The modified characteristic finite difference fractional steps method for the coupled system of fluid dynamics in porous media and its analysis

For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003.     

Dispersion analysis of the least‐squares finite‐element shallow‐water system

The frequency or dispersion relation for the least‐squares mixed formulation of the shallow‐water equations is analysed. We consider the use of different approximation spaces corresponding to co‐located and staggered meshes, respectively. The study includes the effect of Coriolis, and the dispersion properties are compared analytically and graphically with those of the mixed Galerkin formulation. Numerical solutions of a test problem to simulate slow Rossby modes illustrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd.     

Analysis and finite element simulations of a second‐order fluid model in a bounded domain

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Least‐squares finite element method on adaptive grid for PDEs with shocks

We apply the least‐squares finite element method with adaptive grid to nonlinear time‐dependent PDEs with shocks. The least‐squares finite element method is also used in applying the deformation method to generate the adaptive moving grids. The effectiveness of this method is demonstrated by solving a Burgers' equation with shocks. Computational results on uniform grids and adaptive grids are compared for the purpose of evaluation. The results show that the adaptive grids can capture the shock more sharply with significantly less computational time. For moving shock, the adaptive grid moves correctly with the shock. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Theoretical Study of Weakly Bound Dimers between Hydrogen Fluoride and Some Polar Molecules

Weakly bound linear and bent dimers, FH—X (where X = CO, OC, CNH, NCH, N₂O and ON₂), are investigated using the DFT B3LYP and ab initio MP2 methods with the same basis sets (6–311++G(3df,2pd)). The strengths of the H—C or H—N H‐bonds in dimers FH—CO, FH—CNH, and FH—N₂O are compared with those of the H—O or H—N H‐bonds in dimers FH—OC, FH—NCH, and FH—ON₂. The results obtained for the H‐bond distances, the elongation effect of the HF bond, the red shift of the HF stretching frequency, and the energy difference between the dimer and the charge transfer reveal that the H‐bonds of the first group of dimers are stronger than those of the second. The Gibbs energies calculated for the six dimer formations indicate that the weakly bound dimers are unstable at room temperature (T = 298 K) (FH—X's → FH + X's, ΔG < 0).     

脉冲泄流时土壤条件对冲击接地阻抗的影响

 为了探寻电流脉冲泄流时，设备的接地是否有效可靠，用FDTD法分析了脉冲泄流时均一土壤、分层土壤及局部改善土壤的电导率对冲击接地阻抗（TGR）的影响。结果表明：大地电导率对冲击接地阻抗的影响很大；对均一土壤，TGR随大地电导率的增大而减小，大地电导率越大，TGR对接地体的埋深越不敏感。对分层土壤，接地体要埋在大地电导率大的土壤层中，且不要靠近交界面；局部改善大地导电性能对降低TGR效果明显，TGR对改善区域的体积非常敏感，而当电导率大于一定值时，大地电导率的再增加，对TGR的影响不明显。     

声纹信号-图形差分场增强和多头自注意力机制的变压器工作状态辨识方法*

为提升电力变压器工作状态的智能监测水平,提出声纹信号-图形差分场增强和多头自注意力机制的变压器工作状态辨识方法。基于图形差分场技术将声纹信号映射为二维图像,再借助多头注意力机制的视觉转换器实现图像信息的深层挖掘与状态辨识,采用梯度加权类激活映射实现分类结果的可解释性分析。搭建了包含变压器4种典型工作状态下的实验模拟测试系统平台,实验结果表明：所提方法不仅能够有效表征变压器声纹信号的状态特征,且分类辨识精度相较于“时频图+引入多头注意力机制的变换网络”与“图形差分场+引入残差模块的卷积神经网络”的常规方法有显著提升,提升约6%,同时也具备较好的鲁棒性,可为电气设备的故障检测研究提供一定参考。     

The Optimal Error Estimate of the Fully Discrete Locally Stabilized Finite Volume Method for the Non-Stationary Navier-Stokes Problem

This paper proves the optimal estimations of a low-order spatial-temporal fully discrete method for the non-stationary Navier-Stokes Problem. In this paper, the semi-implicit scheme based on Euler method is adopted for time discretization, while the special finite volume scheme is adopted for space discretization. Specifically, the spatial discretization adopts the traditional triangle P1−P0 trial function pair, combined with macro element form to ensure local stability. The theoretical analysis results show that under certain conditions, the full discretization proposed here has the characteristics of local stability, and we can indeed obtain the optimal theoretic and numerical order error estimation of velocity and pressure. This helps to enrich the corresponding theoretical results.     

TRANSIENT TORSIONAL WAVE IN FINITE HOLLOW CYLINDER WITH INITIAL AXIAL STRESS

An analytical solution is obtained for transient torsional vibration of a finite hollow cylinder with initial axial stress. The cylinder is subjected to dynamic shearing stress at the internal surface and is fixed at the external surface. The basic equations are presented and the solution is obtained by means of Fourier series expansion technique and the separation of variables method. The effects of the initial stress on the natural frequencies and transient torsional responses are presented and discussed.     

Lossless Medical Image Compression by Using Difference Transform

This paper introduces a new method of compressing digital images by using the Difference Transform applied in medical imaging. The Difference Transform algorithm performs the decorrelation process of image data, and in this way improves the encoding process, achieving a file with a smaller size than the original. The proposed method proves to be competitive and in many cases better than the standards used for medical images such as TIFF or PNG. In addition, the Difference Transform can replace other transforms like Cosine or Wavelet.