求解二阶线性常微分方程的一个显式差分格式

在求解常微分方程的方法中,有限差分法是使用最广泛的方法之一。考虑一个二阶线性常微分方程的边值问题,利用有限差分法,建立了一个具有二阶精度的显式差分格式。首先,通过讨论该显式差分格式的系数矩阵,证明了该显式差分格式解的存在性。然后,通过定义的3种不同范数之间的关系,证明了显式差分格式解的收敛性和稳定性。最后,通过计算机编程对实例的计算,验证了该显式差分格式的数值结果具有二阶精度,并且该显式格式数值结果绘制的图形稳定、光滑,与解析结果吻合较好。     

求解二阶线性常微分方程的一个显式差分格式

在求解常微分方程的方法中,有限差分法是使用最广泛的方法之一。考虑一个二阶线性常微分方程的边值问题,利用有限差分法,建立了一个具有二阶精度的显式差分格式。首先,通过讨论该显式差分格式的系数矩阵,证明了该显式差分格式解的存在性。然后,通过定义的3种不同范数之间的关系,证明了显式差分格式解的收敛性和稳定性。最后,通过计算机编程对实例的计算,验证了该显式差分格式的数值结果具有二阶精度,并且该显式格式数值结果绘制的图形稳定、光滑,与解析结果吻合较好。     

地下水流的有限分析数值解

本文介绍了一种求解地下水流问题的有限分析法,该方法将解析解结合到数值方法中,从而提高了计算精度,改善了稳定性。算例表明,在网格尺寸相同的情况下,有限分析解比有限差分解高一个数量级,与解析解吻合很好。     

ADI BAROTROPIC OCEAN MODEL FOR SIMULATON OF KUROSHIO INTRUSION INTO CHINA SOUTHEASTERN WATERS

In this numerical model for simulating the Kuroshio intrusion into the East and South China Seas,vertically averaged marine hydrodynamic equations governing ocean currents and long-period waves areapproximated by a set of two-time-level semi-implicit finite difference equations. The major terms in-cluding the local acceleration, sea-surface slope, Coriolis force and the bottom friction are approxi-mated with the Crank-Nicholson scheme, which is of second order accuracy. The advection terms are app-roximated with the Leith scheme. The difference equations are split into two sets of alternating directionimplicit quations, each of which has a tridiagonal matrix and can be easily solved. The model reproduces a major Kuroshio intrusion north of Luzon Island, one north of Taiwan Island, andone west of the Tokara Strait. The model shows a current system running from the Luzon Strait to the coastof Vietnam and Hainan Island, through the Taiwan Strait and then into the Tsushima Strait. The summerand winter monso     

Accuracy of the staggered-grid finite-difference method of the acoustic wave equation for marine seismic reflection modeling

Seismic wave modeling is a cornerstone of geophysical data acquisition, processing, and interpretation, for which finite-difference methods are often applied. In this paper, we extend the velocity-pressure formulation of the acoustic wave equation to marine seismic modeling using the staggered-grid finite-difference method. The scheme is developed using a fourth-order spatial and a second-order temporal operator. Then, we define a stability coefficient (SC) and calculate its maximum value under the stability condition. Based on the dispersion relationship, we conduct a detailed dispersion analysis for submarine sediments in terms of the phase and group velocity over a range of angles, stability coefficients, and orders. We also compare the numerical solution with the exact solution for a P-wave line source in a homogeneous submarine model. Additionally, the numerical results determined by a Marmousi2 model with a rugged seafloor indicate that this method is sufficient for modeling complex submarine structures.     

承压稳定井流的有限分析方程

本文根据井在节点与不在节点两种情形，给出了承压稳定井流的有限分析方程．计算结果表明，在网格尺寸相同的条件下，有限分析方法给出的结果比有限差分法高一个数量级，且与解析解拟合甚好．     

A numerical model for tidal currents in the Changjiang River estuary

A generalized finite difference scheme is presented for the solution of two-dimensioned tidal current equations (averaged over the depth of water). This method has been used to simulate the tidal currents in the Changjiang River estuary, with computed results being in good agreement with the field observations. The two-dimensional domain consists of triangular elements with acute angles. First- and second-order partial derivatives are defined at nodal points. In addition, the basic tidal current equations contain an extra term to account for horizontal eddy viscosity. The method has the great advantage of allowing a wide flexibility in configuration simulation, thereby exhibiting the capability to arbitrarily subdivide the region of interest as well as to provide a more accurate boundary shape, and what is more, it offers savings in computing costs. This paper was published in Chinese in the Ocean. et Limn. Sinica.16(1):18–27, 1985     

瞬变电磁法三维模拟计算研究进展

瞬变电磁法应用于矿产资源、环境工程等领域.目前主流的瞬变电磁三维正演模拟方法包括积分方程法、有限差分法、有限体积法和有限元法.随着观测环境的复杂化以及探测精度要求的提高,有必要研究瞬变电磁法高精度三维模拟计算,以便推动数据处理解释方法的进步.本文系统介绍了瞬变电磁三维正演计算研究进展,分析了准静态差分方程的构建和发射源...     

ADI barotropic ocean model for simulation of Kuroshio intrusion into China southeastern waters

In this numerical model for simulating the Kuroshio intrusion into the East and South China Seas, vertically averaged marine hydrodynamic equations governing ocean currents and long-period waves are approximated by a set of two-time-level semi-implicit fimite difference equations. The major terms including the local acoeleration, sea-surface slope, Coriolis force and the bottom friction are approximated with the Crank-Nicholson scheme, which is of second order accuracy. The advection terms are approximated with the Leith scheme. The difference equations are split into two sets of alternating direction implicit equations, each of which has a tridiagonal matrix and can be easily solved. The model reproduces a major Kuroshio intrusion north of Luzon Island, one north of Taiwan Island, and one west of the Tokara Strait. The model shows a current system running from the Luzon Strait to the coast of Vietnam and Hainan Island, through the Taiwan Strait and then into the Tsushima Strait. The summer and winter monsoons generate several eddies in the South China Sea. Project supported by the National Natural Science Foundation of China.     

重磁线性反演的正则化方法

重磁线性反演最后都要归结于解数据方程。由于重磁数据方程是奇异方程,通常大多数解方程组的方法都失效。因此,本文采用了正则化方法,通过模型试验,证明了该方法具有解奇异方程和压制高频干扰的功能。为了保证反演结果的可靠,本文提出了一套比较可行的处理资料过程。最后,反演计算了山西太原盆地的莫霍面和居里等温而,其结果与已有的地质、地球物理资料相吻合。     

Dynamic process simulation with a Savage-Hutter type model for the intrusion of landslide into river

Natural damming of rivers by mass movements is a very common and potentially dangerous phenomena which has been documented all over the world. In this paper, a two-layer model of Savage-Hutter type is presented to simulate the dynamic procedure for the intrusion of landslide into rivers. The two-layer shallow water system is derived by depth averaging the incompressible Navier-Stokes equations with the hydrostatic assumption. A high order accuracy scheme based on the finite volume method is proposed to solve the presented model equations. Several numerical tests are performed to verify the realiability and feasibility of the proposed model. The numerical results indicate that the proposed method can be competent for simulating the dynamic process of landslide intrusion into the river. The interaction effect between both layers has a significant impact on the landslide movement, water fluctuation and wave propagation.     

高精度曲面建模的一种快速算法

 高精度曲面建模(HASM)是一种全新的曲面建模方法,其整个过程可分为偏微分方程的离散、采样方程建立和代数方程组求解3个阶段。目前所采用的求解对称正定方程组的方法主要是共轭梯度法。为了解决HASM的计算速度问题,本文给出了2种新的预处理共轭梯度算法,分别为不完全Cholesky分解共轭梯度法和对称逐步超松弛预处理共轭梯度法。实验表明,不完全Cholesky分解共轭梯度法收敛速度最快,且这2种预处理方法均比其他方法具有更快的收敛速度。     

基于有限元修正节理岩质边坡稳定性计算的解析解

采用有限元方法探讨在人工开挖或自然侵蚀环境下,岩质边坡体内应力场的变化及节理发育形成机理,并采用有限元强度折减法对后缘具有张节理边坡的稳定性影响因素进行敏感性对比分析,进而得出具有非贯通节理边坡稳定性计算的修正解析解.结果表明:卸荷及风化作用导致边坡体由表及里出现应力重分布及应力集中的现象,使边坡后缘由顶部向下发育一簇...     

A FINITE ELEMENT SHALLOW WATER CIRCULATION MODEL FOR TOLO HARBOUR, HONG KONG

Numerical solution of two-dimensional shallow water equations has been achieved by the finite element method. In this work, the governing equations were first converted into different equations suitable for explicit, forward marching, integration in the time domain. A second order Taylor's series expansion was used for the continuity equation and an "upwind" differencing was incorporated in the nonlinear convective terms in the momentum equations.The model was applied to Tolo Harbour in Hong Kong. Velocity vector plots and surface elevations obtained from the calculations are reasonably consistent with the expected tidal response of the systems.     

CHARACTER OF SIMPLIFIED NAVIER-STOKES EQUATIONS FOR NEAR THE LEADING EDGE PART OF TWO-DIMENSIONAL LAMINAR FLOW PAST A FLAT PLATE

Starting from the Simplified Navier-Stokes(SNS)equations presented at first by Godovachev-Kuzmin-Tsopov,and Gao Zhi,Davis,the authors analyze the character of the SNS equations for the laminarflow near the leading edge of a flat plate and far away from the plate by using the Weiner—Hopf meth-od and Fourier transform.It is proved that the solution of the SNS equations agree with the solution of the Navier-Stokes equations for flow near the leading edge of the plate and far away from the plate.How to match the solution of the SNS equations to the Blasius solution of the boundary layer equationsis also discussed.     

基于量子纠缠时钟测量的抗差卡尔曼卫星钟差预报

基于纠缠光子对二阶相关函数的时间特性分析,设计时钟同步测量方案,并考虑传播过程中色散效应及衰减等对精度的影响。该方案可提供均值1 ns、精度0.01 ns的同步信息。利用该方案获得观测数据,结合顾及哈达玛方差的抗差卡尔曼方法估计出卫星钟差模型系数,进行钟差预测。仿真表明,该方案预测精度与IGS预报星历产品精度相当,且钟差初始值更精确。     

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基于DEM的5节点二阶差分坡度算法模型与实验分析

 坡度作为最基本的地形因子,是构建地学分析模型的基础数据,基于格网DEM的坡度计算模型的精度分析一直是地学分析的重要研究内容。本文通过分析计算坡度的 差分模型误差来源及特征,提出了一种新的模型——5节点二阶差分模型。其基本思想是顾及多距离邻近点高程信息,采用5×5分析窗口,建立单倍格网和两倍格网的差分计算线性组合模型。并通过数学分析的理论推导证明该模型可以显著提高计算精度。实验选取典型数学曲面并对其采用不同的分辨率(1m和5m)进行离散化精度验证。计算结果表明,与现有的差分模型相比,5节点二阶差分模型可以显著提高坡度的精度,对应于两种分辨率的DEM,该模型计算坡度的精度可以分别提高7×10⁴倍、3×10³倍以上,表明该模型对于高分辨率DEM数据更为适用。本研究不仅丰富了数字地形分析的方法体系,为相关地学模型分析提供更精确的坡度数据,而且为将来改进地形曲率因子等计算模型提供了一定的参 考和借鉴。     

GNSS水汽层析的约束条件方程变权代数重构算法

基于传统代数重构算法（algebraic reconstruction technique, ART）提出一种约束条件方程变权的代数重构算法(variable weight algebraic reconstruction technique, VWART),利用2019-08香港地区CORS网GNSS观测数据进行实验,选用京士柏探空气象站探空数据进行验证分析。结果表明,相比于传统代数重构算法,变权代数重构算法的精度、稳定性和可靠性均有所提高。以探空数据为例,其RMSE降低20.334%;在不同程度降水条件下,变权代数重构算法反演的垂直水汽廓线分布均优于传统代数重构算法。     

基于信息损失量的坡度精度分析

从DEM中可获取众多地形因子。其中,坡度作为基本的地形因子,其精度对于退耕还林、水土流失评估等研究具有重要影响。但是,由于DEM只能是真实地表形态的近似表达。如何模拟坡度误差的规律成为研究的热点。本文在黄土高原地区选取代表不同地貌类型的神木、绥德、延川、富县和宜君5个研究样区,以1:1万地形图为基本数据源,建立不同分辨率的DEM,用以分析坡度信息损失量随DEM分辨率变化的规律。故此,提出了基于单个栅格方式的坡度信息量损失指标,并在每一样区随机选取的20个子实验样区得到了其与DEM分辨率的函数关系,以及相关的经验公式,据此求得所需的最适宜DEM分辨率,并在每一样区随机地选取16个子样区进行了检验。