首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 15 毫秒
1.
A simple local error estimator is presented for time integration schemes in dynamic analysis. This error estimator involves only a small computational cost. The time step size is adaptively adjusted so that the local error at each time step is within a prescribed accuracy. It is found that the estimator performs well under various circumstances and provides an economical adaptive process. Attempts to estimate the global time integration error are also reported.  相似文献   

2.
Developing robust and efficient numerical solution methods for Richards' equation (RE) continues to be a challenge for certain problems. We consider such a problem here: infiltration into unsaturated porous media initially at static conditions for uniform and non-uniform pore size media. For ponded boundary conditions, a sharp infiltration front results, which propagates through the media. We evaluate the resultant solution method for robustness and efficiency using combinations of variable transformation and adaptive time-stepping methods. Transformation methods introduce a change of variable that results in a smoother solution, which is more amenable to efficient numerical solution. We use adaptive time-stepping methods to adjust the time-step size, and in some cases the order of the solution method, to meet a constraint on nonlinear solution convergence properties or a solution error criterion. Results for three test problems showed that adaptive time-stepping methods provided robust solutions; in most cases transforming the dependent variable led to more efficient solutions than untransformed approaches, especially as the pore-size uniformity increased; and the higher-order adaptive time integration method was robust and the most efficient method evaluated.  相似文献   

3.
三维大模型数值计算因巨大的单元和结点数目而非常耗时,在地震响应分析中受计算时间步长的限值则更加耗时。在饱和砂土动力液化计算平台上开发时域离散误差评估方法和时间步长自适应调整的计算程序,并成功应用于三维堤坝地震液化响应分析。时域离散误差包括土骨架的位移误差和单元孔压误差,通过定义孔压误差影响系数计算出混合误差,根据混合误差和设定的误差允许值进行计算步长的自适应调整。在三维堤坝地震液化数值模拟中,采用自适应时间步长法有效避免小步长精确但耗时、大步长省时而不精确的缺点。在大模型和超大模型计算中,最优调整每一步的计算时间步长,完美实现既节省时间又不失精度的时域离散策略。  相似文献   

4.
In this paper, we present a post-processing technique and an a posteriori error estimate for the Newmark method in structural dynamic analysis. By post-processing the Newmark solutions, we derive a simple formulation for linearly varied third-order derivatives. By comparing the Newmark solutions with the exact solutions expanded in the Taylor series, we achieve the local post-processed solutions which are of fifth-order accuracy for displacements and fourth-order accuracy for velocities in one step. Based on the post-processing technique, a posteriori local error estimates for displacements, velocities and, thus, also the total energy norm error estimate are obtained. If the Newmark solutions are corrected at each step, the post-processed solutions are of third-order accuracy in the global sense, i.e. one-order improvement for the original Newmark solutions is achieved. We also discuss a method for estimating the global time integration error. We find that, when the total energy norm is used, the sum of the local error estimates will give a reasonable estimate for the global error. We present numerical studies on a SDOF and a 2-DOF example in order to demonstrate the performance of the proposed technique.  相似文献   

5.
Efficient, robust simulation of groundwater flow in the unsaturated zone remains computationally expensive, especially for problems characterized by sharp fronts in both space and time. Standard approaches that employ uniform spatial and temporal discretizations for the numerical solution of these problems lead to inefficient and expensive simulations. In this work, we solve Richards’ equation using adaptive methods in both space and time. Spatial adaption is based upon a coarse grid solve and a gradient error indicator using a fixed-order approximation. Temporal adaption is accomplished using variable order, variable step size approximations based upon the backward difference formulas up to fifth order. Since the advantages of similar adaptive methods in time are now established, we evaluate our method by comparison with a uniform spatial discretization that is adaptive in time for four different one-dimensional test problems. The numerical results demonstrate that the proposed method provides a robust and efficient alternative to standard approaches for simulating variably saturated flow in one spatial dimension.  相似文献   

6.
Conventional finite-difference modelling algorithms for seismic forward modelling are based on a time-stepping scheme with a constant (global) time step. Large contrasts in the velocity model or in the spatial sampling rate cause oversampling in time for some regions of the model. The use of locally adjustable time steps can save large amounts of computation time for certain modelling configurations. The computation of spatial derivatives across the transition zone between regions of the model with different temporal sampling requires the definition of the wavefield at corresponding time levels on both sides of the transition zone. This condition can be obtained by extrapolation in time, which is inaccurate, or by multiple time integration in the transition zone. The error in the latter solution is of the same order as the conventional time-stepping scheme because both methods are based on the same iteration formula. The technique of multiple time integration simply requires the use of different sizes of time step. It is applicable only for certain factors of variation of the time step.  相似文献   

7.
Despite the widespread application of nonlinear mathematical models, comparative studies of different models are still a huge task for modellers. This is because a large number of trial and error processes are needed to develop each model, so the workload will be multiplied into an unmanageable level if many types of models are involved. This study presents an efficient approach by using the Gamma test (GT) to select the input variables and the training data length, so that the trial and error workload can be greatly reduced. The methodology is tested in estimating solar radiation at the Brue catchment, UK. Several nonlinear models have been developed efficiently with the aid of the GT, including local linear regression, multi-layer perceptron (MLP), Elman neural network, neural network auto-regressive model with exogenous inputs (NNARX) and adaptive neuro-fuzzy inference system (ANFIS). This work is only feasible within the time and resources constraint, due to the GT in reducing huge workload of the trial and error process.  相似文献   

8.
Time integration methods that adapt in both the order of approximation and time step have been shown to provide efficient solutions to Richards' equation. In this work, we extend the same method of lines approach to solve a set of two-phase flow formulations and address some mass conservation issues from the previous work. We analyze these formulations and the nonlinear systems that result from applying the integration methods, placing particular emphasis on their index, range of applicability, and mass conservation characteristics. We conduct numerical experiments to study the behavior of the numerical models for three test problems. We demonstrate that higher order integration in time is more efficient than standard low-order methods for a variety of practical grids and integration tolerances, that the adaptive scheme successfully varies the step size in response to changing conditions, and that mass balance can be maintained efficiently using variable-order integration and an appropriately chosen numerical model formulation.  相似文献   

9.
Two types of implicit time-stepping algorithms have been proposed recently for pseudodynamic tests. The first type consists of an algorithm which relies on Newton iterations to satisfy the equations of motion. The second type consists of an algorithm which is based on the Operator-Splitting technique and does not require any numerical iteration. While one or the other has been preferred by some researchers, these time-stepping algorithms have not been analysed and compared under a uniform setting. In this paper, a concise summary of these schemes is presented, and they are evaluated in a consistent manner in terms of numerical dissipation, frequency distortion and experimental errors. The analytical results are validated by numerical simulations as well as experimental results. It is shown that the algorithm based on Newton iterations can control experimental error effects effectively by means of an error-correction procedure. The algorithm based on the Operator-Splitting technique demonstrates similar performance provided the I-Modification is adopted.  相似文献   

10.
Adaptive time stepping with embedded error control is applied to the mixed form of Richards equation. It is the first mathematically based adaptive scheme applied to this form of Richards equation. The key to the method is the approximation of the local truncation error of the scheme in terms of the pressure head, although, to enforce mass conservation, the principal time approximation is based on the moisture content. The time stepping scheme is closely related to an implicit Thomas–Gladwell approximation and is unconditionally stable and second-order accurate. Numerical trials demonstrate that the new algorithm fully automates stepsize selection and robustly constrains temporal discretisation errors given a user tolerance. The adaptive mechanism is shown to improve the performance of the non-linear solver, providing accurate initial solution estimates for the iterative process. Furthermore, the stepsize variation patterns reflect the adequacy of the spatial discretisation, here accomplished by linear finite elements. When sufficiently dense spatial grids are used, the time step varies smoothly, while excessively coarse grids induce stepsize oscillations.  相似文献   

11.
The simple Lanczos method presented in a recent paper by the writers, with application to single vector loads, is extended to include a more general dynamic loading represented as a linear combination of k vectors (load patterns). The result is a set of orthogonal vectors that is used to transform the equations of motion to a banded form, the half-bandwidth of which becomes k + 1. When k is small relative to the number of equations, this approach provides for a very efficient time-stepping solution.  相似文献   

12.
太湖叶绿素a同化系统敏感性分析   总被引：1，自引：1，他引：0  
太湖叶绿素a同化系统对于不同参数的敏感性将直接影响到该系统能否精确的估算太湖叶绿素a的浓度分布.利用2009年4月21日环境一号卫星(HJ-1B CCD2)影像数据反演太湖叶绿素a浓度场信息.以此作为背景场信息,结合基于集合均方根滤波的太湖叶绿素a同化系统,分析和评价了样本数目、同化时长、背景场误差、观测误差和模型误差对于同化系统性能的影响.结果表明:从计算成本、系统运行时间和同化效果等方面分析,当集合样本数目达到30~40左右时同化系统取得了较好的结果;同化系统对于背景场误差的估计变化不是很敏感,即初始场的估计是否准确对于同化系统的性能影响不是很大;同化系统对于模型误差和观测误差的变化较为敏感,不同的测试点位由于水体动力学性质不一,其敏感性的表现形式有所差异;利用数据同化方法可以有效地估算太湖叶绿素a浓度.  相似文献   

13.
Richards’ equation (RE) is commonly used to model flow in variably saturated porous media. However, its solution continues to be difficult for many conditions of practical interest. Among the various time discretizations applied to RE, the method of lines (MOL) has been used successfully to introduce robust, accurate, and efficient temporal approximations. At the same time, a mixed-hybrid finite element method combined with an adaptive, higher order time discretization has shown benefits over traditional, lower order temporal approximations for modeling single-phase groundwater flow in heterogeneous porous media. Here, we extend earlier work for single-phase flow and consider two mixed finite element methods that have been used previously to solve RE using lower order time discretizations with either fixed time steps or empirically based adaption. We formulate the two spatial discretizations within a MOL context for the pressure head form of RE as well as a fully mass-conservative version. We conduct several numerical experiments for both spatial discretizations with each formulation, and we compare the higher order, adaptive time discretization to a first-order approximation with formal error control and adaptive time step selection. Based on the numerical results, we evaluate the performance of the methods for robustness and efficiency.  相似文献   

14.
Jackson CR 《Ground water》2012,50(5):736-745
An automatic time-stepping algorithm is presented, based on the intensity of driving groundwater recharge, that improves the simulation of groundwater level fluctuations in regional models while maintaining model run-times. The algorithm is implemented in the ZOOMQ3D finite difference groundwater flow code and controls the discretization of time using two user-defined criteria: a maximum time-step length and a maximum recharge per time-step. Daily recharge is accumulated in time until either of these criteria is violated when the model then calculates a solution. The efficiency and accuracy of the algorithm is tested using an idealized groundwater model and an existing regional groundwater model of a UK aquifer. The approach is illustrated using simulations of high groundwater levels and associated groundwater flood events in a responsive, high-diffusivity aquifer. Simulations using the automatic time-stepping technique are presented that reduce the maximum absolute error in groundwater level by 45% and the run-time by 51% compared to models using conventional, a priori defined stress-periods and time-steps.  相似文献   

15.
This paper is concerned with application of the h-adaptive finite element method to dynamic analysis of a pile in liquefiable soil considering large deformation. In finite element analysis of pile behavior in liquefiable soil during an earthquake, especially considering large deformation of liquefied ground, error due to discretization in the zone near the pile becomes very large. Our purpose was to refine the approximation of the finite element method. The updated Lagrangian formulation and a cyclic elasto-plastic model based on the kinematic hardening rule were adopted to deal with the nonlinearity of the soil. The mixed finite element and finite difference methods together with the u-p formulation and Biot's two-phase mixture theory were used. To improve the accuracy and increase the efficiency of finite element analysis, an h-adaptive scheme that included a posteriori error estimation and h-version mesh refinement was applied to the analysis. The calculated results of effective stress were smoothed locally by the extrapolation method and smoothed stress was used to calculate the L2 norm of the effective stress error in the last step of the calculation of each time increment. The mesh was refined by a fission procedure based on the indication of the error estimate As a numerical example, a soil–pile interaction system loaded cyclically was analyzed by our method.  相似文献   

16.
We propose a spatially and temporally adaptive solution to Richards’ equation based upon a local discontinuous Galerkin approximation in space and a high-order, backward difference method in time. We cast our approach in terms of a general, decoupled adaption algorithm based upon operators. We define non-unique instances of all operators to result in an adaption method from within the general class of methods that is defined. We formally decouple the spatial adaption from the temporal adaption using a method of lines approach and limit the temporal truncation error so that the total error is dominated by the spatial component. We use a multiple grid approach to guide adaption and support the data structures. Spatial adaption decisions are based upon error and regularity indicators, which are economical to compute. The resultant methods are compared for two test problems. The results show that the proposed adaption methods are superior to methods that adapt only in time and that in cases in which the problem has sufficient smoothness, adapting the order of the elements in addition to the grid spacing can further improve the efficiency of this robust solution approach.  相似文献   

17.
Numerical models for reactive transport can be used to estimate the breakthrough of a contaminant in a pumping well or at other receptors. However, as natural aquifers are highly heterogeneous with unknown spatial details, reactive transport predictions on the aquifer scale require a stochastic framework for uncertainty analysis. The high computational demand of spatially explicit reactive-transport models hampers such analysis, thus motivating the search for simplified estimation tools. We suggest performing an electron balance between the reactants in the infiltrating solution and in the aquifer matrix to obtain the hypothetical time of dissolved-reactant breakthrough at a receptor if the reaction with the matrix was instantaneous. This time we denote as the advective breakthrough time for instantaneous reaction (τinst ). It depends on the amount of the reaction partner present in the matrix, the mass flux of the dissolved reactant, and the stoichiometry. While the shape of the reactive-species breakthrough curve depends on various kinetic parameters, the overall timing scales with τinst . We calculate the latter by particle tracking. The effort of computing τinst is so low that stochastic calculations become feasible. We apply the concept to a two-dimensional test case of aerobic respiration and denitrification. A detailed spatially explicit reactive-transport model includes microbial dynamics. Scaling the time of local breakthrough curves observed at individual points by τinst decreased the variability of electron-donor breakthrough curves significantly. We conclude that the advective breakthrough time for instantaneous reaction is efficient in estimating the time over which an aquifer retains its degradation potential.  相似文献   

18.
一种激发极化法2.5维正演的自适应有限元方法（英文）   总被引：2，自引：2，他引：0  
传统的基于结构化网格有限元法采用的单元比较规则如矩形等,且网格剖分和加密要靠手动实现,所以传统的基于结构化网格有限元法不能准确和灵活地模拟复杂介质。本文采用易于模拟复杂介质模型的非结构化三角形网格进行剖分,且利用对偶加权后验误差估计指导网格自动细化过程,然后在电位模拟的基础上计算雅可比偏导矩阵,并依据Seigel（1959）理论实现激发极化法2.5维自适应有限元正演模拟算法。通过对垂直接触面模型进行正演分析,接收点附近网格得到了明显加密,电位数值解平均相对误差收敛到0.4%,视极化率平均相对误差收敛到1.2%,表明经自适应网格细化后,该算法数值解最终能收敛到精确解附近。最后对两个较复杂模型进行了正演计算与分析,进一步验证了该算法的准确性和灵活性。  相似文献   

19.
《Advances in water resources》2003,26(11):1189-1198
A two-dimensional finite element based overland flow model was developed and used to study the accuracy and stability of three numerical schemes and watershed parameter aggregation error. The conventional consistent finite element scheme results in oscillations for certain time step ranges. The lumped and the upwind finite element schemes are tested as alternatives to the consistent scheme. The upwind scheme did not improve on the stability or the accuracy of the solution, while the lumped scheme provided stable and accurate solutions for time steps twice the size of time steps needed for the consistent scheme. A new accuracy based dynamic time step estimate for the two-dimensional overland flow kinematic wave solution is developed for the lumped scheme. The newly developed dynamic time step estimates are functions of the mesh size, and time of concentration of the watershed hydrograph. Due to lack of analytical solutions, the time step was developed by comparing numerical solutions of various levels of discretization to a reference solution using a very fine mesh and a very small time step. The time step criteria were tested on a different set of problems and proved to be adequate for accurate and stable solutions. A sensitivity analysis for the watershed slope, Manning’s roughness coefficient and excess rainfall rate was conducted in order to test the effect of parameter aggregation on the stability and accuracy of the solution. The results of this analysis show that aggregation of the slope data resulted in the highest error. The roughness coefficient had a smaller effect on the solution while the rainfall intensity did not show any significant effect on the flow rate solution for the range of rainfall intensity used. This work pioneers the challenge of providing guidelines for accurate and stable numerical solutions of the two-dimensional kinematic wave equations for overland flow.  相似文献   

20.
A method is presented to estimate the elastic parameters and thickness of media that are locally laterally homogeneous using P‐wave and vertically polarized shear‐wave (SV‐wave) data. This method is a ‘layer‐stripping’ technique, and it uses many aspects of common focal point (CFP) technology. For each layer, a focusing operator is computed using a model of the elastic parameters with which a CFP gather can be constructed using the seismic data. Assuming local homogeneity, the resulting differential time shifts (DTSs) represent error in the model due to anisotropy and error in thickness. In the (τ?p) domain, DTSs are traveltimes Δτ that connect error in layer thickness z, vertical slowness q, and ray parameter p. Series expansion is used to linearize Δτ with respect to error in the elastic parameters and thickness, and least‐squares inversion is used to update the model. For stability, joint inversion of P and SV data is employed and, as pure SV data are relatively rare, the use of mode‐converted (PSV) data to represent SV in the joint inversion is proposed. Analytic and synthetic examples are used to demonstrate the utility and practicality of this inversion.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号