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1.
传统动力学法的观测方程以6个初始轨道参数和先验力模型为初值进行线性化,其线性化误差随积分弧长拉长而增大.本文直接以重力卫星的几何观测轨道为初值进行线性化,其线性化误差与轨道弧长无关,且不需要初始重力场模型和初始轨道参数.导出了基于卫星轨道观测值反演重力场模型的相关公式,利用JPL公布的RL02版本2008年全年的GRACE双星轨道数据和加速度计数据解算了90阶次的地球重力场模型TJGRACE01S,并以EGM2008模型为基准与其他模型进行了比较分析,结果表明:TJGRACE01S模型直到90阶次的大地水准面累积误差为17.6 cm,优于同阶次的EIGEN-CHAMP03S和EIGEN-CHAMP05S模型,前27阶位系数整体精度优于EIGEN-GRACE01S,前15阶位系数整体精度与EIGEN-GRACE02S模型精度大致相当.利用美国8221个GPS水准点数据的分析结果也表明,本文模型也优于同阶次的EIGEN-CHAMP03S和EIGEN-CHAMP05S模型. 相似文献
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GRAPES_GFS中三维参考大气的研究:理论设计和理想试验 总被引：4，自引：0，他引：4
参考大气的选取对于半隐式半拉格朗日（Semi-Implicit Semi-Lagrangian,简称SISL）模式动力框架的计算精度至关重要。中国气象局数值预报中心自主研发的GRAPES_GFS（Global Regional Assimilation and PrEdiction System,Global Forecast System）采用基于等温大气构造的一维参考大气,该方法求解简单、易于实现,但无量纲气压和位势温度扰动量的数量级较大,降低空间计算精度的同时,由于非线性项较大,使得时间计算精度较低。借鉴近年来世界上各主要业务中心的数值模式框架搭建方法,拟在GRAPES_GFS的动力框架中引入不随时间变化且满足静力平衡的三维参考大气,使得积分过程中参考大气可以尽量地靠近模式大气,提高空间计算精度的同时,减小非线性项的数量级,进而提高时间积分的计算精度。本研究重新推导了引入三维参考大气之后模式动力学方程组的求解过程,通过若干个理想试验验证了理论方法以及代码实现的正确性,说明新的三维参考大气可以有效地提高模式动力框架的计算精度。 相似文献
3.
A method based on the linearization of the limit state functions (LSFs) is applied to evaluate the reliability of series geotechnical systems. The approach only needs information provided by first order reliability method (FORM) results: the vector of reliability indices, β, of the LSFs composing the system; and their correlation matrix, R. Two common geotechnical problems—the stability of a slope in layered soil and a circular tunnel in rock—are employed to demonstrate the simplicity, accuracy and efficiency of the suggested procedure, and advantages of the linearization approach with respect to alternative computational tools are discussed. It is also found that, if necessary, the second order reliability method (SORM)—that approximates the true LSF better than FORM—can be employed to compute better estimations of the system’s reliability. 相似文献
4.
An updated linear computer model for meandering rivers with incision has been developed. The model simulates the bed topography, flow field, and bank erosion rate in an incised meandering channel. In a scenario where the upstream sediment load decreases （e.g., after dam closure or soil conservation）, alluvial river experiences cross section deepening and slope flattening. The channel migration rate might be affected in two ways： decreased channel slope and steeped bank height. The proposed numerical model combines the traditional one-dimensional （1D） sediment transport model in simulating the channel erosion and the linear model for channel meandering. A non-equilibrium sediment transport model is used to update the channel bed elevation and gradations. A linear meandering model was used to calculate the channel alignment and bank erosion/accretion, which in turn was used by the 1D sediment transport model. In the 1D sediment transport model, the channel bed elevation and gradations are represented in each channel cross section. In the meandering model, the bed elevation and gradations are stored in two dimensional （2D） cells to represent the channel and terrain properties （elevation and gradation）. A new method is proposed to exchange information regarding bed elevations and bed material fractions between 1D river geometry and 2D channel and terrain. The ability of the model is demonstrated using the simulation of the laboratory channel migration of Friedkin in which channel incision occurs at the upstream end. 相似文献
5.
We have developed a new method to analyze the power law based non-Darcian flow toward a well in a confined aquifer with and without wellbore storage. This method is based on a combination of the linearization approximation of the non-Darcian flow equation and the Laplace transform. Analytical solutions of steady-state and late time drawdowns are obtained. Semi-analytical solutions of the drawdowns at any distance and time are computed by using the Stehfest numerical inverse Laplace transform. The results of this study agree perfectly with previous Theis solution for an infinitesimal well and with the Papadopulos and Cooper’s solution for a finite-diameter well under the special case of Darcian flow. The Boltzmann transform, which is commonly employed for solving non-Darcian flow problems before, is problematic for studying radial non-Darcian flow. Comparison of drawdowns obtained by our proposed method and the Boltzmann transform method suggests that the Boltzmann transform method differs from the linearization method at early and moderate times, and it yields similar results as the linearization method at late times. If the power index n and the quasi hydraulic conductivity k get larger, drawdowns at late times will become less, regardless of the wellbore storage. When n is larger, flow approaches steady state earlier. The drawdown at steady state is approximately proportional to r1−n, where r is the radial distance from the pumping well. The late time drawdown is a superposition of the steady-state solution and a negative time-dependent term that is proportional to t(1−n)/(3−n), where t is the time. 相似文献
6.
We have derived an analytical solution for two-region flow toward a well in a confined aquifer based on a linearization method. The two-region flow includes Izbash non-Darcian flow near the well and Darcian flow in the rest of the aquifer. The wellbore storage is also considered. The type curves in the non-Darcian and Darcian flow domains are obtained by a numerical Laplace inversion method incorporated in MATLAB programs. We have compared our results with the one-region Darcian flow model (Theis). Our solutions agree with those of Sen [Sen Z. Type curves for two-region well flow. J Hydr Eng 1988;114(12):1461–84] which were obtained using the Boltzmann transform at late times for fully turbulent flow, while some difference has been found at early and moderate times. We have defined a dimensionless non-Darcian hydraulic conductivity term which is shown to be a key parameter for analyzing the two-region flow. A smaller dimensionless non-Darcian hydraulic conductivity results in a larger drawdown in the non-Darcian flow region at late times. However, the dimensionless non-Darcian hydraulic conductivity does not affect the slope of the dimensionless drawdown versus the logarithmic dimensionless time in the non-Darcian flow region at late times. The dimensionless non-Darcian hydraulic conductivity does not affect the late time drawdown in the Darcian flow region. 相似文献
7.
本文以罗斯贝方程和爱因斯坦的引力波方程为例,讨论线性化和形式分析构成的物理实在性的失落,及相应“长波”和“引力波”理论存在的问题。 相似文献
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9.
Badam Singh Kushvah 《Astrophysics and Space Science》2009,323(1):57-63
Linearization of the Hamiltonian is being performed in the generalized photogravitational Chermnykh’s problem. The normal
form of the second order part of the Hamiltonian have been found. The effect of radiation pressure, gravitational potential
from the belt have been examined analytically and numerically 相似文献
10.
André Deprit Antonio Elipe Sebastián Ferrer 《Celestial Mechanics and Dynamical Astronomy》1994,58(2):151-201
The method for processing perturbed Keplerian systems known today as the linearization was already known in the XVIIIth century; Laplace seems to be the first to have codified it. We reorganize the classical material around the Theorem of the Moving Frame. Concerning Stiefel's own contribution to the question, on the one hand, we abandon the formalism of Matrix Theory to proceed exclusively in the context of quaternion algebra; on the other hand, we explain how, in the hierarchy of hypercomplex systems, both the KS-transformation and the classical projective decomposition emanate by doubling from the Levi-Civita transformation. We propose three ways of stretching out the projective factoring into four-dimensional coordinate transformations, and offer for each of them a canonical extension into the moment space. One of them is due to Ferrándiz; we prove it to be none other than the extension of Burdet's focal transformation by Liouville's technique. In the course of constructing the other two, we examine the complementarity between two classical methods for transforming Hamiltonian systems, on the one hand, Stiefel's method for raising the dimensions of a system by means of weakly canonical extensions, on the other, Liouville's technique of lowering dimensions through a Reduction induced by ignoration of variables. 相似文献