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1.
Mehl S 《Ground water》2006,44(4):583-594
This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems. 相似文献
2.
A study on the dynamic characteristics of rigid foundations with special geometries such as square or circular with concentric internal holes, is presented. The foundations are resting on a homogeneous, linear elastic halfspace and are subjected to external forces or seismic wave excitation. Both ‘relaxed’ and ‘non-relaxed’ boundary conditions at the interface between the foundation and the halfspace are considered, and several parametric studies are conducted to assess the influence of either type of boundary conditions upon each of the possible modes of vibration. Results for massive and massless foundations are presented in time and frequency domains for impulsive and harmonic excitations, respectively. A time domain boundary element method (BEM) developed by the authors for the solution of a class of 3-D soil-structure interaction (SSI) problems is used for all the analyses reported in this work. The accuracy and efficiency of the method and the BEM models developed in this work are assessed on the basis of comparison studies with published results. 相似文献
3.
This methods note examines the use of adaptive underrelaxation of Picard iterations to accelerate the solution convergence for nonlinear ground water flow problems. Ground water problems are nonlinear when drains, phreatophytes, stream aquifer, and similar features are simulated. Typically, simple Picard iterations are used to address such nonlinear problems. Nevertheless, the convergence rate can be slow, or convergence cannot be obtained. However, convergence often can be accelerated using Picard iterations with adaptive underrelaxation, and convergence often can be obtained where it otherwise would not occur. 相似文献
4.
To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range fplays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection rangef The proposed method is shown to be efficient and to yield accurate results. 相似文献
5.
S. Boominathan
K. Senathipathi
V. Jayaprakasam
《Soil Dynamics and Earthquake Engineering》1991,10(8):402-406The concept of reinforced earth has not become popular in the case of foundations for buildings. Presumably, the practical difficulties in application and the exorbitant cost have outweighed the beneficial aspects of ‘Reinforced Earth’ in such applications. Block foundations which are usually provided for machines to take care of the dynamic loads are small and compact and the improvement of the base with reinforcements should not be a difficult or impractical proposition. In this investigation, the feasibility of improving the dynamic properties of soil b ase by applying high modulus materials, such as steel wires and low modulus materials as geotextiles, and a combination of both have been studied in a standard forced vertical block resonance test. The feasibility and the supremacy of the ‘Reinforced Earth’ with the reinforced bases of (i) mild steel frame stiffened with high tensile wires (ii) sand coated geotextiles with the inclusion of a thin layer of frictional sand and (iii) sand coated geotextiles stiffened with welded mesh, have been brought out. 相似文献
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7.
处理转换计算在重磁资料解释中发挥着重要的作用,但一些计算如向下延拓、化极等有时是很不稳定的,在频率域中则表现为其转换因子具有明显的放大作用,所以其FFT理论计算结果是不稳定的.因此,很多研究工作都是围绕增加计算的稳定性、提高计算效果进行的,其中迭代法是近来在研究中受到普遍重视的方法技术,并取得了较好的成果.但也存在对迭代法研究还不够深入,对其存在的缺点认识不够充分、客观等问题,例如,迭代法进行延拓及化极等计算时,对一些具体应用虽能在一定程度上获得较好的计算结果,但却存在计算结果并不会随着迭代次数的增加而得到持续改善的问题,对于原本不稳定的计算,迭代法在迭代次数比较大时,所得的结果依然是不稳定的.为此,本文在对迭代法进行分析研究的基础上,进一步推导了迭代法的通式,并分析了对迭代法收敛性影响的各种因素.分析结果表明:迭代法收敛到FFT理论直接计算结果的决定因素是计算过程中如何选择原始数据到目标数据的映射函数;在选择了合适的映射函数的情况下,迭代次数不仅仅是决定计算成本,而是决定结果好坏的关键因素;增加迭代次数虽然能够使计算收敛到FFT直接计算理论结果,但如果该理论结果本身就是不稳定的,则迭代法计算如果收敛,也是收敛到一个不稳定的结果.所以针对位场处理转换中一些不稳定计算采用迭代法,并没有从根本上解决计算的不稳定性问题. 相似文献
8.
Donald L. Baker 《Ground water》1995,33(2):259-263
The “modified Picard” iteration method, which offers global mass conservation, can also be described as a form of Newton's iteration with lagged nonlinear coefficients. It converges to a time step with first-order discretization error. This paper applies second- and third-order diagonally implicit Runge Kutta (DIRK) time steps to the modified Picard method in one example. It demonstrates improvements over the first-order time step in rms error and error-times-effort model quality by factors ranging from two to over two orders of magnitude, showing that the “modified Picard” and DIRK methods are compatible. 相似文献
9.
Dewatered or "dry" grid cells in the USGS ground water modeling software MODFLOW may cause nonphysical artifacts, trigger convergence failures, or interfere with parameter estimation. These difficulties can be avoided in two dimensions by modifying the spatial differencing scheme and the iterative procedure used to resolve nonlinearities. Specifically, the spatial differencing scheme is modified to use the water level on the upstream side of a pair of adjacent cells to calculate the saturated thickness and hence intercell conductance for the pair. This makes it possible to explicitly constrain the water level in a cell to be at or above the cell bottom elevation without introducing nonphysical artifacts. Thus constrained, all initially active cells will remain active throughout the simulation. It was necessary to replace MODFLOW's Picard iteration method with the Newton-Raphson method to achieve convergence in demanding applications involving many dry cells. Tests using a MODFLOW variant based on the new method produced results nearly identical to conventional MODFLOW in situations where conventional MODFLOW converges. The new method is extremely robust and converged in scenarios where conventional MODFLOW failed to converge, such as when almost all cells dewatered. An example application to the Edwards Aquifer in south-central Texas further demonstrates the utility of the new method. 相似文献
10.
Most lead brought to the Mediterranean Sea has an anthropogenic origin and is mainly transported through the atmosphere. Atmospheric Pb was continuously collected at Cap Ferrat in 1986 and 1987. From this study, the estimation of the anthropogenic Pb flux on the whole Western Mediterranean was, averaged on 1986 and 1987 data, 4080 t. Assuming that the atmospheric anthropogenic Pb input varied in this course of time similarly to the consumption of Pb added to gasolines in France, the mean annual flux could be calculated: 3.95 kg km−2 yr−1, that is an annual input of 3360 t yr−1. Reaching the sea, this metal seems to become rapidly bound to phytoplankton. Grazing by zooplankton leads to the production of faecal pellets which frequently contain rather high metal concentrations. The sinking rate of pellets of various zooplankton species is high; within a few days pellets may reach deep-sea sediments. After deposition, Pb is released from this organic-rich material during early diagenesis. In most cases, it, therefore, returns to the overlaying water body by ascending diffusion. But, in a deep-sea area of approximately 80 000 km2 where Mn oxide precipitation occurs in surficial sediments, Pb seems to remain stored by coprecipitation processes. By considering the lead stored in ‘excess’ in the surficial sediment of the deep-sea area, we estimate that a mean annual anthropogenic Pb amount ranging from 800 up to 1080 t was stored every year from 1950. On the same area, taking into account the Pb loss at the straits, the ‘direct’ atmospheric input to the sea bottom is, on average, 184 t yr−1. The remaining part, that is (800–1080)−184=(616–896) t yr−1, corresponds to an additional ‘indirect’ Pb flux in water due to Pb released from sediments of the surrounding areas where it does not remain stored. 相似文献
11.
Lars Landner 《Marine pollution bulletin》1994,29(6-12):593-598
The changing concepts and challenges that the process industry has to face in relation to environmental protection are discussed. The original requirements on industry to reduce emissions of contaminants through the installation of filters and waste water treatment facilities or through process modification and introduction of ‘clean production’ strategies were mainly based on economic and technical considerations rather than on an effort to avoid environmental impacts. The introduction of concepts such as ‘assimilative capacity of the environment’ and ‘critical load’ provided useful instruments for setting effect-related emission standards, resulting in acceptable environmental protection. However, the actual requirement for ‘sustainability’ has forced industry to focus not only on controlling emissions of contaminants and pollutants, but to take a global environmental approach, including the choice of raw materials and energy sources, recycling and re-utilization of wastes and to take responsibility for the fate of their products, during their whole lifecycle. 相似文献
12.
Morton's complementary relationship areal evapotranspiration (CRAE) model was originally designed to provide regional estimates of monthly evapotranspiration. Often, however, hydrologists and others require estimates of evapotranspiration for field-sized land units under a specific land use, for shorter intervals of time. This paper examines CRAE with respect to the algorithms used to describe different terms and its applicability to reduced spatial and temporal scales.
Daily estimates by CRAE of atmospheric radiation fluxes during the summer months are compared with monitored values. It is shown that errors in estimation of the extra-terrestrial flux, the transmittancy of clouds to short-wave radiation, the surface albedo and the net long-wave flux result in standard deviations of the difference between ‘modelled’ and ‘measured’ net all-wave radiation for 1-, 5- and 10-day periods of 2.58, 1.8 and 1.50 MJm−2 day−1 respectively.
The assumption in CRAE that the vapour transfer coefficient is independent of wind speed may lead to appreciable error in computing evapotranspiration. A procedure for incorporating a wind correction factor is described and the improvement in estimating regional evaporation is illustrated.
Comparisons of evapotranspiration estimates by CRAE and measurements obtained from soil moisture and precipitation observations in the semi-arid, cold-climate Prairie region of western Canada demonstrate that the assumptions that the soil heat flux and storage terms are negligible, lead to large overestimation by the model during periods of soil thaw. 相似文献
13.
The errors in surface runoff prediction by neglecting the relationship between infiltration rate and overland flow depth 总被引：9，自引：0，他引：9
Many simplifications are used in modeling surface runoff over a uniform slope. A very common simplification is to determine the infiltration rate independent of the overland flow depth and to combine it afterward with the kinematic-wave equation to determine the overland flow depth. Another simplication is to replace the spatially variable infiltration rates along the slope i(x, t) due to the water depth variations h(x,t) with an infiltration rate that is determined at a certain location along the slope. The aim of this study is to evaluate the errors induced by these simplications on predicted infiltration rates, overland flow depths, and total runoff volume. The error analysis is accomplished by comparing a simplified model with a model where the interaction between the overland flow depth and infiltration rate is counted. In this model, the infiltration rate is assumed to vary along the slope with the overland flow depth, even for homogeneous soil profiles. The kinematic-wave equation with interactive infiltration rate, calculated along the slopy by Richard's equation, are then solved by a finite difference scheme for a 100-m-long uniform slope. In the first error analysis, we study the effect of combining an ‘exact’ and ‘approximate’ one-dimensional infiltration rate with the kinematic-wave equation for three different soil surface roughness coefficients. The terms ‘exact’ and ‘approximate’ stand for the solution of Richard's equation with and without using the overland flow depth in the boundary condition, respectively. The simulations showed that higher infiltration rates and lower overland flow depths are obtained during the rising stage of the hydrograph when overland flow depth is used in the upper boundary condition of the one-dimensional Richard's equation. During the recession period, the simplified model predicts lower infiltration rates and higher overland flow depths. The absolute relative errors between the ‘exact’ and ‘approximate’ solutions are positively correlated to the overland flow depths which increase with the soil surface roughness coefficient. For this error analysis, the relative errors in surface runoff volume per unit slope width throughout the storm are much smaller than the relative errors in momentary overland flow depths and discharges due to the alternate signs of the deviations along the rising and falling stages. In the second error analysis, when the spatially variable infiltration rate along the slope i(x, t) is replaced in the kinematic-wave equation by i(t), calculated at the slope outlet, the overland flow depth is underestimated during the rising stage of the hydrograph and overestimated during the falling stage. The deviations during the rising stage are much smaller than the deviations during the falling stage, but they are of a longer duration. This occurs because the solution with i(x, t) recognizes that part of the slope becomes dry after rainfall stops, while overland flow still exists with i(t) determined at the slope outlet. As obtained for the first error analysis, the relative errors in surface runoff volume per unit slope width are also much smaller than the relative errors in momentary overland flow depths and discharges. The relation between the errors in overland flow depth and discharge to different mathematical simplifications enables to evaluate whether certain simplifications are justified or more computational efforts should be used. 相似文献
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15.
In the last two decades, the effects of forest management on streams, riparian zones, and floodplains have become of much interest. In general, there is agreement that such areas should be maintained in a state approximating naturalness, although it is recognised that definition of this state is usually difficult or impossible. A diversity of management effects has been recognised and, in some cases quantified. For upland catchments, issues particularly relate to direct disturbance of the zone, changes in the flow of woody debris into the stream, or disturbance to the environment by effects generated upstream or downstream. For many areas, a particularly important commercial aspect is the definition of a ‘stream’, as this can impose many expensive and severe restrictions on management of the land. For large rivers, a common issue is the effect of river management on flooding forests. In each case, the issues are complex, information is difficult to collect, and there are fundamental difficulties in going from anecdotal observation to data. Currently, most information appears to be at a relatively local level, and there is a very inadequate knowledge base to give a more holistic overview, although the concept of ‘cumulative effects’, with the effects accumulated over both space and time, has much potential value. There are many opportunities for work in this field. 相似文献
16.
Simulating sensitivity of soil moisture and evapotranspiration under heterogeneous soils and land uses 总被引：9，自引：0，他引：9
Soil moisture (SM) plays an important role in land surface and atmospheric interactions. It modifies energy balance at the surface and the rate of water cycling between the land and atmosphere. In this paper we provide a sensitivity assessment of SM and ET for heterogeneous soil physical properties and for three land uses including irrigated maize, rainfed maize, and grass at a climatological time-scale by using a water balance model. Not surprisingly, the study finds increased soil water content in the root zone throughout the year under irrigated farming. Soil water depletes to its lowest level under rainfed maize cultivation. We find a ‘land use’ effect as high as 36 percent of annual total evapotranspiration, under irrigated maize compared to rainfed maize and grass, respectively. Sensitivity analyses consisting of comparative simulations using the model show that soil characteristics, like water holding capacity, influence SM in the root zone and affect seasonal total ET estimates at the climatological time-scale. This ‘soils’ effect is smaller than the ‘land use’ effect associated with irrigation but, it is a source of consistent bias for both SM and ET estimates. The ‘climate’ effect basically masks the ‘soils’ effect under wet conditions. These results lead us to conclude that appropriate representation of land use, soils, and climate are necessary to accurately represent the water and energy balance in real landscapes. 相似文献
17.
Assessing the extent of local trace metal pollution in marine atmospheric particulates presents a number of difficulties, and one potential approach to the problem has been evaluated by reference to a series of aerosols from the lower troposphere over the Eastern Mediterranean. This region, which is less remote from the continents than open-ocean areas, has two significantly different atmospheric particulate catchments: being bordered in the north by nations having industrialized, semi-industrialized and rural economies, and in the south by the North African desert belt. The elemental chemistry of the particulates is illustrated in terms of the distributions of Fe and Pb, which are presented in the form of enrichment factor diagrams, and is shown to be essentially controlled by the dilution of a ‘European’ background material, common to ‘remote’ regions of the latitudinal belt, with crust-derived, desert components. Major local perturbations in the dilution relationship can occur when either crust-derived or pollutant components strongly dominate the total particulate population. The extent of these local perturbations can be tentatively assessed using appropriate enrichment factor diagrams, which offer a framework within which to interpret the elemental chemistry of marine atmospheric particulates providing sufficient data is available for their construction. By using such an EF diagram it is suggested that the Eastern Mediterranean atmospheric particulates have not suffered local pollution on a gross scale with respect to Pb. 相似文献
18.
《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
19.
Olivia Jensen Jacques Hinderer David J. Crossley 《Physics of the Earth and Planetary Interiors》1995,90(3-4)
In recent years, several claims of detection of weak harmonic signals in the sub-tidal band of frequencies of high-quality gravimeter data have been made. Here, we review our attempts at confirming Smylie's claim of detection of the Slichter mode of inner-core oscillation using the same four data sets he and his colleagues used. We further examine the homogeneous 2 year data sets obtained from the superconducting gravimeters sited in Strasbourg and at Cantley, Quebec. We show that the power spectra of tidal-reduced, pressure and slew-corrected gravity residuals from these data are indistinguishable from a random walk process except in narrow bands dominated by residual earth tides and by harmonics of the diurnal thermal-atmospheric tide. Such a random ‘brown’ residual could result from mechanical instabilities and electronic noise in the instruments themselves, from site-specific tectonic noise, from local hydrological variations and pier instabilities or it could derive from unaccounted for variability in the atmospheric pressure in the vicinity of the instruments. We argue that the homogeneous 2 year data sets show no evidence whatever of Slichter harmonics even though our preprocessing methods reduce ‘apparent noise levels’ in the core-mode band by almost an order magnitude in comparison with the four data sets originally employed by Smylie et al. and, in their first attempted confirmation of his claimed discovery, by Jensen et al. 相似文献
20.
The priorities for the protection of the seas have been discussed extensively. Many consider that the problem of marine pollution can only be solved on the basis of joint international actions. This is particularly true for the various countries bordering on the North Sea. To implement such ‘Joint Actions’, a new understanding of safety, namely ‘global maritime safety’ should be discussed with all those involved. 相似文献