用对角质量矩阵时有限单元特征值问题的准确度

本文讨论的对角化质量矩阵是在动能积分的公式中将积分点取在有限单元的结点上而得到的,本文给出了用这种矩阵时,固有频率、固有振型和对应的应力的对角化误差与动能积分的代数精确度、插值位移场的多项式的阶次、应变能中导数的最高阶数的关系,利用这些关系和多个算例讨论了对角化质量矩阵的应用性问题。     

用有限解析差分格式数值求解化学输运方程

本文用有限解析差分格式研究在多孔介质中化学输运问题的数值模型,系统地计算结果表明:1.有限解析差分格式能够消除数值弥散和伪振荡; 2.随着弥散数(Peclct数)的减小(增加),浓度突破曲线将延迟到达和形状变陡,最终趋近浓度对流曲线;3.当流速数增加后,非稳态吸附对浓度分布的影响趋近稳态吸附的影响。     

On general form of Navier-Stokes equations and implicit factored scheme

A general weak conservative form of Navier-Stokes equations expressed with respect to non-orthogonal Curvilinear coordinates and with primitive variables was obtained by using tensor analysis technique, where the contravariant and covariant velocity components were employed. Compared with the current coordinate transformation method, the established equations are concise and forthright, and they are more convenient to be used for solving problems in body-fitted curvilinear coordinate system. An implicit factored scheme for solving the equations is presented with detailed discussions in this paper. For n-dimensional flow the algorithm requires n-steps and for each step only a block tridiagonal matrix equation needs to be solved. It avoids inverting the matrix for large systems of equations and enhances the speed of arithmetic. In this study, the Beam- Warming’s implicit factored schceme is extended and developed in non-orthogonal curvilinear coordinate system.     

A kind of distortion of mean velocity profile in pipe Poiseuille flow and its stability behaviour

This paper presents a kind of distortion of Hagen-Poiseuille velocity profile in pipe Poiseuille flow. This distortion can be regarded as a general expression of the influence on the mean flow by nonlinear interaction of various components of axisymmetric perturbations. Through the investigation of the stability behaviour of this velocity profile, this paper obtains unstable result induced by axisymmetric perturbations for the first time, and thus presents a new possible approach which leads to instability of Hagen-Poiseuille flow.     

一维多介质可压缩Euler方程的高精度RKDG有限元方法

采用RKDG有限元目的、Level Set目的和改进的带"Isentropic"修正的Ghost Fluid目的模拟了一维多介质可压缩Euler方程,其中Euler方程、Level Set方程和重新初始化方程都采用了三阶精度的RKDG有限元目的进行离散,并对一维两种介质可压缩流体进行了数值实验,得到了较高分辨率的计算结果.     

负离子元素杂质破坏模型

探讨了HfO₂薄膜中负离子元素杂质破坏模型，并得出薄膜中的杂质主要来源于 镀膜材料. 用电子束蒸发方法沉积两种不同Cl元素含量的HfO₂薄膜，测定薄膜 弱吸收和损伤阈值来验证负离子元素破坏模型. 结果表明，随着Cl元素含量的增加薄膜的弱 吸收增加损伤阈值减小. 这主要是因为负离子元素在蒸发过程中形成挥发性的气源中心而产 生缺陷，缺陷在激光辐照过程中又形成吸收中心. 因此负离子元素的存在将加速薄膜的破坏 . 关键词： 负离子元素杂质 缺陷 吸收     

ICF空心微球靶传热的有限元分析

 为分析冷冻靶丸外部温度场，应用ANSYS软件对ICF空心微球靶的热传递进行了有限元分析。建立了单元传热的几何物理模型，靶丸微球呈空间均匀分布，计算区域由三个同心球壳组成，分别为液体层、靶丸壳层以及氦气层，氦气层厚度为球壳层厚度的7倍。模型左右两边界设为绝热边界条件，采用智能自动划分网格,设定参数为3，单元类型为三角形。模拟表明，在靶丸工作温度为24 K的情况下，为保持靶丸气泡受力平衡，自洽得到靶丸内部温度梯度为14.02 K/cm，以此求解出所施加的外部温度场为7.758 K/cm。将计算值与现有的实验结果进行了比较，模拟结果与国外实验值(8.2 K/cm)吻合得较好。     

固体的热膨胀系数

 本文由Grüneisen第二定则出发，采用普适能量函数作为原子间相互作用势能函数，计算立方晶体金属元素和几种NaCl型结构的碱卤晶体的线膨胀系数。计算值与实验值符合得很好。     

阻抗复合消声器声学性能有限元预测方法及分析

为计算和分析具有复杂结构的阻抗复合式消声器的宽频消声性能,建立了一种高效声学有限元方法,给出了不同边界条件下的边界积分处理细节,得到有限元全局系数矩阵表达式,设计出计算程序框架以实现这些算法,其求解规模和计算速度与商业软件相比有优势。为计算阻抗复合式消声器的传递损失,通过阻抗管测量和数据拟合得到了吸声材料声学特性的经验公式。计算和测量了两通穿孔阻抗复合式消声器的传递损失,二者良好的吻合验证了声学有限元方法和计算程序的正确性。研究表明,插管长度影响消声器在中高频段的消声特性,右侧隔板上穿孔会消除共振峰,中高频消声性能随着出口管穿孔率的增加而提升。     

Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations

Several two-level iterative methods based on nonconforming finite element methods are applied for solving numerically the 2D/3D stationary incompressible MHD equations under different uniqueness conditions. These two-level algorithms are motivated by applying the m iterations on a coarse grid and correction once on a fine grid. A one-level Oseen iterative method on a fine mesh is further studied under a weak uniqueness condition. Moreover, the stability and error estimate are rigorously carried out, which prove that the proposed methods are stable and effective. Finally, some numerical examples corroborate the effectiveness of our theoretical analysis and the proposed methods.