成像角膜曲率计的光学设计

为了提高角膜曲率计的测量精度,借助于现代光电子技术,设计了一款高精度的成像角膜曲率计.系统包括环形物、一次成像系统、角膜、二次成像系统和CCD探测器.首先在ZEMAX软件中,设计了成像角膜曲率计的一次成像系统和二次成像系统,分别对两个成像系统进行优化设计;然后通过半透半反镜组将一次成像系统和二次成像系统拼接,组成成像角膜曲率计的光学系统,并对其进行整体的优化设计.最后,利用TracePro对所得的环形像进行模拟和分析.结果表明:所设计的成像角膜曲率计的测量范围约为30~60D(对应角膜曲率半径5.5~11 mm),测量精度在角膜曲率半径7.8 mm时达到0.072D.     

结合DEM的红边-近红外植被指数提取城市植被信息

随着生活水平的不断提高,城市植被已成为衡量城市宜居性的重要标准之一,对城市生物多样性评估和保护起到非常重要的作用。因此,合理规划城市植被是解决环境问题和提高生活质量的重要手段。因此,城市植被的提取和监测成为重中之重的任务。目前,城市植被提取一方面受到地域和物种的影响,另一方面也受到地形和建筑物阴影的影响。为解决上述问题,提出了一种结合数字高程模型(DEM)的红边-近红外植被指数模型（RENVI）。首先选取了3景经过辐射定标和大气校正的具有红边波段、且光谱和空间分辨率较高的Worldview-3遥感影像;然后,根据红边波段对于植被具有较高的敏感性,且红边范围内的光谱数据与反映植被生长状况的参数有较好的相关关系原理,采用DEM模型和红边波段光谱差异,有效去除地形和建筑物阴影;最后,在可见光波段范围内建立红边光谱-近红外光谱构建特征空间,构建了红边-近红外植被指数模型,同时与归一化植被指数（NDVI）和增强型植被指数（EVI）进行城市植被提取的定性和定量对比分析。定性分析是利用真实植被影像参考图与模型提取植被影像进行视觉分析;后者是采用用户精度、生产者精度、总体精度和Kappa系数进行量化分析。定性分析表明：NDVI和EVI提取城市植被,由于建筑和道路像元混淆在植被中,产生了错分和漏分的问题。RENVI较好地消除了阴影像元与植被像元混淆问题,能准确的提取城市植被,减少了冗余度,增加了植被指数的信息量。定量分析表明：RENVI模型较NDVI和RVI能够准确提取城市植被,3景影像总体精度分别为89%,81.4%和91.8%,Kappa系数分别为0.852 8,0.791 3和0.905 2。综上所述,该方法有效提高了城市植被提取精度,并取得了较好的提取视觉效果。     

变系数情形下Criss-Cross三角形线性元的渐近展式与超收敛

本文讨论了二阶椭圆方程变系数情形下Criss-Cross三角形线性元的超收敛性质,得到了有限元的渐进展式、外推及高精度组合公式等结果.     

A high‐order accurate method for two‐dimensional incompressible viscous flows

A high‐order accurate solution method for complex geometries is developed for two‐dimensional flows using the stream function–vorticity formulation. High‐order accurate spectrally optimized compact schemes along with appropriate boundary schemes are used for spatial discretization while a two‐level backward Euler implicit scheme is used for the time integration. The linear system of equations for stream function and vorticity are solved by an inner iteration while contravariant velocities constitute outer iterations. The effect of curvilinear grids on the solution accuracy is studied. The method is used to compute Cartesian and inclined driven cavity, flow in a triangular cavity and viscous flow in constricted channel. Benchmark‐like accuracy is obtained in all the problems with fewer grid points compared to reported studies. Copyright © 2006 John Wiley & Sons, Ltd.     

Finite volume multigrid prediction of laminar natural convection: Bench-mark solutions

A finite volume multigrid procedure for the prediction of laminar natural convection flows is presented, enabling efficient and accurate calculations on very fine grids. The method is fully conservative and uses second-order central differencing for convection and diffusion fluxes. The calculations start on a coarse (typically 10 × 10 control volumes) grid and proceed to finer grids until the desired accuracy or maximum affordable storage is reached. The computing times increase thereby linearly with the number of control volumes. Solutions are presented for the flow in a closed cavity with side walls at different temperatures and insulated top and bottom walls. Rayleigh numbers of 10⁴, 10⁵ and 10⁶ are considered. Grids as fine as 640 × 640 control volumes are used and the results are believed to be accurate to within 0–01%. Second-order monotonic convergence to grid-independent values is observed for all predicted quantities.     

Minimum time‐step criteria for the Galerkin finite element methods applied to one‐dimensional parabolic partial differential equations

The finite element method has been well established for numerically solving parabolic partial differential equations (PDEs). Also it is well known that a too large time step should not be chosen in order to obtain a stable and accurate numerical solution. In this article, accuracy analysis shows that a too small time step should not be chosen either for some time‐stepping schemes. Otherwise, the accuracy of the numerical solution cannot be improved or can even be worsened in some cases. Furthermore, the so‐called minimum time step criteria are established for the Crank‐Nicolson scheme, the Galerkin‐time scheme, and the backward‐difference scheme used in the temporal discretization. For the forward‐difference scheme, no minimum time step exists as far as the accuracy is concerned. In the accuracy analysis, no specific initial and boundary conditions are invoked so that such established criteria can be applied to the parabolic PDEs subject to any initial and boundary conditions. These minimum time step criteria are verified in a series of numerical experiments for a one‐dimensional transient field problem with a known analytical solution. The minimum time step criteria developed in this study are useful for choosing appropriate time steps in numerical simulations of practical engineering problems. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Retracted and replaced: A flow‐condition‐based interpolation finite element procedure for triangular grids

A flow‐condition‐based interpolation finite element scheme is presented for use of triangular grids in the solution of the incompressible Navier–Stokes equations. The method provides spatially isotropic discretizations for low and high Reynolds number flows. Various example solutions are given to illustrate the capabilities of the procedure. This article and been retracted and replaced. See retraction and replacement notice DOI: 10.1002/fld.1247 . Copyright © 2005 John Wiley & Sons, Ltd.     

具有周期振荡系数二阶椭圆型方程的双尺度高精度算法

本文考虑了一类具有周期振荡系数二阶椭圆型方程边值问题,提出了基于双尺度渐近展开式的高精度有限元算法,并给出严格的证明。     

Implementation of some higher-order convection schemes on non-uniform grids

A generalized formulation is applied to implement the quadratic upstream interpolation (QUICK) scheme, the second-order upwind (SOU) scheme and the second-order hybrid scheme (SHYBRID) on non-uniform grids. The implementation method is simple. The accuracy and efficiency of these higher-order schemes on non-uniform grids are assessed. Three well-known bench mark convection-diffusion problems and a fluid flow problem are revisited using non-uniform grids. These are: (1) transport of a scalar tracer by a uniform velocity field; (2) heat transport in a recirculating flow; (3) two-dimensional non-linear Burgers equations; and (4) a two-dimensional incompressible Navier-Stokes flow which is similar to the classical lid-driven cavity flow. The known exact solutions of the last three problems make it possible to thoroughly evaluate accuracies of various uniform and non-uniform grids. Higher accuracy is obtained for fewer grid points on non-uniform grids. The order of accuracy of the examined schemes is maintained for some tested problems if the distribution of non-uniform grid points is properly chosen.