A three‐point time discretization technique for parabolic partial differential equations

The Crank–Nicolson scheme has second‐order accuracy, but often leads to oscillations affecting numerical stability. On the other hand, the implicit scheme is free from oscillation, but it has only first‐order accuracy. In this work, a three‐point discretization scheme with variable time step is presented for the time marching of parabolic partial differential equations. The method proposed has second‐order accuracy, is unconditionally stable and dampens spurious oscillations of the numerical results. The application and effectiveness of the new method are demonstrated through several numerical examples. It is shown that, unlike the Crank–Nicolson method, the approach proposed produces no oscillatory response irrespective of the time step adopted. Copyright © 2010 John Wiley & Sons, Ltd.     

Exponential time integrators for stochastic partial differential equations in 3D reservoir simulation

The transport of chemically reactive solutes (e.g. surfactants, CO₂ or dissolved minerals) is of fundamental importance to a wide range of applications in oil and gas reservoirs such as enhanced oil recovery and mineral scale formation. In this work, we investigate exponential time integrators, in conjunction with an upwind weighted finite volume discretisation in space, for the efficient and accurate simulation of advection–dispersion processes including non-linear chemical reactions in highly heterogeneous 3D oil reservoirs. We model sub-grid fluctuations in transport velocities and uncertainty in the reaction term by writing the advection–dispersion–reaction equation as a stochastic partial differential equation with multiplicative noise. The exponential integrators are based on the variation of constants solution and solve the linear system exactly. While this is at the expense of computing the exponential of the stiff matrix representing the finite volume discretisation, the use of real Léja point or the Krylov subspace technique to approximate the exponential makes these methods competitive compared to standard finite difference-based time integrators. For the deterministic system, we investigate two exponential time integrators, the second-order accurate exponential Euler midpoint (EEM) scheme and exponential time differencing of order one (ETD1). All our numerical examples demonstrate that our methods can compete in terms of efficiency and accuracy compared with standard first-order semi-implicit time integrators when solving (stochastic) partial differential equations that model mixing and chemical reactions in 3D heterogeneous porous media. Our results suggest that exponential time integrators such as the ETD1 and EEM schemes could be applied to typical 3D reservoir models comprising tens to hundreds of thousands unknowns.     

Evaluation of potential evapotranspiration methods for Ghana

Three methods — a modified 1948 Penman (Walker 1957), Thornthwaite (1948) and Papadakis (1961) — were considered for the estimation of potential evapotranspiration (PE) values for Ghana. Under the varying weather and climatic conditions over the country, the modified Penman method was found to be most suitable for estimating PE values for Ghana.     

浅水方程数值计算方法的研究

求解以水位为变量的连续方程,并根据Navier-Stokes方程压力修正算法的基本思想,建立了浅水方程的水位修正算法,放宽了对离散时间步长的限制.通过对离散方程系数矩阵的重新构造,建立了高分辨率有限元格式,该格式既具有较高的离散精度又避免了数值解的伪振荡.对动量方程的阻力项做负坡线性化处理,提高了露滩计算的稳定性.数值模拟结果与解析解吻合良好,表明所建立的数值计算方法是正确的和可靠的.     

Evaluation of thermal equations of state for CO2 in numerical simulations

Three commonly used thermal equations of state for carbon dioxide, as well as the ideal gas law, have been compared against a large number of measurement data taken from the literature. Complex equations of state reach a higher accuracy than simple ones. The inaccuracy of the density function can cause large errors in fluid property correlations, such as heat capacity or viscosity. The influence of this inaccuracy on the results of numerical simulations have been evaluated by two examples: The first one assumes isothermal gas expansion from a volume, while the second one considers heat transport along a fracture. For both examples, different equations of state have been utilized. The simulations have been performed on the scientific software platform OpenGeoSys. The difference among the particular simulation results is significant. Apparently small errors in the density function can cause considerably different results of otherwise identical simulation setups.     

差动式双作用液动冲击器冲锤动力学方程的研究和应用

为了优化差动式双作用液动冲击器结构,本文建立了该型冲击器的数值模拟程序,用于之后结构参数与输出性能的影响关系研究。基于流体连续性方程、水击现象、水垫阻力、伯努利方程、压力损失等理论,建立了阀锤系统在三个运动阶段的力学模型;以冲锤或活阀为受力分析对象,建立了阀锤系统在每个阶段的动力方程;基于有限差分原理,利用MATLAB GUI进行程序编写,建立了数值模拟程序,运用实验数据拟合修正后的数值模拟程序输出性能参数与该型液动冲击器在实际工况下的输出性能参数基本一致。通过对背压的研究,阐述了背压的组成;利用建立的程序探究了背压对差动式双作用液动冲击器输出性能的影响规律并分析了原因。     

Highly efficient iterative methods for solving linear equations of three-dimensional sphere discontinuous deformation analysis

The efficiency of solving equations plays an important role in implicit-scheme discontinuous deformation analysis (DDA). A systematic investigation of six iterative methods, namely, symmetric successive over relaxation (SSOR), Jacobi (J), conjugate gradient (CG), and three preconditioned CG methods (ie, J-PCG, block J-PCG [BJ-PCG], and SSOR-PCG), for solving equations in three-dimensional sphere DDA (SDDA) is conducted in this paper. Firstly, simultaneous equations of the SDDA and iterative formats of the six solvers are presented. Secondly, serial and OpenMP-based parallel computing numerical tests are done on a 16-core PC, the result of which shows that (a) for serial computing, the efficiency of the solvers is in this order: SSOR-PCG > BJ-PCG > J-PCG > SSOR>J > CG, while for parallel computing, BJ-PCG is the best solver; and (b) CG is not only the most sensitive to the ill-condition of the equations but also the most time consuming under both serial and parallel computing. Thirdly, to estimate the effects of equation solvers acting on SDDA computations, an application example with 10 000 spheres and 200 000 calculation steps is simulated on this 16-core PC using serial and parallel computing. The result shows that SSOR-PCG is about six times faster than CG for serial computing, while BJ-PCG is about four times faster than CG for parallel computing. On the other hand, the whole computation time using BJ-PCG for parallel computing is 3.37 hours (ie, 0.061 s per step), which is about 36 times faster than CG for serial computing. Finally, some suggestions are given based on this investigation result.     

洪水对非防洪工程建设项目影响评价方法研究

讨论了洪水对洪泛区或滞蓄洪区中非防洪工程建设项目影响评价方法,包括洪灾直接经济损失和间接经济损失的估算方法,洪灾发生时含有有毒物质的非防洪工程建设项目对环境的影响,以及对地下水的污染等影响评价方法.这些方法是洪水对非防洪工程建设项目影响评价的核心,也是整个影响评价的重点和难点所在.这些方法可为制定洪水对洪泛区非防洪工程建设项目影响评价指南或规范提供科学依据.     

Stability properties of the Newmark,Houbolt and Wilson θ methods

This paper analysis the stability of several methods for obtaining numerical solutions of second-order ordinary differential equations. The methods are popular in structural and geotechnical engineering applications and are direct, that is they do not require the transformation of the second-order equation into a first-order system. They include Newmark's method in both implicit and explicit forms, Wilson's θ-method, Houbolt's method and some variants on this latter method. We shall examine the stability of the methods when applied to the second-order scalar test equation where a and c are real.     

Evaluation of image analysis methods used for quantification of particle angularity

Angularity is an important parameter in the characterization of particle morphology that is used to interpret the transport history of particles in sedimentary deposits. In the past, visual classification using silhouette charts was widely used to determine particle angularity, but this approach is subjective and time‐consuming. With advances in modern image analysis techniques and low‐cost software packages, it is possible to rapidly quantify particle angularity more objectively than using visual classification methods. This study re‐examines the performance of three existing image analysis methods and one new image analysis procedure, applied to six rock and sediment samples that were visually different in angularity. To facilitate comparison between the angularity results, measurements were reduced to rankings for each aggregate sample. These results show that the four image analysis methods rank the angularity of the samples differently, and that none rank the mean angularity index in the same order as the angularity ranking using visual classification. Therefore, further research is needed to develop an image analysis method that can quantify the angularity of sedimentary particles more precisely.     

Evaluation of equivalent medium methods for stress wave propagation in jointed rock mass

This paper evaluates the existing equivalent medium methods for jointed rock mass and further develops the equivalent viscoelastic medium method proposed by the authors. The advantages and limitations of different equivalences to the discontinuous rock mass are discussed. Theoretical derivation of stress wave propagation through the equivalent viscoelastic medium is carried out by adopting the Fourier transformation method, and the parameters of the equivalent viscoelastic medium method are determined analytically. The frequency dependence and the wave attenuation phenomenon can be properly described when the imaginary terms of the complex moduli of the rock mass are included. The results show that the equivalent viscoelastic medium method is able to predict the effective velocity and the stress wave transmission coefficient in a rock mass more accurately than the conventional effective elastic moduli methods. An example of the stress wave propagation through rock mass with parallel joints shows that the equivalent viscoelastic medium method is promising and worthy to be further explored for application in practical rock engineering problems. Copyright © 2011 John Wiley & Sons, Ltd.     

Accuracy and efficiency of time integration methods for 1D diffusive wave equation

The diffusive wave approximation of the Saint-Venant equations is commonly used in hydrological models to describe surface flow processes. Numerous numerical approaches can be used to solve this highly nonlinear equation. Nonlinear time integration schemes—also called methods of lines (MOL)—were proven very efficient to solve other nonlinear problems in geosciences but were never considered to deal with surface flow modeling with the diffusive wave equation. In this paper, we study the relative performance of different time and space integration schemes by comparing the results obtained with classical approaches and with nonlinear time integration approaches. The results show that (i) the integration method with a higher order in space shows high accuracy regarding an integrated indicator such as the global mass balance error but is less accurate regarding local indicators, and (ii) nonlinear time integration techniques perform better than classical ones. Overall, it seems that integration techniques combining nonlinear time integration and a low spatial order need to be considered when developing hydrological modeling tools owing to their simplicity of implementation and very good performance.     

水文时间序列周期识别的新思路与两种新方法

针对水文序列周期识别的困难,提出首先对原序列处理,再识别周期的新思路,同时提出两种新方法:一种是模拟延长序列法,即通过建模延长原序列,再应用最大熵谱分析法(MESA)对延长序列识别周期;另一种方法是构建主频序列法,应用小波重构法重构原序列主频部分,然后应用MESA对重构序列进行周期识别。结合实例,运用多种方法对同一序列进行周期识别。分析结果表明:由于受序列长度偏短、偏态性、复杂随机成分等因素的影响,传统单一处理方法(周期图法、FFT、MESA、小波分析)周期识别效果并不理想,而使用两种新方法可以有效地减小或消除上述因素的影响,周期识别效果有明显改善。     

Evaluation of image processing methods for geological interpretation in the different environments in Libya

This study evaluates the use of image processing techniques and methodologies of digital integration of multi-disciplinary geoscientific data to reduce the ambiguity in geological interpretations in different geological environments in Libya. To realize this objective, three areas were selected for this study; Eljufra, an arid environment; the mountainous environment Tarhunah; and the Jifara Plain, a coastal plain environment. Two types of remote sensing data were used in this study: Landsat Enhanced Thematic Mapper Plus (ETM+) and European Remote Sensing Satellite. The digital elevation model extracted from Shuttle Radar Topography Mission and digital topographic maps scale 1:50,000 were used for remote sensing interpretation. GIS and remote sensing-based methods were used to process and integrate all raster and vector layers data. This study offered dramatic benefits for geological interpretations and provided new insights into the efficiency of image processing methods in different geological environments.     

Oxygen-containing functional groups in land-derived humic acids—I. Evaluation by derivatization methods

Determinations of reactive oxygen-containing functional groups were performed by usual chemical derivatization methods of four humic acids isolated from soils and deltaic sediments. Statistical tests and calculations based on elemental analysis demonstrated the validity and limits of these techniques and allowed us to identify from 60 to 71% of the total humic oxygen. Oxygen budgets of humic acids are discussed.     

黄土高填方场地工后沉降预测模型性能评估方法

工后沉降预测结果是黄土高填方场地变形稳定性评价和建筑物规划布局的重要参考依据。为遴选适合黄土高填方场地的工后沉降预测模型,基于某典型黄土高填方工程的实测沉降数据,分析了工后沉降曲线的变化规律和发展趋势,建立了17种回归参数模型,提出了模型预测效果的评价指标和方法。结果表明：（1）该工程填方区工后沉降历时曲线呈“缓变型”变化,土方填筑完工初期无陡增段,随时间增加沉降速率逐步降低,尚未出现沉降趋于稳定的水平段;（2）将外推预测误差、内拟合误差和后验误差比最小化作为综合控制目标,可遴选出理想的回归参数模型;（3）MMF模型（Ⅱ型）和双曲线模型具有较高的预测精度、较好的稳定性和较强的适应性,在17种模型中的预测效果最佳;（4）沉降数据的变化越平稳,模型预测效果越好;（5）增大建模数据的时间跨度,会提升预测精度,但增大至一定值后,预测精度提升效果不再显著。     

确定大跨连续刚构桥地震动输入时程方法比较

以上海某大跨度连续钢构桥梁的场地为例,讨论动水压力对河谷场地土层地震响应的影响,通过对建筑结构抗震规范反应谱生成时程,采用一维、二维模型分别计算得到场地地震动输入时程。对比可以看出,考虑动水压力将会大大减小场地的竖向地震动反应,而动水压力对水平向的地震响应影响不大;反应谱生成时程的方法与一维模型计算得到的时程均与采用考虑场地地形变化的二维模型的计算结果有较大的区别;二维模型计算得到的时程反应谱的卓越周期超出规范反应谱的平台段。最后,讨论了河谷场地对周围场地的影响范围,结果表明河水及河谷对周围场地水平方向的影响范围是沿河谷外侧5倍土层深度或140倍河谷深度,在该范围内的建筑物均应考虑河谷的影响。     

Evaluation of graphical and multivariate statistical methods for classification of water chemistry data

A robust classification scheme for partitioning water chemistry samples into homogeneous groups is an important tool for the characterization of hydrologic systems. In this paper we test the performance of the many available graphical and statistical methodologies used to classify water samples including: Collins bar diagram, pie diagram, Stiff pattern diagram, Schoeller plot, Piper diagram, Q-mode hierarchical cluster analysis, K-means clustering, principal components analysis, and fuzzy k-means clustering. All the methods are discussed and compared as to their ability to cluster, ease of use, and ease of interpretation. In addition, several issues related to data preparation, database editing, data-gap filling, data screening, and data quality assurance are discussed and a database construction methodology is presented. The use of graphical techniques proved to have limitations compared with the multivariate methods for large data sets. Principal components analysis is useful for data reduction and to assess the continuity/overlap of clusters or clustering/similarities in the data. The most efficient grouping was achieved by statistical clustering techniques. However, these techniques do not provide information on the chemistry of the statistical groups. The combination of graphical and statistical techniques provides a consistent and objective means to classify large numbers of samples while retaining the ease of classic graphical presentations. Electronic Publication     

Evaluation of Alexandria Eastern Harbor evaporation estimate methods

The best evaporation estimate method for Alexandria Eastern Harbor has been derived following the evaluation of performance of five evaporation estimate methods, namely, (1) Bowen ratio energy balance (BREB), (2) De Bruin–Keijman (DK), (3) Priestley–Taylor (PT), (4) Brutsaert–Stricker (BS), and (5) Penman (PM), based on two consecutive summer seasons of 2010 and 2011 data. Different statistical measurements of goodness of fit, namely, coefficient of determination (R²), root mean square error (RMSE), relative bias (RB), and index of agreement (D) have been chosen for the evaluation of the performance. When the Bowen ratio is known a priori, the DK and PT methods have been found the best evaporation estimate methods. The responses of the three methods BREB, DK, and PT were found comparable to each other, while the PM method response differed to match with the responses of the other three methods. The Bowen ration (β) of 0.05 and Priestley–Taylor (PT) coefficient (α) of 1.23 derived from the analysis can be extended for evaporation estimates in Alexandria Eastern Harbor, Egypt.     

吹填砂土地基的不同加固方法效果评价

某港口堆场地基由砂土吹填而成,地基承载力约为65kPa,为使地基达到150kPa的承载要求,必须对该吹填砂土地基进行处理。根据场区不同的地层条件、使用功能和地基强度,设计分别采用插板振冲、插板强夯、不插板强夯三种加固方法进行试验。试验检测结果表明,三种加固方法处理后的地基承载力均能满足设计,插排强夯效果最佳。