矩形校正公式的误差分析

This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively.It also displays an analysis on convergence order of compound corrector formulas for rectangular rule.Examples of numerical calculation have validated theoretical analysis.     

On streamline diffusion arising in Galerkin FEM with predictor/multi‐corrector time integration

In the present paper, the author shows that the predictor/multi‐corrector (PMC) time integration for the advection–diffusion equations induces numerical diffusivity acting only in the streamline direction, even though the equations are spatially discretized by the conventional Galerkin finite element method (GFEM). The transient 2‐D and 3‐D advection problems are solved with the PMC scheme using both the GFEM and the streamline upwind/Petrov Galerkin (SUPG) as the spatial discretization methods for comparison. The solutions of the SUPG‐PMC turned out to be overly diffusive due to the additional PMC streamline diffusion, while the solutions of the GFEM‐PMC were comparatively accurate without significant damping and phase error. A similar tendency was seen also in the quasi‐steady solutions to the incompressible viscous flow problems: 2‐D driven cavity flow and natural convection in a square cavity. Copyright © 2002 John Wiley & Sons, Ltd.     

计算机产生全息图对补偿器检测的技术研究

用一种计算全息板代替补偿器零检验光路中理想的大型非球面,实现对补偿器的定量检验.用于检测补偿器旋转对称的二元反射式全息板根据非球面方程设计,并确定其光程差,再由激光直写(精度可达0.6μm)来制作完成,合成相当于理想非球面反射波前.其检测精度小于λ/10.补偿器的参量由抛物面和三级球差理论确定.     

The equilibrium limit of a constitutive model for two-phase granular mixtures and its numerical approximation

In this paper we analyze the equilibrium limit of the constitutive model for two-phase granular mixtures introduced in Papalexandris (2004) [13], and develop an algorithm for its numerical approximation. At, equilibrium, the constitutive model reduces to a strongly coupled, overdetermined system of quasilinear elliptic partial differential equations with respect to the pressure and the volume fraction of the solid granular phase. First we carry a perturbation analysis based on standard hydrostatic-type scaling arguments which reduces the complexity of the coupling of the equations. The perturbed system is then supplemented by an appropriate compatibility condition which arises from the properties of the gradient operator. Further, based on the Helmholtz decomposition and Ladyzhenskaya’s decomposition theorem, we develop a projection-type, Successive-Over-Relaxation numerical method. This method is general enough and can be applied to a variety of continuum models of complex mixtures and mixtures with micro-structure. We also prove that this method is both stable and consistent hence, under standard assumptions, convergent. The paper concludes with the presentation of representative numerical results.     

A meshless method using the radial basis functions for numerical solution of the regularized long wave equation

This article discusses on the solution of the regularized long wave (RLW) equation, which is introduced to describe the development of the undular bore, has been used for modeling in many branches of science and engineering. A numerical method is presented to solve the RLW equation. The main idea behind this numerical simulation is to use the collocation and approximating the solution by radial basis functions (RBFs). To avoid solving the nonlinear system, a predictor‐corrector scheme is proposed. Several test problems are given to validate the new technique. The numerical simulation, includes the propagation of a solitary wave, interaction of two positive solitary waves, interaction of a positive and a negative solitary wave, the evaluation of Maxwellian pulse into stable solitary waves and the development of an undular bore. The three invariants of the motion are calculated to determine the conservation properties of the algorithm. The results of numerical experiments are compared with analytical solution and with those of other recently published methods to confirm the accuracy and efficiency of the presented scheme.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Nonlinear corrector for Reynolds-averaged Navier-Stokes equations

The scope of this paper is to present a nonlinear error estimation and correction for Navier-Stokes and Reynolds-averaged Navier-Stokes equations. This nonlinear corrector enables better solution or functional output predictions at fixed mesh complexity and can be considered in a mesh adaptation process. After solving the problem at hand, a corrected solution is obtained by solving again the problem with an added source term. This source term is deduced from the evaluation of the residual of the numerical solution interpolated on the h/2 mesh. To avoid the generation of the h/2 mesh (which is prohibitive for realistic applications), the residual at each vertex is computed by local refinement only in the neighborhood of the considered vertex. One of the main feature of this approach is that it automatically takes into account all the properties of the considered numerical method. The numerical examples point out that it successfully improves solution predictions and yields a sharp estimate of the numerical error. Moreover, we demonstrate the superiority of the nonlinear corrector with respect to linear corrector that can be found in the literature.     

共形光学技术

共形头罩可大大减小空气阻力,提高导弹在速度与射程方面的性能。介绍了精确共形光学技术,设计的关键在于校正共形头罩在全部视场的动态像差,讨论了采用旋转/平移位相板、拱形校正器等像差校正方法。简要说明了共性头罩加工、试验及应用状况,指出共形光学技术是未来高速导弹整流罩技术的发展方向。     

Simpson校正公式

给出了Simpson校正公式的截断误差,分析了复化Simpson校正公式的收敛阶.数值算例验证了理论分析的正确性.     

自适应光学波前校正器技术发展现状

波前校正器是自适应光学系统中的关键部件,相关技术已得到了多年的积累与发展。本文介绍了多种目前常用的波前校正器件,包括分离促动器连续表面变形镜、拼接子镜变形镜、薄膜变形镜、双压电片变形镜、微电子机械系统变形镜以及基于液晶技术的空间光调制器和自适应次镜等,给出了它们的实现方式及其基本工作原理,并从空间校正频率和校正速度等方面对各校正器的性能进行了比较。最后,总结了在新应用的需求下,波前校正器件的技术创新及发展趋势。     

中国散裂中子源旋转线圈测量系统研制

中国散裂中子源(CSNS)加速器主要由一台直线加速器、一台快循环加速器以及低能、高能输运线组成。针对CSNS加速器部分直流磁铁研制了一套旋转线圈测量系统。对系统的研制方案、功能、精度、完成的磁铁类型以及部分测量结果进行介绍。该系统解决了CSNS批量磁铁之间的不同中心高度、质量、有效长度、磁场强度的兼容性难题。经过测试运行,积分场测量重复性误差好于±0.02%,空间谐波重复性误差好于0.005%,磁中心测量重复性误差好于±0.03 mm,顺利完成了中国散裂中子源工程150台多种类型磁铁的检测任务。