Finite element analysis and approximation of Burgers’‐Fisher equation

In this article, the authors present finite element analysis and approximation of Burgers’‐Fisher equation. Existence and uniqueness of weak solution is proved by Galerkin's finite element method for non‐smooth initial data. Next, a priori error estimates of semi‐discrete solution in norm, are derived and the convergence of semi‐discrete solution is established. Then, fully discretization of the problem is done with the help of Euler's backward method. The nonlinearity is removed by lagging it to previous known level. The scheme is found to be convergent. Positivity of fully discrete solution is discussed, and bounds on time step are discovered for which the solution preserves its positivity. Finally, numerical experiments are performed on some examples to demonstrate the effectiveness of the scheme. The proposed scheme found to be fast, easy and accurate.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1652–1677, 2017     

An inverse backward problem for degenerate parabolic equations

This work studies the inverse problem of reconstructing an initial value function in the degenerate parabolic equation using the final measurement data. Problems of this type have important applications in the field of financial engineering. Being different from other inverse backward parabolic problems, the mathematical model in our article may be allowed to degenerate at some part of boundaries, which may lead to the corresponding boundary conditions missing. The conditional stability of the solution is obtained using the logarithmic convexity method. A finite difference scheme is constructed to solve the direct problem and the corresponding stability and convergence are proved. The Landweber iteration algorithm is applied to the inverse problem and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown initial value is recovered very well.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1900–1923, 2017     

具有缺失数据的Eichhorn模型

为了解决在Eichhorn乘法扰动模型中存在的项目无回答问题,对敏感变量总体均值在辅助变量总体均值已知与未知条件下提出了比率插补方法.理论比较和数值模拟得出的结果表明提出的插补方法比传统的方法效率更高.     

三维随机分析的响应曲面法

本文采用“响应曲面法”设计了三维随机分析程序，可对多种材料组成的三维结构进行破坏概率计算，并在Ｗｉｎｄｏｗｓ下实现了计算结果的可视化。     

Dynamic Stability of a Fluid-Coveying Cantilevered Pipe on an Additional Combined Support

Based on an analytical study, a numerical analysis is made of the dynamic stability of a cantilevered steel pipe conveying a fluid. The pipe is modeled by a beam restrained at the left end and supported by a special device (a rotational elastic restraint plus a Q-apparatus) at the right end. The numerical analysis reveals that the critical velocity of the fluid depends on the governing parameters of the problem such as the ratio of the fluid mass to the pipe mass per unit length and the rotational elastic constant at the right end     

扩散方程单内点精细积分法与差分法比较研究

一维扩散方程初值问题可以用全域或子域精细积分求解。子域积分可以采用不同数量的内点，单内点是其最简单的情况。当单内点精细积分中的传递函数即指数函数用其泰勒展开式的一阶近似来替代时，精细积分转化为差分方程。本文研究了这一对应关系。各种常见差分格式均找到了对应的单点精细积分格式，并在单点精细积分一般公式中得到了统一表达形式     

用样条法研究高速滑行体的运动

研究高速滑行体在规则波浪中滑行时，得到了二阶常微分方程组，本文应用样条插值求积方法和三次样条配点计算，求解滑行体在不同波浪条件下的纵倾和升沉的响应．实例计算结果与实验值比较一致．     

Advanced response surface method for mechanical reliability analysis

Based on the classical response surface method (RSM), a novel RSM using improved experimental points (EPs) is presented for reliability analysis. Two novel points are included in the presented method. One is the use of linear interpolation, from which the total EPs for determining the RS are selected to be closer to the actual failure surface; the other is the application of sequential linear interpolation to control the distance between the surrounding EPs and the center EP, by which the presented method can ensure that the RS fits the actual failure surface in the region of maximum likelihood as the center EPs converge to the actual most probable point (MPP). Since the fitting precision of the RS to the actual failure surface in the vicinity of the MPP, which has significant contribution to the probability of the failure surface being exceeded, is increased by the presented method, the precision of the failure probability calculated by RS is increased as well. Numerical examples illustrate the accuracy and efficiency of the presented method.     

The low Reynolds number turbulent flow and mixing in a confined impinging jet reactor

Turbulent mixing takes an important role in chemical engineering, especially when the chemical reaction is fast compared to the mixing time. In this context a detailed knowledge of the flow field, the distribution of turbulent kinetic energy (TKE) and its dissipation rate is important, as these quantities are used for many mixing models. For this reason we conduct a direct numerical simulation (DNS) of a confined impinging jet reactor (CIJR) at Re = 500 and Sc = 1. The data is compared with particle image velocimetry (PIV) measurements and the basic flow features match between simulation and experiment. The DNS data is analysed and it is shown that the flow is dominated by a stable vortex in the main mixing duct. High intensities of turbulent kinetic energy and dissipation are found in the impingement zone which decrease rapidly towards the exit of the CIJR. In the whole CIJR the turbulence is not in equilibrium. The strong mixing in the impingement zone leads to a rapid development of a monomodal PDF. Due to the special properties of the flow field, a bimodal PDF is generated in cross-sections downstream the impingement zone, that slowly relaxes under relaminarising conditions. The time required for meso-mixing is dominating the overall mixing performance.     

基于虚拟响应信号的结构参数时域辨识研究

在充分考虑线性动力系统的时域响应特性以及小波包分析的频率空间剖分特性的基础上,提出了一种基于虚拟响应信息提取的信号去噪新方法.虚拟响应虽然没有在结构动力检测过程中真实发生,但却是在某种激励下可以实现的一个响应,因此,根据虚拟响应信息同样可以进行结构系统的动力识别.数值研究表明,对于地脉动响应这种有效信号频带与噪声频带相互覆盖的低信噪比信号而言,小波阈值去噪法已无能为力,而基于虚拟响应信息提取的信号去噪方法则有较好的去噪效果.