共查询到20条相似文献，搜索用时 781 毫秒
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The groundwater response of coastal aquifers to tidal forcing is described by Laplace's equation coupled with the nonlinear phreatic-free surface boundary condition. Here we describe fluctuations in the water table using two small parameters, extending previous work by proposing an ansatz to compute higher order, semi-analytical solutions. The new solutions are compared with known lower order solutions. The relative difference between the linear solution and higher order solutions can reach up to 30% of the linear solution for shallow beaches. The new solutions exhibit a reduction in the over height of the groundwater fluctuations compared with the lower order solutions. In addition, the super elevation of the water table, both near shore and as the aquifer tends landward, is examined with the inclusion of higher order terms. 相似文献
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Water Resources - An initial–boundary value problem for the one-dimensional nonlinear parabolic second-order partial differential equation that describes water movement in soil is considered.... 相似文献
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倾斜地层地震液化和滑移的有限元分析 总被引：1，自引：0，他引：1
应用饱和多孔介质动力学分析倾斜地层的土壤动力线性反应、液化和液化滑移问题，地下水位上的地层简化为单相介质层，饱和夹砂层看作是两相介质，水是可压缩的，采用双曲线非线性本构关系，考虑了砂土的剪胀性、刚度退化、滞回特性和土水相对运动等因素。基于土力学模型，建立了适用于分析非自由场地液化的动力方程组，基于是否考虑发生渗流问题，同时建立了两种离散形式：一种是以土骨架位移和水位移为未知量的矩阵方程，另一种是以土骨架位移、水位移和孔隙水压力为未知量的矩阵方程，初步分析了适用于多孔介质波动模拟的离散模型的人工边界问题，形成的方法将有助于问题的解决。 相似文献
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P. Latinopoulos 《Advances in water resources》1984,7(3):137-140
Analytical solutions for groundwater flow in unconfined rectangular aquifers are presented for the case of recharge from rectangular areas. The linearised differential equation of the flow is solved using Laplace and finite Fourier transforms. The problem concerns the response of finite aquifers to periodic (seasonal) recharge schemes of variable duration. Results can be obtained for various combinations of Dirichlet and Neumann boundary conditions and can be easily used in a preliminary study of water resources management. 相似文献
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《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
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In this paper we derive some similarity solutions of a nonlinear equation associated with a free boundary problem arising
in the shallow-water approximation in glaciology. In addition we present a classical potential symmetry analysis of this second-order
nonlinear degenerate parabolic equation related to non-Newtonian ice sheet dynamics in the isothermal case. After obtaining
a general result connecting the thickness function of the ice sheet and the solution of the nonlinear equation (without any
unilateral formulation), a particular example of a similarity solution to a problem formulated with Cauchy boundary conditions
is described. This allows us to obtain several qualitative properties on the free moving boundary in the presence of an accumulation-ablation
function with realistic physical properties. 相似文献
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Estimation of vertical water fluxes from temperature time series by the inverse numerical computer program FLUX‐BOT 
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下载免费PDF全文 The application of heat as a hydrological tracer has become a standard method for quantifying water fluxes between groundwater and surface water. The typical application is to estimate vertical water fluxes in the shallow subsurface beneath streams or lakes. For this purpose, time series of temperatures in the surface water and in the sediment are measured and evaluated by a vertical 1D representation of heat transport by advection and conduction. Several analytical solutions exist to calculate the vertical water flux from the measured temperatures. Although analytical solutions can be easily implemented, they are restricted to specific boundary conditions such as a sinusoidal upper temperature boundary. Numerical solutions offer higher flexibility in the selection of the boundary conditions. This, in turn, reduces the effort of data preprocessing, such as the extraction of the diurnal temperature variation from the raw data. Here, we present software to estimate water fluxes based on temperatures—FLUX‐BOT. FLUX‐BOT is a numerical code written in MATLAB that calculates vertical water fluxes in saturated sediments based on the inversion of measured temperature time series observed at multiple depths. FLUX‐BOT applies a centred Crank–Nicolson implicit finite difference scheme to solve the one‐dimensional heat advection–conduction equation. FLUX‐BOT includes functions for the inverse numerical routines, functions for visualizing the results, and a function for performing uncertainty analysis. We present applications of FLUX‐BOT to synthetic and to real temperature data to demonstrate its performance. 相似文献
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A convection-diffusion equation arises from the conservation equations in miscible and immiscible flooding, thermal recovery, and water movement through desiccated soil. When the convection term dominates the diffusion term, the equations are very difficult to solve numerically. Owing to the hyperbolic character assumed for dominating convection, inaccurate, oscillating solutions result. A new solution technique minimizes the oscillations. The differential equation is transformed into a moving coordinate system which eliminates the convection term but makes the boundary location change in time. We illustrate the new method on two one-dimensional problems: the linear convection-diffusion equation and a non-linear diffusion type equation governing water movement through desiccated soil. Transforming the linear convection diffusion equation into a moving coordinate system gives a diffusion equation with time dependent boundary conditions. We apply orthogonal collocation on finite elements with a Crank-Nicholson time discretization. Comparisons are made to schemes using fixed coordinate systems. The equation describing movement of water in dry soil is a highly non-linear diffusion-type equation with coefficients varying over six orders of magnitude. We solve the equation in a coordinate system moving with a time-dependent velocity, which is determined by the location of the largest gradient of the solution. The finite difference technique with a variable grid size is applied, and a modified Crank-Nicholson technique is used for the temporal discretization. Comparisons are made to an exact solution obtained by similarity transformation, and with an ordinary finite difference scheme on a fixed coordinate system. 相似文献
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Detailed monitoring of the groundwater table can provide important data about both short‐ and long‐term aquifer processes, including information useful for estimating recharge and facilitating groundwater modeling and remediation efforts. In this paper, we presents results of 4 years (2002 to 2005) of monitoring groundwater water levels in the Rio Claro Aquifer using observation wells drilled at the Rio Claro campus of São Paulo State University in Brazil. The data were used to follow natural periodic fluctuations in the water table, specifically those resulting from earth tides and seasonal recharge cycles. Statistical analyses included methods of time‐series analysis using Fourier analysis, cross‐correlation, and R/S analysis. Relationships could be established between rainfall and well recovery, as well as the persistence and degree of autocorrelation of the water table variations. We further used numerical solutions of the Richards equation to obtain estimates of the recharge rate and seasonable groundwater fluctuations. Seasonable soil moisture transit times through the vadose zone obtained with the numerical solution were very close to those obtained with the cross‐correlation analysis. We also employed a little‐used deep drainage boundary condition to obtain estimates of seasonable water table fluctuations, which were found to be consistent with observed transient groundwater levels during the period of study. 相似文献
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Nathan Paldor 《地球物理与天体物理流体动力学》2013,107(3):171-191
Abstract It is shown that the inclusion of the nonlinear terms in the equations of motion of a coupled density front of zero potential vorticity results in wave solutions which merely propagate with time. The linear theory, on the other hand, predicts an exponential temporal growth. The nonlinear equation admits steady solutions representing standing waves whereas if the nonlinear terms are omitted no steady solutions exist. The general initial value problem is difficult to solve numerically since the linear problem is ill posed. In addition we prove that the general similarity solution of the nonlinear equation tends to zero for large times, at any point in space, regardless of the initial condition. 相似文献
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Andy Louwyck Alexander Vandenbohede Griet Heuvelmans Marc Van Camp Kristine Walraevens 《Ground water》2023,61(1):100-110
The water budget myth, which is the idea that safe pumping must not exceed the initial recharge, gave rise to a controversy about the role of recharge in assessing the sustainability of groundwater development. To refute the concept of safe yield, a simplified water budget equation is used, which equals the total pumping rate to the sum of capture and storage change. Since initial recharge and discharge are canceled out from this equation, it is concluded that sustainable pumping has nothing to do with recharge. Investigating the assumptions underlying this equation, it is seen that it expresses the superposition principle, which implicitly assumes the groundwater reservoir can be depleted indefinitely and boundary conditions are an infinite source of water. To evaluate sustainability, however, the limits of the aquifer system must be examined accurately. Theoretically, this can only be accomplished applying nonlinear models, in which case setting up the simplified water budget equation is impossible without knowing the initial conditions. Hence, excluding recharge when assessing sustainable pumping may not be done inconsiderately, which is illustrated by two examples. An analytical solution, developed by Ernst in 1971 to simulate flow to a well in a polder area with a nonlinear function for drainage, even shows that it is not necessarily a misconception to assume the cone of depression stops expanding when the pumping rate is balanced by the infiltration rate. 相似文献
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Hillel Rubin 《Advances in water resources》1983,6(2):96-105
Stratification of the density in groundwater flow stems from the contact between water which contains minerals in low concentration with water containing a high concentration of minerals. The flow in such a flow field should be simulated by solving simultaneously the equations of continuity, motion and solute transport, because solute concentration affects the dynamics of the flow. Such an approach is generally associated with complicated calculations and numerical schemes subject to problems of convergence and stability, as the basic equations are highly nonlinear.This study applies the phenomenological boundary layer approximation, and suggests a reference to three different zones in the flow field: (a) fresh water zone, (b) transition zone, and (c) mineralized water zone. In zones (a) and (c) it is assumed that the potential flow theory can be applied. In zone (b) the flow is nonpotential but the basic similarity conditions typical to boundary layers exist.The approach suggested in this study simplifies the mathematical models that should be used for the flow field simulation. This approach is especially attractive in cases where the Dupuit approximation is applicable. In such cases very often analytical solutions can be obtained for unidirectional flows. In cases that are too complicated for representation by analytical solutions, the method can be used for the creation of simplified numerical schemes.Various examples in this study demonstrate the application of the method for various field problems associated with steady state as well as unsteady state conditions.The simplicity of the method makes it useful for variety of problems. It can be used even by small institutions and small consulting firms, who have usually access to minicomputers and microprocessors. 相似文献
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The direct finite element method is a type commonly used for nonlinear seismic soil-structure interaction(SSI) analysis. This method introduces a truncated boundary referred to as an artificial boundary meant to divide the soilstructure system into finite and infinite domains. An artificial boundary condition is used on a truncated boundary to achieve seismic input and simulate the wave radiation effect of infinite domain. When the soil layer is particularly thick, especially for a three-dimensional problem, the computational efficiency of seismic SSI analysis is very low due to the large size of the finite element model, which contains an whole thick soil layer. In this paper, an accurate and efficient scheme is developed to solve the nonlinear seismic SSI problem regarding thick soil layers. The process consists of nonlinear site response and SSI analysis. The nonlinear site response analysis is still performed for the whole thick soil layer. The artificial boundary at the bottom of the SSI analysis model is subsequently relocated upward from the bottom of the soil layer(bedrock surface) to the location nearest to the structure as possible. Finally, three types of typical sites and underground structures are adopted with seismic SSI analysis to evaluate the accuracy and efficiency of the proposed efficient analysis scheme. 相似文献
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Yang-De Feng Yue-Sheng Wang Zi-Mao Zhang 《Soil Dynamics and Earthquake Engineering》2003,23(4):303-311
A 2D time domain boundary element method (BEM) is developed to study the dynamic response of a cylinder embedded in soil. The interface is assumed in contact with Coulomb friction. For the incident wave strong enough, local slip may occur along the interface. We suppose a pressure enough high is applied on the interface so that separation is impossible. The present problem is indeed a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (slip and stick regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embedded in an infinite solid. Numerical results for the near field solutions are presented. The nonlinear nature of the system is discussed. 相似文献
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The ultimate specific yield, i.e. the specific yield under steady‐state condition, is generally dependent on the water table depth in the shallow groundwater systems. This paper presents a new expression to describe this relationship. The expression is based on the relationship between soil water content–soil depths below ground surface near the saturation zone, i.e. water content profile, which can be fitted by the van Genuchten model. Because this model is highly nonlinear, a Taylor series expansion was used to solve the integral equation for specific yield in our study. The new expression was verified by a drainage experiment, and the results demonstrated that the new expression is reliable for eolian sand when the range of water table fluctuation is less than 30 cm. The expression is easily applicable because knowledge of the water content profile near the saturation zone is the only requirement. Compared with the expression obtained from the Brooks–Corey model, the new expression can be used for a variety of aquifer and soil media. The improved accuracy of the specific yield provides a better estimate of discharge rates in shallow groundwater systems with water table fluctuations. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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Marius Todsen 《Journal of Hydrology》1973,20(4):311-326
The partial differential equation which governs the seepage of water in unsaturated and saturated porous media is solved numerically by a generalized Newton iteration technique for two models, one ditch drainage model and one earth dam model. For each model, which is two-dimensional, a few hypothetical soils with different moisture retention curves are considered. In both models only drainage from an initially saturated soil occurs; thus, the problem of hysteresis is avoided. The results of the computations are compared with those of corresponding saturated (pure groundwater) models; solutions obtained earlier by this author and others.
Computational instability phenomena appear when the slope of the retention curves is made steep, i.e., for poorly-graded soils. 相似文献
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S. Eeman A. LeijnseP.A.C. Raats S.E.A.T.M. van der Zee 《Advances in water resources》2011,34(2):291-302
In regions with saline groundwater, fresh water lenses may develop due to rainwater infiltration. The amount of fresh water that is available for e.g. agricultural crops depends on the thickness of the lens and the extent of mixing between fresh and saline water. In this paper, we consider the mixing of fresh water and upward moving saline ground water in low-lying deltaic areas. The parameters that dominate the flow and transport problem are investigated using dimensionless groups and scaled sensitivities. We characterize the numerically simulated thicknesses of the lens and of the mixing zone by spatial moments. Rayleigh number and mass flux ratio, which is the ratio of the salt water seepage and the precipitation, determine the thickness of the fresh water lens. The local thickness of the mixing zone is mainly influenced by the dispersive/diffusive groups and the mass flux ratio. In addition, convergence of streamlines towards an outflow boundary affects the thickness, particularly in the vicinity of this boundary.Analytical and numerical steady state solutions for lens thickness are compared, taking into account upward seepage, for the two cases with and without a density difference between lens and underlying groundwater. Agreement between the numerical and analytical solutions for the lens thickness is good except when the mass flux ratio becomes small. For zero mass flux ratio, it is implicitly assumed in the analytical solution that salt water is stagnant, and that is unrealistic. Relative contributions of longitudinal and transversal hydrodynamic dispersion and diffusion to the thickness of the mixing zone are quantified numerically for different phases of lens formation. Longitudinal dispersion dominates in the early stages of lens formation, while diffusion and transversal dispersion dominate at steady state. 相似文献
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The Laplace domain solutions have been obtained for three-dimensional groundwater flow to a well in confined and unconfined wedge-shaped aquifers. The solutions take into account partial penetration effects, instantaneous drainage or delayed yield, vertical anisotropy and the water table boundary condition. As a basis, the Laplace domain solutions for drawdown created by a point source in uniform, anisotropic confined and unconfined wedge-shaped aquifers are first derived. Then, by the principle of superposition the point source solutions are extended to the cases of partially and fully penetrating wells. Unlike the previous solution for the confined aquifer that contains improper integrals arising from the Hankel transform [Yeh HD, Chang YC. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 2006;26:471–80], numerical evaluation of our solution is relatively easy using well known numerical Laplace inversion methods. The effects of wedge angle, pumping well location and observation point location on drawdown and the effects of partial penetration, screen location and delay index on the wedge boundary hydraulic gradient in unconfined aquifers have also been investigated. The results are presented in the form of dimensionless drawdown-time and boundary gradient-time type curves. The curves are useful for parameter identification, calculation of stream depletion rates and the assessment of water budgets in river basins. 相似文献