基于单位四元数描述的单像空间后方交会

在3维空间里,四元数可以非常方便地表示空间方位、空间向量间的旋转、平移和缩放等关系。将四元数理论引入到摄影测量领域,用单位四元数对坐标旋转矩阵进行描述,提出了一种采用单位四元数描述航摄像片位置与姿态的单张像片空间后方交会新方法。该方法与传统方法相比,在平差时避免了频繁的三角函数运算,不仅收敛速度快,而且精度高。     

Sensitivity equations for hyperbolic conservation law-based flow models

The present paper focuses on the governing equations for the sensitivity of the variables to the parameters in flow models that can be described by one-dimensional scalar, hyperbolic conservation laws. The sensitivity is shown to obey a hyperbolic, scalar conservation law. The sensitivity is a conserved scalar except in the case of discontinuous flow solutions, where an extra, point source term must be added to the equations in order to enforce conservation. The propagation speed of the sensitivity waves being identical to that of the conserved variable in the original conservation law, the system of conservation laws formed by the original hyperbolic equation and the equation satisfied by the sensitivity is linearly degenerate. A consequence on the solution of the Riemann problem is that rarefaction waves for the variable of the original equation result in vacuum regions for the sensitivity. The numerical solution of the hyperbolic conservation law for the sensitivity by finite volume methods requires the implementation of a specific shock detection procedure. A set of necessary conditions is defined for the discretisation of the source term in the sensitivity equation. An application to the one-dimensional kinematic wave equation shows that the proposed numerical technique allows analytical solutions to be reproduced correctly. The computational examples show that first-order numerical schemes do not yield satisfactory numerical solutions in the neighbourhood of moving shocks and that higher-order schemes, such as the MUSCL scheme, should be used for sharp transients.     

A micro-mechanical investigation of the dynamic response and liquefaction of saturated granular soils

A coupled continuum-discrete hydromechanical model was utilized to analyze the meso-scale pore fluid flow and micro-scale solid phase deformation of saturated granular soils. The fluid motion was idealized using averaged Navier–Stokes equations and the discrete element method was employed to model the solid particles. Well established semi-empirical relationships were used to quantify the fluid–particle interactions. Numerical simulations were conducted to investigate the mechanisms of granular deposit liquefaction in the presence of a critical upward pore fluid flow as well as when subjected to a dynamic base excitation. The outcome of these simulations was consistent with experimental observations and revealed valuable information on the micro-mechanical characteristics of soil liquefaction and associated loss of stiffness and strength.     

Refinement of predictive reaeration equations for a typical Indian river

Dissolved oxygen mass balance has been computed for different reaches of River Kali in western Uttar Pradesh (India) to obtain the reaeration coefficient (K₂). A total of 270 field data sets have been collected during the period from March 1999 to February 2000. Eleven most popular predictive equations, used for reaeration prediction and utilizing mean stream velocity, bed slope, flow depth, friction velocity and Froude number, have been tested for their applicability in the River Kali using data generated during field survey. The K₂ values computed from these predictive equations have been compared with the K₂ values observed from dissolved oxygen balance measurements in the field. The performance of predictive equations have been evaluated using error estimation, namely standard error (SE), normal mean error (NME), mean multiplicative error (MME) and correlation statistics. The equations developed by Smoot and by Cadwallader and McDonnell showed comparatively better results. Moreover, a refined predictive equation has been developed using a least‐squares algorithm for the River Kali that minimizes error estimates and improves correlation between observed and computed reaeration coefficients. Copyright © 2001 John Wiley & Sons, Ltd.     

Rotating Stratified Heterogeneous Oblate Spheroid in Newtonian Physics

By solving the Euler hydrodynamical equations we have obtained closed form solutions for the angular velocities and pressures of a three stratified non-confocal heterogeneous oblate spheroid. Limiting and particular solutions cases, such as a spheroid with N layers, a stratified spheroid with the same eccentricities, as well as confocal layered spheroids are also explicitly written down. As an application, we have numerically estimated planet Earth's outer and inner cores' ellipticities to be _o=1/413.318 and _i=1/424.616, respectively. These Earth's ellipticities values are in good agreement with those found in the literature.     

A mathematical and numerical model for reactive fluid flow systems

We formulate mathematical and numerical models for multispecies, multi-phase and non-isothermal reactive fluid flow in porous media focusing on the chemical reactions and the transport of solutes. Mass conservation and stability in the time integration are emphasized. We use cell-centered finite volume differencing in space and an implicit Runge-Kutta method in time. Assuming two space dimensions, we introduce flux approximation for arbitrarily shaped convex quadrilaterals. On equidistant and variable sized rectangular grids we choose limited κ= related schemes to approximate the advective flux and the central difference scheme for the diffusive flux. On non-rectangular grids we recommend the VF9 scheme for the estimation of the diffusive flux. Our model exists as a code. This revised version was published online in July 2006 with corrections to the Cover Date.     

A study on theory of second-order adjoint model

The adjoint approach, one of the variational data assimilation (VDA) methods, is now widely used for fitting numerical models of meteorology and oceanography tO the observaions. The fundamental idea is to minimize a cost function, which is sum of Squares in the differences betweenthe data and their model counterparts, by adjllsting the independent model variables such as initialvalue, boundary value and Parameters. The numerical model is an operator maPPing the independent model variables i…     

多向不规则波绕射的数值模拟

采用有限元求解Ｂｏｕｓｓｉｎｅｓｑ方程数值计算模型,对单突堤和双突堤的波浪绕射进行了数值模拟,并与物模试验进行对比验证。模拟结果表明入射波浪的方向分布对波浪的绕射具有明显的影响,使防波堤后的波浪增大,开阔区域的浪浪减小,波浪的方向分布对港内波浪的分布具有一定的均化作用。     

横观各向同性饱和土体三维粘弹性动力分析

采用针对横观各向同性饱和土体u-w形式三维粘弹性动力方程,考虑土骨架的粘弹性性质且基于粘弹性理论,通过运用Fourier 展开、Laplace 和Hankel 积分变换方法和引入中间变量,将含有粘弹性参数的六元二阶偏微分运动控制方程组,化为2组各含4个未知变量的常微分方程组,从而给出了柱坐标系下粘弹性横观各向同性饱和土体在非轴对称动力荷载作用下的瞬态反应的土骨架位移分量、孔隙流体相对于土骨架的位移分量瞬态反应一般解。在此基础上,引入初始条件和边界条件,对垂直向和水平向动力荷载作用下半空间边值问题进行了求解。根据动力时域解答的一般解,利用Laplace和Hankel 数值逆变换技术,编制了相应的数值计算程序。并进行了实例验证和弹性、粘弹性解的对比分析。结果表明,在进行横观各向同性饱和土体动力分析时,考虑土骨架的粘弹性是必要的。