利用伴随法优化非线性潮汐模型的开边界条件Ⅰ．伴随方程的建立及“孪生"数值试验   总被引：1，自引：1，他引：0  

韩桂军  马继瑞  刘克修  李冬 《海洋学报》2000,22(6)

本研究采用基于最优控制理论的伴随法,把观测资料同化到陆架海域潮汐数值模型中去,优化开边界条件,提高数值预报的精度．潮汐模型的控制方程为考虑平流项、非线性底摩擦和侧向涡动粘性项的非线性浅水方程组;采用Lagrange乘子法建立了伴随模型．研究分两部分：第一部分即本文,建立非线性浅水方程模型的伴随方程、给出目标函数的梯度,并实现“孪生”数值试验;第二部分另文给出．  相似文献   

Numerical simulation of transport and dispersion of side-discharged sewage in tidal flow     

Liang Shuxiu  Shen Yongming  Sun Zhaochen  Ni Haoqing 《海洋学报(英文版)》2000,19(2):137-144

  相似文献   

潮汐水域中污水侧向排放的数值模拟   总被引：5，自引：1，他引：4  

梁书秀  沈永明  孙昭晨  倪浩清 《海洋学报》2000,22(2):113-119

基于N-S方程,采用深度平均的应力-通量代数全场模型,模拟流场及热水或污染物侧向排入大水体的各向异性的输移扩散规律。模型中采用深度平均的连续、动量、浓度方程进行潮汐流动的数值模拟计算,潮流采用非对称潮流,模拟结果给出了一个周期内流场、污染物浓度场随时间的变化特征。所得的数值结果与他人的模型实验结果非常一致,而较其他结果更合理,说明本模型的合理性和可靠性。  相似文献   

关于二阶伴随模型的理论研究   总被引：9，自引：2，他引：7  

韩桂军  何柏荣  马继瑞  李冬 《海洋学报》2000,22(3):15-19

Hesse矩阵-目标函数关于控制变量的二阶偏导数形成的矩阵,在变分数据同化过程中以及敏感性分析等方面起着重要的作用;它可以通过建立数学模型的一阶和二阶伴随模型求得.以浅水方程模型为例,利用泛函的Gâteaux微分和Hilbert空间上伴随算子的概念,导出了一阶和二阶伴随模型并由此得到Hesse矩阵.改进了Zhi Wang等(1992)建立的二阶伴随模型理论.  相似文献   

三角形网格下求解二维浅水方程的和谐Godunov格式   总被引：16，自引：3，他引：13       下载免费PDF全文

潘存鸿 《水科学进展》2007,18(2):204-209

为保证计算格式的和谐性,通过特殊的底坡源项处理技术,在三角形网格上建立了求解二维浅水流动方程的具有空间二阶精度的Godunov格式。应用准确Riemann解求解法向数值通量,用改正的干底Riemann解处理动边界问题。经典型算例和钱塘江河口涌潮计算验证,表明模型健全,分辨率高,具有较大的推广应用价值。  相似文献   

A semianalytical approach for solving first-order perturbation equations of dissolution-timescale reactive infiltration instability problems in fluid-saturated rocks     

Chongbin Zhao  Bruce E. Hobbs  Alison Ord 《国际地质力学数值与分析法杂志》2020,44(15):2070-2092

This paper presents a semianalytical approach for solving first-order perturbation (FOP) equations, which are used to describe dissolution-timescale reactive infiltration instability (RII) problems in fluid-saturated rocks. The proposed approach contains two parts because the chemical dissolution reaction divides the whole problem domain into two subdomains. In the first part, the interface-condition substitution strategy is used to derive the analytical expressions of purely mathematical solutions for the FOP equations in the upstream subdomain, where the dissolution chemical reaction is ceased and the FOP equations are weakly coupled. In the second part, the finite element method (FEM) is used to derive the analytical expressions of numerical solutions for the FOP equations in the downstream subdomain, where the dissolution chemical reaction needs to be considered and the FOP equations are strongly coupled so that it is impossible to derive purely mathematical solutions for them. Particular attention is paid to the development of the element-by-element forward marching strategy, which is associated with the use of the FEM for solving this new kind of scientific problem. The related analytical results demonstrated that (1) both the dynamic characteristic of a reactive infiltration system and the dimensionless wavenumber can have pronounced influences on the distribution of the FOP dimensionless acid concentration within the entire domain of the dissolution-timescale RII problems in fluid-saturated rocks and (2) the FOP dimensionless acid concentration distribution exhibits two significantly different patterns in the upstream and downstream subdomains of the dissolution-timescale RII system.  相似文献   

Hamilton's equations of motion for non-conservative systems     

Frank Thomas Tveter 《Celestial Mechanics and Dynamical Astronomy》1994,60(4):409-419

This paper deals with the Hamilton equations of motion and non conservative forces. The paper will show how the Hamilton formalism may be expanded so that the auxiliary equations for any problem may be found in any set of canonical variables, regardless of the nature of the forces involved. Although the expansion does not bring us closer to an analytical solution of the problem, it's simplicity makes it worth noticing.The starting point is a conservative system (for instance a satellite orbiting an oblate planet) with a known Hamiltonian (K) and canonical variables {Q, P}. This system is placed under influence of a non-conservative force (for instance drag-force). The idea is then to use, as far as possible, the same definitions used in the conservative problem, in the process of finding the auxiliary equations for the perturbed system.  相似文献   

关于正确建立渗流数学模型的若干问题     

郭东屏 《地球科学与环境学报》1988,(4)

在某些文献中,有原则性问题的渗流数学模型不乏其见。本文什对问题发生的原因,论述了关于正确建立渗流数学模型的若干要点,给出了体现要点的若干实例分析。  相似文献   

Figures of equilibrium in close binary systems     

J. A. López Ortí  A. López García  R. López Machí 《Celestial Mechanics and Dynamical Astronomy》1992,53(4):311-322

The equilibrium configurations of close binary systems are analyzed. The autogravitational, centrifugal and tidal potentials are expanded in Clairaut's coordinates. From the set of the total potential angular terms an integral equations system is derived. The reduction of them to ordinary differential equations and the determination of the boundary conditions allow a formulation of the problem in terms of a single variable.  相似文献   

Wavelet analysis and applications to some dynamical systems     

Ph. Bendjoya  E. Slezak 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):231-262

For about five years the wavelet transform technique has given interesting results in a great number of different fields such as mathematics, quantum mechanics, signal analysis and image processing, cluster analysis... The wavelet transform appears as a new time-frequency method which is particularly well-suited to detect and to localize discontinuities and scaling behaviours in signals. The main properties of the wavelet transform and its improvements over classical analyzing methods are summarized. Some results among the first applications to the dynamical systems are presented: solution of partial differential equations, fractal and turbulence characterization, and asteroid family determination from cluster analysis.  相似文献