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1.
本文提出了一种计算不规则起伏地形中SH波散射的有效方法——局域边界元法.本方法基于传统边界元法,为计算复杂地表散射问题提供了一种更加高效的解决方案.根据地震波满足的边界积分方程中牵引力格林函数的特性,我们将自由边界分解成水平部分和起伏部分.通过公式推导,可将水平部分的位移由起伏部分的位移通过格林函数线性叠加表示,因此只需对起伏部分的位移进行直接求解,从而极大地减少了待求解的未知数个数,显著提高了计算效率.通过与半圆形山谷SH波平面波入射的解析解比较,验证了方法的正确性.数值模型比较显示,局域边界元模拟结果与传统边界元数值解完全吻合,但是大幅提高了计算效率.因此,局域边界元法可以作为模拟不规则地形中地震波散射的有效工具. 相似文献
2.
Kinematic equations have been utilized in the past for modeling erosion from a sloping plane subject to rainfall. This paper, part I in a series of two, presents analytical solutions of these equations under the assumption of constant effective rainfall of indefinite duration. These solutions contain a function which is related to a generalization of Dawson's integral. Some pertinent properties of this function are briefly discussed. The solutions obtained by previous investigators constitute a part of the solutions developed here. In part II the solutions are derived for the case when the duration of the effective rainfall is finite. 相似文献
3.
The role of hand calculations in ground water flow modeling 总被引：1，自引：0，他引：1
Haitjema H 《Ground water》2006,44(6):786-791
Most ground water modeling courses focus on the use of computer models and pay little or no attention to traditional analytic solutions to ground water flow problems. This shift in education seems logical. Why waste time to learn about the method of images, or why study analytic solutions to one-dimensional or radial flow problems? Computer models solve much more realistic problems and offer sophisticated graphical output, such as contour plots of potentiometric levels and ground water path lines. However, analytic solutions to elementary ground water flow problems do have something to offer over computer models: insight. For instance, an analytic one-dimensional or radial flow solution, in terms of a mathematical expression, may reveal which parameters affect the success of calibrating a computer model and what to expect when changing parameter values. Similarly, solutions for periodic forcing of one-dimensional or radial flow systems have resulted in a simple decision criterion to assess whether or not transient flow modeling is needed. Basic water balance calculations may offer a useful check on computer-generated capture zones for wellhead protection or aquifer remediation. An easily calculated "characteristic leakage length" provides critical insight into surface water and ground water interactions and flow in multi-aquifer systems. The list goes on. Familiarity with elementary analytic solutions and the capability of performing some simple hand calculations can promote appropriate (computer) modeling techniques, avoids unnecessary complexity, improves reliability, and is likely to save time and money. Training in basic hand calculations should be an important part of the curriculum of ground water modeling courses. 相似文献
4.
《Advances in water resources》2002,25(3):279-291
An analytical approach is presented for solving problems of steady, two-dimensional groundwater flow with inhomogeneity boundaries. A common approach for such problems is to separate the problem domain into two homogeneous domains, search for solutions in each domain, and then attempt to match conditions, either exactly or approximately, along the inhomogeneity boundary. Here, we use classical solutions to problems with inhomogeneity boundaries with simple geometries, and map conformally the entire domain onto a new one. In this way, existing solutions are used to solve problems with more complex, and more practical, boundary geometries. The approach is general, but subject to some restrictions on the mapping functions that may be used.Using this approach, we develop explicit analytical solutions for two problems of practical interest. The first problem addresses aquifer interaction across a gap in an impermeable separating layer; flow regimes are defined and the interaction is quantified. The second solution represents flow in the vertical plane to a partially clogged stream bed that is partially penetrating the aquifer; the stream bed is modeled as a thin layer of low-permeability silt. Flow regimes for groundwater surface–water interaction are quantified analytically. 相似文献
5.
David E. Dougherty 《Ground water》1989,27(4):564-569
Abstract. Type curves, and drawdown analysis curves of other sorts, have a well-established position in the ground-water profession. Although a plethora of solutions to well hydraulics problems exists, many of these arc not available in useful type curve formats. lpurthcr, if one wants to perform parameter estimation using many of these solutions, a computer-based form of the solution is needed. Those who have programmed analytical solutions know the difficulties that will be encountered in coding even the most innocuous-looking result. In this paper, a computer-based method of type curve generation is prcscnted based on Stehfest's method of inverting the Laplace transform solution of ground-water flow problems. The latter are usually easier to obtain than a complete closed-form solution. The method is very robust for a large class of well hydraulics problems. A companion diskette with FORTRAN source and executable example program is available from the author. 相似文献
6.
Multi‐objective particle swarm optimization for generating optimal trade‐offs in reservoir operation
A multi‐objective particle swarm optimization (MOPSO) approach is presented for generating Pareto‐optimal solutions for reservoir operation problems. This method is developed by integrating Pareto dominance principles into particle swarm optimization (PSO) algorithm. In addition, a variable size external repository and an efficient elitist‐mutation (EM) operator are introduced. The proposed EM‐MOPSO approach is first tested for few test problems taken from the literature and evaluated with standard performance measures. It is found that the EM‐MOPSO yields efficient solutions in terms of giving a wide spread of solutions with good convergence to true Pareto optimal solutions. On achieving good results for test cases, the approach was applied to a case study of multi‐objective reservoir operation problem, namely the Bhadra reservoir system in India. The solutions of EM‐MOPSOs yield a trade‐off curve/surface, identifying a set of alternatives that define optimal solutions to the problem. Finally, to facilitate easy implementation for the reservoir operator, a simple but effective decision‐making approach was presented. The results obtained show that the proposed approach is a viable alternative to solve multi‐objective water resources and hydrology problems. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
7.
Ioannis K. Nikolos Maria Stergiadi Maria P. Papadopoulou George P. Karatzas 《水文研究》2008,22(17):3337-3348
Classical optimization methodologies based on mathematical theories have been developed for the solution of various constrained environmental design problems. Numerical models have been widely used to represent an environmental system accurately. The use of methodologies such as artificial neural networks (ANNs), which approximate the complicated behaviour and response of physical systems, allows the optimization of a large number of case scenarios with different set of constraints within a short period of time, whereas the corresponding simulation time using a numerical model would be prohibitive. In this paper, a combination of an ANN with a differential evolution algorithm is proposed to replace the classical finite‐element numerical model in water resources management problems. The objective of the optimization problem is to determine the optimal operational strategy for the productive pumping wells located in the northern part of Rhodes Island in Greece, to cover the water demand and maintain the water table at certain levels. The conclusions of this study show that the use of ANN as an approximation model could (a) significantly reduce the computational burden associated with the accurate simulation of complex physical systems and (b) provide solutions very close to the optimal ones for various constrained environmental design problems. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
8.
The riparian zone is in intimate contact with the river and, as such, is a critical zone for understanding hydrological problems. This paper presents a general modelling methodology for the assessment of riparian hydrological processes. It is applicable to a wide range of riparian spaces and incorporates current expertise in numerical methods. A core part of the modelling methodology is the random walk particle method (RWPM). We develop an RWPM as part of the ESTEL2D subsurface flow model, test it against analytical solutions and apply it to the simulation of parcels of water as they move through the riparian zone. The modelling methodology provides a new opportunity to assess fundamental hydrological process issues such as the proportioning of pre‐event and event water storm runoff, and reversals of flow in floodplains. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
9.
This is Part-II of a two-part article that presents analytical solutions to multi-species reactive transport equations coupled through sorption and sequential first-order reactions. In Part-I, we provide the mathematical derivations and in this article we discuss the computational techniques for implementing these solutions. We adopt these techniques to develop a general computer code and use it to verify the solutions. We also simplify the general solutions for various special-case transport scenarios involving zero initial condition, identical retardation factors and zero advection. In addition to this, we derive specialized solution expressions for zero dispersion and steady-state conditions. Whereever possible, we compare these special-case solutions against previously published analytical solutions to establish the validity of the new solution. Finally, we test the new solution against other published analytical and semi-analytical solutions using a set of example problems. 相似文献
10.
Boundary-value problems (BVPs) for seismic rays generally have multiple solutions. In practical applications the number of solutions can be large. The algorithm presented below solves a one-parameter family of BVPs and makes it easy to obtain all the solutions of a BVP. 相似文献
11.
The role played by the diffraction field on the problem of seismic site effects is studied. For that purpose we solve and analyze simple scattering problems under P and SV in-plane wave assumptions, using two well known direct boundary-element-based numerical methods. After establishing the difference between scattered and diffracted motions, and introducing the concept of artificious and physically based incoming fields, we obtain the amplitude of the Fourier spectra for the diffracted part of the response: this is achieved after establishing the connection between the spatial distribution of the transfer function over the studied simple topographies and the diffracted field. From the numerical simulations it is observed that this diffracted part of the response is responsible for the amplification of the surface ground motions due to the geometric effect. Furthermore, it is also found that the diffraction field sets in a fingerprint of the topographic effect in the total ground motions. These conclusions are further supported by observations in the time-domain in terms of snapshots of the propagation patterns over the complete computational model. In this sense the geometric singularities are clearly identified as sources of diffraction and for the considered range of dimensionless frequencies it is evident that larger amplifications are obtained for the geometries containing a larger number of diffraction sources thus resulting in a stronger topographic effect. The need for closed-form solutions of canonical problems to construct a robust analysis method based on the diffraction field is identified. 相似文献
12.
Auroral electron transport calculations are a critical part of auroral models. We evaluate a numerical solution to the transport and energy degradation problem. The numerical solution is verified by reproducing simplified problems to which analytic solutions exist, internal self-consistency tests, comparison with laboratory experiments of electron beams penetrating a collision chamber, and by comparison with auroral observations, particularly the emission ratio of the N2 second positive to N+ 2 first negative emissions. Our numerical solutions agree with range measurements in collision chambers. The calculated N22P to N+ 21N emission ratio is independent of the spectral characteristics of the incident electrons, and agrees with the value observed in aurora. Using different sets of energy loss cross sections and different functions to describe the energy distribution of secondary electrons that emerge from ionization collisions, we discuss the uncertainties of the solutions to the electron transport equation resulting from the uncertainties of these input parameters. 相似文献
13.
Harn C. Chen 《地震工程与结构动力学》1993,22(1):63-74
An efficient numerical algorithm is developed to solve the quadratic eigenvalue problems arising in the dynamic analysis of damped structural systems. The algorithm can even be applied to structural systems with non-symmetric matrices. The algorithm is based on the use of Arnoldi's method to generate a Krylov subspace of trial vectors, which is then used to reduce a large eigenvalue problem to a much smaller one. The reduced eigenvalue problem is solved and the solutions are used to construct approximate solutions to the original large system. In the process, the algorithm takes full advantage of the sparseness and symmetry of the system matrices and requires no complex arithmetic, therefore, making it very economical for use in solving large problems. The numerical results from test examples are presented to demonstrate that a large fraction of the approximate solutions calculated are very accurate, indicating that the algorithm is highly effective for extracting a number of vibration modes for a large dynamic system, whether it is lightly or heavily damped. 相似文献
14.
Analytical solutions to debris avalanche problems involving shock waves are derived. The debris avalanche problems are described in two different coordinate systems, namely, the standard Cartesian and topography-linked coordinate systems. The analytical solutions can then be used to test debris avalanche numerical models. In this article, finite volume methods are applied as the numerical models. We compare the performance of the finite volume method with reconstruction of the conserved quantities based on stage, height, and velocity to that of the conserved quantities based on stage, height, and momentum for solving the debris avalanche problems involving shock waves. The numerical solutions agree with the analytical solution. In addition, both reconstructions lead to similar numerical results. This article is an extension of the work of Mangeney et al. (Pure Appl Geophys 157(6–8):1081–1096, 2000). 相似文献
15.
Moshe Sniedovich 《Advances in water resources》1978,1(4):183-190
The dynamic programming recursive procedure has provided an efficient method for solving a variety of sequential decision problems related to water resources systems. In many investigations Bellman's principle of optimality is used as a proof for the optimality of the dynamic programming solutions. In this paper the dynamic programming procedure is systematically studied so as to clarify the relationship between Bellman's principle of optimality and the optimality of the dynamic programming solutions.Our main result is that although the principle is valid, in order to use it as a proof for the optimality of the dynamic programming solution certain modeling requirements should be met.The mathematical model presented in this paper provides a convenient framework for the modeling and analysis of dynamic programming problems encountered by in water resources management studies.The results derived here resolve few of the fundamental questions raised in the literature regarding the validity of Bellman's principle of oplimality and the optimality of the dynamic programming solutions. 相似文献
16.
《Advances in water resources》2001,24(6):667-676
Gradient-based nonlinear programming (NLP) methods can solve problems with smooth nonlinear objectives and constraints. However, in large and highly nonlinear models, these algorithms can fail to find feasible solutions, or converge to local solutions which are not global. Evolutionary search procedures in general, and genetic algorithms (GAs) specifically, are less susceptible to the presence of local solutions. However, they often exhibit slow convergence, especially when there are many variables, and have problems finding feasible solutions in constrained problems with “narrow” feasible regions. In this paper, we describe strategies for solving large nonlinear water resources models management, which combine GAs with linear programming. The key idea is to identify a set of complicating variables in the model which, when fixed, render the problem linear in the remaining variables. The complicating variables are then varied by a GA. This GA&LP approach is applied to two nonlinear models: a reservoir operation model with nonlinear hydropower generation equations and nonlinear reservoir topologic equations, and a long-term dynamic river basin planning model with a large number of nonlinear relationships. For smaller instances of the reservoir model, the CONOPT2 nonlinear solver is more accurate and faster, but for larger instances, the GA&LP approach finds solutions with significantly better objective values. The multiperiod river basin model is much too large to be solved in its entirety. The complicating variables are chosen here so that, when they are fixed, each period's model is linear, and these models can be solved sequentially. This approach allows sufficient model detail to be retained so that long-term sustainability issues can be explored. 相似文献
17.
The fundamental solutions of axisymmetric elastodynamic problem for the multilayered half-space due to an impulsive ring source acting within a layered elastic media are derived in time domain with the aid of Laplace–Hankel mixed transform and transfer matrix techniques. In addition, an effective numerical procedure, which utilizes the fast Hankel transform algorithm, is also proposed to calculate these solutions. Illustrative examples have been given to demonstrate that the fundamental solutions can be readily evaluated and the numerical results are of high accuracy. The present solutions can be directly applied to determine the transient wave fields caused by a seismic source and show the potential application to the elastodynamic problems solved by the boundary element method. 相似文献
18.
Numerical simulation of an unsaturated flow equation 总被引：1，自引：1，他引：0
A numerical model for an unsaturated flow problem by using the finite element method is established in order to simulate liquid
moisture flow In an unsaturated zone with homogeneous soil and deep subsurface water, and with different initial and boundary
conditions. For infiltration or evaporation problems, a traditional method usually yields oscillatory non-physics profiles.
However, nonoscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped
finite element method. Moreover, the kind of boundary condition is handled very well.
Project supported by the National Key Project of Fundamental Research ”Climate Dynamics and Climate Prediction Theory“ and
China Postdoctoral Science Foundation. 相似文献
19.
Fault plane solutions in Sichuan-Yunnan rhombic block and their dynamic implications 总被引：1，自引：1，他引：1
Harvard Centroid Moment Tensor (CMT) solutions for earthquakes from 1977 to 2004 showed that the stress fields are obviously different in northwestern Sichuan sub-block (NWSSB), western parts of Central Yunnan sub-block (CYSB) and eastern part of CYSB. The characteristics of the mean stress fields in these three regions are obtained by fitting to CMT solutions. The stress state in NWSSB is characterized by its sub-horizontal tensile principal axis of stress (T axis) in roughly N-S direction and west dipping compressive principal axis of stress (P axis); the one in western part of CYSB is characterized by its ENE dipping T axis and sub-horizontal medium prin-cipal axis of stress (B axis) in roughly N-S direction; the one in eastern part of CYSB is characterized by its sub-horizontal P axis in roughly NNW-SSE direction and sub-horizontal T axis in roughly WSW-ENE direction. Finite element method simulation clearly shows that the Indian Plate imposes great extrusion on Sichuan-Yunnan rhombic block (SYRB) near Assam massif. The value of the simulated compressive principal stress decreases with the distance from Assam massif. The simulated directions of the T axes in SYRB form annular distribution encir-cling Assam. For a homogeneous elastic medium with free boundary conditions on the top and bottom surfaces as well as the displacement boundary conditions derived from the GPS observations on the lateral boundaries, the computation results are consistent with the Harvard CMT solutions in NWSSB and western part of CYSB, while inconsistent with the Harvard CMT solutions in eastern part of CYSB. The inconsistency in eastern part of CYSB can be reduced when it includes inhomogeneous elastic media. The stress states in NWSSB and western part of CYSB revealed by the Harvard CMT solutions are not local, which are mainly controlled by the boundary force on the whole region. On the other hand, the stress state in eastern part of CYSB given by the Harvard CMT solutions is local, which may be affected by local topography, material inhomogeneity, and the drag force underneath. 相似文献
20.
美国哈佛大学1977——2004年的矩心矩张量结果显示, 我国川西北次级地块、 滇中次级地块的西部及滇中次级地块的东部的应力场特征有明显的差别. 应用滑动矢量拟合法, 反演了这三个区域的应力场特征: 川西北次级地块以近南北向的水平主张应力轴和西倾的主压应力轴为特征; 滇中次级地块的西部以倾向北东东的主张应力轴以及近南北的水平中等主应力轴为特征; 滇中次级地块的东部以南西西——北东东向的水平主张应力轴以及北北西——南南东向的水平主压应力轴为特征. 有限元模拟结果清楚地显示出, 川滇地块在阿萨姆楔附近受到来自印度板块的强烈挤压, 随着远离阿萨姆楔, 这种挤压应力逐渐衰减; 同时, 该地区的主张应力方向明显地形成了围绕阿萨姆楔的环线. 其中, 内部物质性质均匀、 地表和底部边界自由、 侧部边界采用GPS观测约束的弹性有限元模拟显示, 在川西北次级地块, 模拟结果与震源机制解结果相一致; 在滇中次级地块, 模拟结果所显示的图象与震源机制解观测结果有差别, 不仅没有显示出与大面积的东部地区的震源机制解相一致的特征, 反而显示出与该地区西部震源机制解相一致的特征. 通过调节地块内部物质的弹性常数, 可以实现在滇中次级地块东部部分地区出现与震源机制 相似文献