically solved by using a modified second‐order Godunov‐projection method on a system of overlapped body‐fitted structured grids. The projection method uses a second‐order fractional step scheme in which the momentum equation is solved to obtain the intermediate velocity field which is then projected on to the space of divergence‐free vector fields. The second‐order Godunov method is applied for numerically approximating the non‐linear convection terms in order to provide a robust discretization for simulating flows at high Reynolds number. In order to obtain the pressure field, the pressure Poisson equation is solved. Overlapping grids are used to discretize the flow domain so that the moving‐boundary problem can be solved economically. Numerical results are then presented to demonstrate the performance of this projection method for a variety of unsteady two‐ and three‐dimensional flow problems formulated in the non‐inertial co‐ordinate systems. Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical method for unsteady compressible boundary layers driven by compression or expansion wave

A numerical analysis is presented for the unsteady compressible laminar boundary layer driven by a compression or expansion wave. Approximate or series expansion methods have been used for the problems because of the characteristics of the governing equations, such as non-linearity, coupling with the thermal boundary layer equation and initial conditions. Here a transformation of the governing equations and the numerical linearization technique are introduced to deal with the difficulties. First, the governing equations are transformed for the initial conditions by Howarth and semisimilarity variables. These transformations reduce the number of independent variables from three to two and the governing equations from partial to ordinary differential equations at the initial point. Next, the numerical linearization technique is introduced for the non-linearity and the coupling with the thermal boundary layer equation. Because the non-linear terms are linearized without sacrifice of numerical accuracy, the solutions can be obtained without numerical iterations. Therefore the exact numerical solution, not approximate or series expansion, can be obtained. Compared with the approximate or series expansion method, this method is much improved. Results are compared with the series expansion solutions.     

Preconditioned Iterative Methods for Linear Equations Arising from the Boundary Element Method

A precondition for the Gauss–Seidel iterative method to solve a linear system of equations arising from the boundary element method for the Laplace and convective diffusion with first-order reaction problems is presented in this paper. The present precondition is based on the elementary matrix operation. We discuss the effect of the precondition in comparison with the Gauss elimination (GE) method in some numerical experiments.     

Godunov–mixed methods for immiscible displacement

The immiscible displacement problem in reservoir engineering can be formulated as a system of partial differential equations which includes an elliptic pressure–velocity equation and a degenerate parabolic saturation equation. We apply a sequential numerical scheme to this problem where time splitting is used to solve the saturation equation. In this procedure one approximates advection by a higher-order Godunov method and diffusion by a mixed finite element method. Numerical results for this scheme applied to gas–oil centrifuge experiments are given.     

Simulation of liquid sloshing in curved‐wall containers with arbitrary Lagrangian–Eulerian method

There are many challenges in the numerical simulation of liquid sloshing in horizontal cylinders and spherical containers using the finite element method of arbitrary Lagrangian–Eulerian (ALE) formulation: tracking the motion of the free surface with the contact points, defining the mesh velocity on the curved wall boundary and updating the computational mesh. In order to keep the contact points slipping along the curved side wall, the shape vector in each time advancement is defined to modify the kinematical boundary conditions on the free surface. A special function is introduced to automatically smooth the nodal velocities on the curved wall boundary based on the liquid nodal velocities. The elliptic partial differential equation with Dirichlet boundary conditions can directly rezone the inner nodal velocities in more than a single freedom. The incremental fractional step method is introduced to solve the finite element liquid equations. The numerical results that stemmed from the algorithm show good agreement with experimental phenomena, which demonstrates that the ALE method provides an efficient computing scheme in moving curved wall boundaries. This method can be extended to 3D cases by improving the technique to compute the shape vector. Copyright © 2007 John Wiley & Sons, Ltd.     

A boundary element formulation for natural convection problems

This paper presents a boundary element formulation employing a penalty function technique for two-dimensional steady thermal convection problems. By regarding the convective and buoyancy force terms in Navier-Stokes equations as body forces, the standard elastostatics analysis can be extended to solve the Navier-Stokes equations. In a similar manner, the standard potential analysis is extended to solve the energy transport equation. Finally, some numerical results are included, for typical natural convection problems, in order to demonstrate the efficiency of the present method.