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1.
《Advances in water resources》2005,28(8):793-806
In this paper, the numerical errors associated with the finite difference solutions of two-dimensional advection–dispersion equation with linear sorption are obtained from a Taylor analysis and are removed from numerical solution. The error expressions are based on a general form of the corresponding difference equation. The variation of these numerical truncation errors is presented as a function of Peclet and Courant numbers in X and Y direction, a Sink/Source dimensionless number and new form of Peclet and Courant numbers in X–Y plane. It is shown that the Crank–Nicolson method is the most accurate scheme based on the truncation error analysis. The effects of these truncation errors on the numerical solution of a two-dimensional advection–dispersion equation with a first-order reaction or degradation are demonstrated by comparison with an analytical solution for predicting contaminant plume distribution in uniform flow field. Considering computational efficiency, an alternating direction implicit method is used for the numerical solution of governing equation. The results show that removing these errors improves numerical result and reduces differences between numerical and analytical solution. 相似文献
2.
A generalized transformation approach for simulating steady-state variably-saturated subsurface flow
A numerical method is proposed to accurately and efficiently compute a direct steady-state solution of the nonlinear Richards equation. In the proposed method, the Kirchhoff integral transformation and a complementary transformation are applied to the governing equation in order to separate the nonlinear hyperbolic characteristic from the linear parabolic part. The separation allows the transformed governing equation to be applied to partially- to fully-saturated systems with arbitrary constitutive relations between primary (pressure head) and secondary variables (relative permeability). The transformed governing equation is then discretized with control volume finite difference/finite element approximations, followed by inverse transformation. The approach is compared to analytical and other numerical approaches for variably-saturated flow in 1-D and 3-D domains. The results clearly demonstrate that the approach is not only more computationally efficient but also more accurate than traditional numerical solutions. The approach is also applied to an example flow problem involving a regional-scale variably-saturated heterogeneous system, where the vadose zone is up to 1 km thick. The performance, stability, and effectiveness of the transform approach is exemplified for this complex heterogeneous example, which is typical of many problems encountered in the field. It is shown that computational performance can be enhanced by several orders of magnitude with the described integral transformation approach. 相似文献
3.
《Advances in water resources》2007,30(4):927-936
A nonlinear model for single-phase fluid flow in slightly compressible porous media is presented and solved approximately. The model assumes state equations for density, porosity, viscosity and permeability that are exponential functions of the fluid (either gas or liquid) pressure. The governing equation is transformed into a nonlinear diffusion equation. It is solved for a semi-infinite domain for either constant pressure or constant flux boundary conditions at the surface. The solutions obtained, although approximate, are extremely accurate as demonstrated by comparisons with numerical results. Predictions for the surface pressure resulting from a constant flux into a porous medium are compared with published experimental data. 相似文献
4.
The secret to successful solute-transport modeling 总被引：6，自引：0，他引：6
Konikow LF 《Ground water》2011,49(2):144-159
5.
极低屈服点软钢阻尼器恢复力模型的研究 总被引：3，自引：0，他引：3
本文通过试验和理论分析探讨极低屈服点软钢阻尼器的恢复力特性。随着塑性变形的发展将恢复力模型中的骨架曲线进行平移,其卸载曲线用Ramberg—Osgood函数来描述,由此得到的恢复力模型定义为骨架平移模型,将其应用于描述极低屈服点软钢阻尼器的恢复力特性、为了验证该馍型的有效性并确定合理的参数,对安装极低屈服点软钢阻尼器的3层钢框架结构进行了拟动力试验．同时用该骨架平移模型模拟极低屈服点软钢阻尼器的恢复力特性进行了大量的弹塑性地震反应分析,通过取用不同平移系数时的数值计算结果与拟动力试验结果的比较,发现平移系数为0．6左右时,该模型具有较高的精度。 相似文献
6.
《Advances in water resources》1998,21(3):237-249
The transport and fate of reactive chemicals in groundwater is governed by equations which are often difficult to solve due to the nonlinear relationship between the solute concentrations for the liquid and solid phases. The nonlinearity may cause mass balance errors during the numerical simulation in addition to numerical errors for linear transport system. We have generalized the modified Picard iteration algorithm of Celia et al.5 for unsaturated flow to solve the nonlinear transport equation. Written in a ‘mixed-form’ formulation, the total solute concentration is expanded in a Taylor series with respect to the solution concentration to linearize the transport equation, which is then solved with a conventional finite element method. Numerical results of this mixed-form algorithm are compared with those obtained with the concentration-based scheme using conventional Picard iteration. In general, the new solver resulted in negligible mass balance errors (< ∥10−8∥%) and required less computational time than the conventional iteration scheme for the test examples, including transport involving highly nonlinear adsorption under steady-state as well as transient flow conditions. In contrast, mass balance errors resulting from the conventional Picard iteration method were higher than 10% for some highly nonlinear problems. Application of the modified Picard iteration scheme to solve the nonlinear transport equation may greatly reduce the mass balance errors and increase computational efficiency. 相似文献
7.
This paper presents the development of a new type of pseudo-dynamic test system, in which a conventional static jack is utilized for loading. Two of the new hardware devices developed for the system are detailed: a hydraulic pump system that can adjust the rate of oil flow using an inverter motor, and a controller that controls the jack's motion with a displacement feedback signal transmitted from a digital displacement transducer. The unique advantages of the system are summarized as: larger force capacity achieved by the static jack, maximum use of hardware devices available in many existing structural testing laboratories, and flexibility for program development accomplished by separating tasks into multiple PCs. The reliability of the system is calibrated first by a pseudo-dynamic test for an SDOF system and then by a pseudo-dynamic test for a ten-storey building model having hysteretic dampers. For the latter test, substructuring techniques have been incorporated. The accuracy of the results obtained is discussed based upon the capacity of the system to control displacement and comparison with numerical results. 相似文献
8.
Seismic response of continuous span bridges through fiber-based finite element analysis 总被引：2，自引：0，他引：2
Chiara Casarotti Rui Pinho 《地震工程与工程振动(英文版)》2006,5(1):119-131
1 Introduction Older design codes based on equivalent elastic force approaches proved to be ineffective in preventing damage caused by destructive earthquakes. After recent major earthquakes (e.g. Northridge 1994, Kobe 1995, and Kocaeli 1999 etc.), the necessity for using more accurate methods, which explicitly account for geometrical nonlinearities and material inelasticity, to evaluate seismic demand on structures, became evident. Within this framework, two analysis tools are currently offe… 相似文献
9.
Jiann‐Mou Chen 《水文研究》2008,22(26):5037-5047
Most methods developed to represent water flow phenomena in an unconfined aquifer with a fully penetrated pumping well are either numerical, such as the well‐known FEMWTER model, or experimental; analytical models of a partially penetrated pumping well are rare. This study employs the linearized Richards equation as the governing equation, with the aid of Fourier Integral Transformation, to obtain an analytical solution of the water content distribution in an unconfined aquifer with a partially penetrated pumping well. The results from this study could serve to substantiate in some sense results from numerical models. In addition, the theory developed herein can be modified to simulate a vacuum‐pressured pumping well since it is derived by considering, among others, the location and length of a well screen with fluxes. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
10.
This study presents a fast algorithm for collapse behavior simulation of space truss structures under extreme earthquake excitation by introducing the Woodbury formula to efficiently solve the structural response caused by material and geometric nonlinearity (hybrid nonlinearity). The Woodbury formula, which is an efficient tool in mathematics for solving low-rank perturbation problems, has successfully been used to improve the efficiency of local material nonlinear analysis but still has difficulties with seismic collapse analysis in which geometric nonlinearity should be considered. In this study, by implementing stiffness matrix decomposition according to the unchanged reference configuration, the effects of hybrid nonlinearity on the change in tangent stiffness of truss structures are uniformly formulated in the form of hybrid nonlinear perturbation to the reference elastic stiffness. Thus, a hybrid nonlinearity separated governing equation can be established, in which the hybrid nonlinear behaviors are depicted by the additional nonlinear degrees of freedom (NLDOFs) separated from the reference system. This allows for employing the Woodbury formula to perform seismic collapse analysis of space truss structures for avoiding the repeated updating of the global stiffness. To overcome the adverse effect of the large NLDOF number caused by the global characteristics of geometric nonlinearity on the efficiency advantages of the Woodbury formula during seismic collapse analysis, an element state judgment strategy and an adaptive restart mechanism are presented to activate only a small number of NLDOFs within critical local regions. The accuracy and efficiency of the proposed method are verified by two numerical examples. 相似文献
11.
等效力控制方法在拟动力试验中的应用 总被引：2，自引：0，他引：2
为了避免用复杂的迭代求解拟动力试验隐式逐步积分方法的非线性运动方程,作者提出了一种用反馈控制求解的方法—等效力控制方法。这篇文章首先介绍等效力控制方法的原理;然后通过数值模拟和试验验证此方法的有效性。数值模拟和试验的结果都表明,当选用合理的等效力控制器参数时,此方法可以取得非常好的稳定性和精度。数值模拟的结果还表明尽管等效力控制方法是以力作为反馈控制的对象,此方法能有效完成对具有负刚度试件的加载。 相似文献
12.
显-隐式组合数值积分算法结合了显式算法无需迭代和隐式算法无条件稳定的各自优点,是结构抗震拟动力试验顺利运行的关键.在对传统显式中央差分法和隐式Newmark β组合算法进行参数修正的基础上,建立了修正CD-Newmark算法,考虑阻尼的影响分析了组合算法的稳定性条件、周期失真率和数值阻尼比,分别得到了试验子结构的稳定性条件和计算子结构无条件稳定的参数合理取值范围,并对计算精度进行了分析.通过算例分析验证了算法的数值特性,从而初步解决了CD-Newmark算法存在稳定性界限过严的问题,为结构抗震拟动力混合试验提供了研究参考. 相似文献
13.
A. C. LIAKOPOULOS Dr. Eng. 《水文科学杂志》2013,58(1):69-110
ABSTRACT The one-dimensional transient downward entry of water in unsaturated soils is investigated theoretically. The mathematical equation describing the infiltration process is derived by combining Darcy's dynamic equation of motion with the continuity and thermodynamic state equations adjusted for the unsaturated flow conditions. The resulting equation together with the corresponding initial and boundary conditions constitues a mathematical initial boundary value problem requiring the solution of a nonlinear partial differential equation of the parabolic type. The volumetric water content is taken as the dependent variable and the time and the position along the vertical direction are taken as the independent variables. The governing equation is of such nature that a solution exists for t > 0 and is uniquely determined if two relationships are defined, together with the specified state of the system, at the initial time t = 0 and at the two boundaries. The two required relations are those of pressure versus permeability and pressure versus volumetric water content. Since the partial differential equation has strong non-linear terms, a discrete solution is obtained by approximating the derivatives with finite-differences at discrete mesh points in the solution domain and integrated for the corresponding initial and boundary conditions. The use of an implicit difference scheme is employed in order to generate a system of simultaneous non-linear equations that has to be solved for each time increment. For n mesh points the two boundary conditions provide two equations and the repetition of the recurrence formula provides n—2 equations, the total being n equations for each time increment. The solution of the system is obtained by matrix inversion and particularly with a back-substitution technique. The FORTRAN statements used for obtaining the solution with an electronic digital computer (IBM 704) are presented together with the input data. Analysis of the errors involved in the numerical solution is made and the stability and convergence of the solution of the approximate difference equation to that of the differential equation is investigated. The method applied is that of making a Fourier series expansion of a whole line of errors and then following the progress of the general term of the series expansion and also the behavior of each constituent harmonic. The errors (forming a continuous function of points in an abstract Banach space) are represented by vectors with the Fourier coefficients constituting a second Banach space. The amplification factor of the difference equation is shown to be always less than unity which guarantees the stability of the employed implicit recurrence scheme. Experiments conducted on a vertical column packed uniformly with very fine sand, show a satisfactory agreement between the theoretically and experimentally obtained values. Many experimental results are shown in an attempt to explain the infiltration phenomenon with emphasis on the shape and movement of the wet front, and the effects of the degree of compaction, initial water content and deaired water on the infiltration rate. 相似文献
14.
A Taylor basis for kinematic nonlinear real-time simulations. Part I: The complete modal derivatives
Despite todays computational power, only small nonlinear numerical substructures may be simulated in real time. The size restriction on the substructures in nonlinear finite element analysis is primarily due to the time-consuming evaluation of the internal restoring forces, which is performed element-by-element in every iteration step. The present work constitutes the first of two papers presenting a method to simulate kinematic nonlinear structures more efficiently. It involves applying a reduced basis with modal derivatives representing the nonlinearities of the system in an efficient way. Previously, the modal derivatives have been determined from a set of approximate governing equations. In the present paper, a novel set of equations governing the complete modal derivatives is derived. This is done by introducing a Taylor series into the free undamped kinematic nonlinear equations of motion. Also, the approximate governing equations are improved by introducing a novel geometric restriction. By way of an example, it is shown that only the modal derivatives determined from the complete set of equations are consistent with the Taylor series. In the second paper, it is shown that the novel modal derivatives may be used in a so-called Taylor basis and that they improve the computational time and stability significantly. 相似文献
15.
Fred T. Tracy 《Journal of Hydrology》1995,170(1-4):199-214
An excellent tool for checking numerical models of unsaturated flow in groundwater is analytical solutions. However, because of the highly nonlinear nature of the governing partial differential equation, only a limited number of analytical solutions are available. This paper first gives some simple 1-D solutions. Next, by use of a transformation, the nonlinear partial differential equation is converted to a linear one for a specific form of the moisture content vs. pressure head and relative hydraulic conductivity vs. pressure head curves. This allows both 2-D and 3-D solutions to be derived, which is done in this paper. Finally, computations from a finite element computer program are compared with results from one of the analytical solutions to illustrate the use of the derived equations. 相似文献
16.
Iterative implicit integration procedure for hybrid simulation of large nonlinear structures 总被引：1，自引：0，他引：1
A fully implicit iterative integration procedure is presented for local and geographically distributed hybrid simulation of the seismic response of complex structural systems with distributed nonlinear behavior. The purpose of this procedure is to seamlessly incorporate experimental elements in simulations using existing fully implicit integration algorithms designed for pure numerical simulations. The difficulties of implementing implicit integrators in a hybrid simulation are addressed at the element level by introducing a safe iteration strategy and using an efficient procedure for online estimation of the experimental tangent stiffness matrix. In order to avoid physical application of iterative displacements, the required experimental restoring force at each iteration is estimated from polynomial curve fitting of recent experimental measurements. The experimental tangent stiffness matrix is estimated by using readily available experimental measurements and by a classical diagonalization approach that reduces the number of unknowns in the matrix. Numerical and hybrid simulations are used to demonstrate that the proposed procedure provides an efficient method for implementation of fully implicit numerical integration in hybrid simulations of complex nonlinear structures. The hybrid simulations presented include distributed nonlinear behavior in both the numerical and experimental substructures. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
17.
1 INTRODUCTION Mountains higher than 100m occupy 63% of the land area in Taiwan. Serious flood disasters and muddy flows usually occur in the rainy season. To reduce the disasters from hillslope development, the government published the Norm of Soil and Water Conservation Treatment (NSWCT) in 1994. One of the most important treatments is that detention ponds and grit chambers are essential facilities for reducing increased peak flow disasters and sediment yield. 309 volumes on soil… 相似文献
18.
An explicit unconditionally stable algorithm for hybrid tests,which is developed from the traditional HHT-α algorithm,is proposed.The unconditional stability is first proven by the spectral radius method for a linear system.If the value of α is selected within [-0.5,0],then the algorithm is shown to be unconditionally stable.Next,the root locus method for a discrete dynamic system is applied to analyze the stability of a nonlinear system.The results show that the proposed method is conditionally stable for dynamic systems with stiffness hardening.To improve the stability of the proposed method,the structure stiffness is then identified and updated.Both numerical and pseudo-dynamic tests on a structure with the collision effect prove that the stiffness updating method can effectively improve stability. 相似文献
19.
Numerical models for simulation of multidimensional unsaturated flow are becoming increasingly available, but relatively little has been reported on the detailed analysis of numerical errors associated with such schemes. For unsaturated-saturated flow, further complexity is introduced to the highly non-linear unsaturated problem as the form of governing equation changes within the flow field. In this paper, two-dimensional simulation of infiltration to a water table is considered. Numerical errors associated with selection of time step, grid geometry, convergence criteria, and the representation of internodal hydraulic conductivity are discussed with respect to moisture content profiles and mass balance error. Although solution sensitivity to numerical parameters is problem specific, the results presented indicate the nature and magnitude of numerical effects which should not be overlooked in model applications. 相似文献
20.
Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation 
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下载免费PDF全文 In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field. 相似文献