大气湍流波前低阶模式的时间功率谱分析

引入规格化的相位谱,推导了大气湍流波前低阶模式（Ｚ－倾斜和Ｇ－倾斜、离焦、像散以及彗差）的时间功率谱,并就水平大气传输、星体目标观测、空间目标监测等几种情况作了实际的数值计算及分析,此外还给出实验结果,分析结果表明：对于水平大气传输模式,倾斜功率谱曲线的低频阶段的指数下降因子为４／３－６β／１１（β为相位谱空间频率的指数下降因子）,离焦、像散和彗差项的功率谱低频段指数下降因子为０;水平大气传输工作     

ICCD型与CCD型弱光哈特曼-夏克波前传感器的性能分析与对比

哈特曼－夏克（Ｈａｒｔｍａｎｎ－Ｓｈａｃｋ）波前传感器由于其光能利用率高、结构简单、通道容量大等突出优点,是目前自适应光学系统波前传感器的主流形式。本文深入分析和比较了目前普遍采用的ＩＣＣＤ型和ＣＣＤ型这两种主要类型的弱光哈特曼－夏克波前传感器的特点和波前相位探测精度,导出了定量分析数学模型,给出了实验结果。此研究结果对弱光哈特曼－夏克波前传感器的技术方案选定和工程设计有指导意义。     

弱光波前传感器质心计算的新方法

 研究了Shack Hartmann波前传感器质心计算的新方法,即最小二乘高斯拟合方法。分析了Shack-Hartmann波前传感器采用一阶矩质心计算位置方法对光斑强度的敏感性,与最小二乘高斯拟合方法进行了比较,并对Shack Hartmann波前传感器的子孔径波前斜率探测的正确性进行了分析。最后的计算结果表明最小二乘高斯拟合法计算子孔径光斑的质心位置可以减小质心探测的误差。     

A fast nested multi‐grid viscous flow solver for adaptive Cartesian/Quad grids

A nested multi‐grid solution algorithm has been developed for an adaptive Cartesian/Quad grid viscous flow solver. Body‐fitted adaptive Quad (quadrilateral) grids are generated around solid bodies through ‘surface extrusion’. The Quad grids are then overlapped with an adaptive Cartesian grid. Quadtree data structures are employed to record both the Quad and Cartesian grids. The Cartesian grid is generated through recursive sub‐division of a single root, whereas the Quad grids start from multiple roots—a forest of Quadtrees, representing the coarsest possible Quad grids. Cell‐cutting is performed at the Cartesian/Quad grid interface to merge the Cartesian and Quad grids into a single unstructured grid with arbitrary cell topologies (i.e., arbitrary polygons). Because of the hierarchical nature of the data structure, many levels of coarse grids have already been built in. The coarsening of the unstructured grid is based on the Quadtree data structure through reverse tree traversal. Issues arising from grid coarsening are discussed and solutions are developed. The flow solver is based on a cell‐centered finite volume discretization, Roe's flux splitting, a least‐squares linear reconstruction, and a differentiable limiter developed by Venkatakrishnan in a modified form. A local time stepping scheme is used to handle very small cut cells produced in cell‐cutting. Several cycling strategies, such as the saw‐tooth, W‐ and V‐cycles, have been studies. The V‐cycle has been found to be the most efficient. In general, the multi‐grid solution algorithm has been shown to greatly speed up convergence to steady state—by one to two orders. Copyright © 2000 John Wiley & Sons, Ltd.     

Adaptive Q‐tree Godunov‐type scheme for shallow water equations

This paper presents details of a second‐order accurate, Godunov‐type numerical model of the two‐dimensional shallow water equations (SWEs) written in matrix form and discretized using finite volumes. Roe's flux function is used for the convection terms and a non‐linear limiter is applied to prevent unwanted spurious oscillations. A new mathematical formulation is presented, which inherently balances flux gradient and source terms. It is, therefore, suitable for cases where the bathymetry is non‐uniform, unlike other formulations given in the literature based on Roe's approximate Riemann solver. The model is based on hierarchical quadtree (Q‐tree) grids, which adapt to inherent flow parameters, such as magnitude of the free surface gradient and depth‐averaged vorticity. Validation tests include wind‐induced circulation in a dish‐shaped basin, two‐dimensional frictionless rectangular and circular dam‐breaks, an oblique hydraulic jump, and jet‐forced flow in a circular reservoir. Copyright © 2001 John Wiley & Sons, Ltd.     

自适应多分辨率方法在反应多相流数值模拟中的应用

将自适应多分辨率方法应用到刚性气体状态方程CJ模型的数值模拟,采用多相流问题的守恒锐利界面格式,通过level-set方法和虚拟流体方法来追踪和处理界面,能够很好地处理时间尺度较大的界面交互问题.利用金字塔型数据结构和多分辨率自适应方法,提高算法的存储效率和计算效率.给出一维和二维的数值算例,证明该算法在反应多相流数值模拟中的稳定性和高效性.     

基于模糊事件概率理论的模糊可靠性分析通用方法

讨论了从已知的模糊信息的隶属函数,确定模糊失效事件的隶属函数的方法,以便能利用模糊事件概率理论进行模糊可靠性分析,给出模糊可靠性分析通用而统一的方法;并给出了强度为几种常用模糊分布时,所确定的模糊失效事件的隶属函数的具体表达式,分析了模糊失效事件的隶属函数的曲线特性。由于获得的模糊失效事件的隶属函数的形式比较复杂,用模糊事件概率理论进行模糊可靠性分析时,不可能得到计算模糊失效事件概率的解析式,因此通过仿真所确定的模糊失效事件的隶属函数的数学期望的方法,估计模糊失效事件的发生概率。本文讨论的通过确定模糊事件的隶属函数,用模糊事件概率理论进行模糊可靠性分析的方法具有普遍意义。     

Survey on Path-Dependent PDEs*

In this paper,the authors provide a brief introduction of the path-dependent partial differential equations(PDEs for short) in the space of continuous paths,where the path derivatives are in the Dupire(rather than Fréchet) sense.They present the connections between Wiener expectation,backward stochastic differential equations(BSDEs for short) and path-dependent PDEs.They also consider the well-posedness of path-dependent PDEs,including classical solutions,Sobolev solutions and viscosity solution...     

自适应设计广义线性回归多维拟似然估计的渐近正态性

本文研究了自适应设计下广义线性回归的拟似然方程∑ni=1xi(yi-μ(xi′β))=0,其中yi是q维向量,xi是p×q阶随机矩阵,在一定条件下证明了方程的解^βn具有渐进正态的性质.     

强爆炸火球辐射流体自适应网格高精度数值模拟

提出一种自适应网格方法,应用于基于Euler方法的强爆炸辐射流体高精度数值求解.通过与Zinn数值结果对比,验证该方法的正确性.研究自适应网格对冲击波和光辐射输出模拟精度的影响,对比不同网格尺度下的计算耗时.在相同的条件下,使用自适应网格与均匀网格加密3倍得到的冲击波超压分布、光辐射输出演化接近,计算效率提升约8.5倍...