Modified Equations for Stochastic Differential Equations

We describe a backward error analysis for stochastic differential equations with respect to weak convergence. Modified equations are provided for forward and backward Euler approximations to Itô SDEs with additive noise, and extensions to other types of equation and approximation are discussed.     

端面泵浦掺Yb3+双包层光纤激光器

从双包层光纤激光器的速率方程出发，得到了光纤中泵浦光与激光的功率分布、输出功率与泵浦功率的关系、腔镜反射率及光纤长度对输出功率的影响。研究结果表明：输出激光功率与光纤长度及后腔镜反射率有很强的依赖关系，存在一个输出功率最大的最佳光纤长度。后腔镜反射率越大，输出激光功率越小；当光纤长度较短时，在输出端放置反射镜使泵浦光高反射，可以提高输出功率和效率。通过对端面泵浦掺Yb3+双包层光纤激光器进行理论分析和实验研究，得到输出激光的中心波长为1088.3nm，斜率效率为33.7%，最大输出功率为1.75W。     

管肋式辐射器排热特性的数值分析与优化设计

为得到按单面辐射方式布置的管肋式空间辐射器的排热特性，建立了相应的数学模型．采用数值模拟方法分析了管内流体温度、肋片几何尺寸和等效热沉温度对辐射器排热特性的影响，得到了不同参数值下辐射器单位面积排热量以及特定参数范围内的辐射器肋片最佳宽度和肋片效率．数值模拟结果对辐射器的工程结构设计以及空间站热管理方案的优化分析具有一定的参考价值．     

多级轴流压气机全工况特性计算

本文使用三维粘性流动计算软件Fine／Numeca,对某十五级轴流压气机进行了内流流场和全工况特性的数值计算尝试。分析了该压气机在设计工况和非设计工况的性能,同时把整机计算结果和前七级叶片的计算结果进行了比较。计算结果表明,当计算的级数较少时,目前的软件和硬件平台可以比较合理地预测压气机的全工况特性;而当计算的级数较多时,准确的数值模拟仍需要更为准确的多级模型和数值方法。     

Meshless simulation of equilibrium swelling/deswelling of pH‐sensitive hydrogels

Hydrogels have been widely used in microelectromechanical systems (MEMS) and Bio‐MEMS devices. In this article, the equilibrium swelling/deswelling of the pH‐stimulus cylindrical hydrogel in the microchannel is studied and simulated by the meshless method. The multi‐field coupling model, called multi‐effect‐coupling pH‐stimulus (MECpH) model, is presented and used to describe the chemical field, electric field, and the mechanical field involved in the problem. The partial differential equations (PDEs) describing these three fields are either nonlinear or coupled together. This multi‐field coupling and high nonlinear characteristics produce difficulties for the conventional numerical methods (e.g., the finite element method or the finite difference method), so an alternative—meshless method is developed to discretize the PDEs, and the efficient iteration technique is adopted to solve the nonlinear problem. The computational results for the swelling/deswelling diameter of the hydrogel under the different pH values are firstly compared with experimental results, and they have a good agreement. The influences of other parameters on the mechanical properties of the hydrogel are also investigated in detail. It is shown that the multi‐field coupling model and the developed meshless method are efficient, stable, and accurate for simulation of the properties of the stimuli‐sensitive hydrogel. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 326–337, 2006     

对流扩散方程带罚函数项的有限体积格式及其分析

1引言 有限体积方法[l]一l’]作为守恒型的离散技术，被广泛应用于工程计算领域.文【2，3} 基于分片常数和分片常向量函数空间，对二维驻定对流扩散方程提出了一类非协调混合 有限体积(Covolume)格式，证明了格式具有。(hl/2)收敛精度.但该格式要求对偶剖分 比较规则，即采用重     

基于界面跟踪方法的汽蚀模型和算法的有效性验证

针对两相附着汽蚀流动机理,基于界面跟踪方法发展了新的汽蚀模型和算法。所发展的汽蚀模型和算法不仅考虑了液相／气相界面处的压力差,而且考虑了耦合Reynolds-Averaged Navier-Stokes方程求解技术得到的流场压力梯度信息来迭代计算附着汽蚀形状。采用具有试验数据的半球形头部圆柱体汽蚀绕流作为算例来验证所提出的汽蚀模型和算法的有效性。采用不同的网格数和松弛因子数值验证了发展的汽蚀模型和算法的有效性。三种汽蚀数下的数值计算结果得到的压力系数分布与试验数据完全吻合。结果表明所提出的汽蚀模型和算法能够准确模拟出汽蚀发生点和汽蚀长度。     

用焓法有限元解相变问题的离散化方法

为了消除应用焓法进行含有相变的有限元传热计算结果呈台阶形的现象,本文作者提出“焓计算单元”和“固相分数”的概念,并将几种一维有限元实施方案的计算结果与精确解对比,说明采用所提出的概念,可以使有限元计算得出更为合理的结果。     

A Dynamic Analysis and Numerical Simulation of Explosive Development of an Extratropical Cyclone Over Land

The present paper has made a dynamic and diagnostic study of the process of explosive deepening of an extratropical cyclone over North China on April 25-26, 1983, in order to gain an insight into the physical mechanism of explosive development of cyclone over land. It turns out that this cyclone occurred in the strong baroclinic zone, and the vorticity and thermal advection triggered the initial development of the cyclone. Subsequently, as the rainfall increased, the effect of condensational heating became more and more important. During the time period of rapid intensification (from 1200GMT 25 to 0000GMT 26 April, 1983, the central surface pressure fell down from 998. 2 to 988. 3 hPa), the peak of diabatic heating profile continuously descended, leading to a rapid increase in heating amount in the lower troposphere. This condition is favorable to the explosive development of rotational circulation or vortex. The numerical simulations have further demonstrated the importance of the lowering of heating p     

Mass transport in gas channels of electrochemical cells with a solid-oxide electrolyte: Allowing for the electrode reaction rates in numerical calculations

The concentration fields, Nusselt number distributions along the electrode, and ratios of concentrations of electrochemically active components at the entrance into and exit out of an electrochemical cell are determined by numerical integration of the convective-diffusion equation for a broad range of rate constants of electrode reactions, Peclet numbers, and geometrical parameters of channels. Three regions of parameter values are revealed. At low reaction rates (K _l < 0.5), mass transfer is completely determined by electrode kinetics; at high rates (K _l > 20), it is completely determined by the diffusion in the gas phase; and in the intermediate region of values of K _l it is necessary to allow for both the diffusion processes and the electrode reactions.Translated from Elektrokhimiya, Vol. 41, No. 3, 2005, pp. 317–324.Original Russian Text Copyright © 2005 by Ezin, Somov.