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1.
《Advances in water resources》2002,25(5):497-511
A new method of local grid refinement for two-dimensional block-centered finite-difference meshes is presented in the context of steady-state groundwater-flow modeling. The method uses an iteration-based feedback with shared nodes to couple two separate grids. The new method is evaluated by comparison with results using a uniform fine mesh, a variably spaced mesh, and a traditional method of local grid refinement without a feedback.Results indicate: (1) The new method exhibits quadratic convergence for homogenous systems and convergence equivalent to uniform-grid refinement for heterogeneous systems. (2) Coupling the coarse grid with the refined grid in a numerically rigorous way allowed for improvement in the coarse-grid results. (3) For heterogeneous systems, commonly used linear interpolation of heads from the large model onto the boundary of the refined model produced heads that are inconsistent with the physics of the flow field. (4) The traditional method works well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 3.6% and errors in cell-to-cell flows up to 25%. 相似文献
2.
Grid refinement is introduced in a numerical groundwater model to increase the accuracy of the solution over local areas without compromising the run time of the model. Numerical methods developed for grid refinement suffered certain drawbacks, for example, deficiencies in the implemented interpolation technique; the non‐reciprocity in head calculations or flow calculations; lack of accuracy resulting from high truncation errors, and numerical problems resulting from the construction of elongated meshes. A refinement scheme based on the divergence theorem and Taylor's expansions is presented in this article. This scheme is based on the work of De Marsily (1986) but includes more terms of the Taylor's series to improve the numerical solution. In this scheme, flow reciprocity is maintained and high order of refinement was achievable. The new numerical method is applied to simulate groundwater flows in homogeneous and heterogeneous confined aquifers. It produced results with acceptable degrees of accuracy. This method shows the potential for its application to solving groundwater heads over nested meshes with irregular shapes. 相似文献
3.
Simple Hydraulic Conductivity Estimation by the Kalman Filtered Double Constraint Method 总被引：1，自引：0，他引：1 
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下载免费PDF全文 This paper presents the Kalman Filtered Double Constraint Method (DCM‐KF) as a technique to estimate the hydraulic conductivities in the grid blocks of a groundwater flow model. The DCM is based on two forward runs with the same initial grid block conductivities, but with alternating flux‐head conditions specified on parts of the boundary and the wells. These two runs are defined as: (1) the flux run, with specified fluxes (recharge and well abstractions), and (2) the head run, with specified heads (measured in piezometers). Conductivities are then estimated as the initial conductivities multiplied by the fluxes obtained from the flux run and divided by the fluxes obtained from the head run. The DCM is easy to implement in combination with existing models (e.g., MODFLOW). Sufficiently accurate conductivities are obtained after a few iterations. Because of errors in the specified head‐flux couples, repeated estimation under varying hydrological conditions results in different conductivities. A time‐independent estimate of the conductivities and their inaccuracy can be obtained by a simple linear KF with modest computational requirements. For the Kleine Nete catchment, Belgium, the DCM‐KF yields sufficiently accurate calibrated conductivities. The method also results in distinguishing regions where the head‐flux observations influence the calibration from areas where it is not able to influence the hydraulic conductivity. 相似文献
4.
An inverse method is developed to simultaneously estimate multiple hydraulic conductivities, source/sink strengths, and boundary conditions, for two-dimensional confined and unconfined aquifers under non-pumping or pumping conditions. The method incorporates noisy observed data (hydraulic heads, groundwater fluxes, or well rates) at measurement locations. With a set of hybrid formulations, given sufficient measurement data, the method yields well-posed systems of equations that can be solved efficiently via nonlinear optimization. The solution is stable when measurement errors are increased. The method is successfully tested on problems with regular and irregular geometries, different heterogeneity patterns and variances (maximum Kmax/Kmin tested is 10,000), and error magnitudes. Under non-pumping conditions, when error-free observed data are used, the estimated conductivities and recharge rates are accurate within 8% of the true values. When data contain increasing errors, the estimated parameters become less accurate, as expected. For problems where the underlying parameter variation is unknown, equivalent conductivities and average recharge rates can be estimated. Under pumping (and/or injection) conditions, a hybrid formulation is developed to address these local source/sink effects, while different types of boundary conditions can also exert significant influences on drawdowns. Local grid refinement near wells is not needed to obtain accurate results, thus inversion is successful with coarse inverse grids, leading to high computation efficiency. Furthermore, flux measurements are not needed for the inversion to succeed; data requirement of the method is thus not much different from that of interpreting classic well tests. Finally, inversion accuracy is not sensitive to the degree of nonlinearity of the flow equations. Performance of the inverse method for confined and unconfined aquifer problems is similar in terms of the accuracy of the estimated parameters, the recovered head fields, and the solver speed. 相似文献
5.
Many ground water modeling efforts use a finite-difference method to solve the ground water flow equation, and many of these models require a relatively fine-grid discretization to accurately represent the selected process in limited areas of interest. Use of a fine grid over the entire domain can be computationally prohibitive; using a variably spaced grid can lead to cells with a large aspect ratio and refinement in areas where detail is not needed. One solution is to use local-grid refinement (LGR) whereby the grid is only refined in the area of interest. This work reviews some LGR methods and identifies advantages and drawbacks in test cases using MODFLOW-2000. The first test case is two dimensional and heterogeneous; the second is three dimensional and includes interaction with a meandering river. Results include simulations using a uniform fine grid, a variably spaced grid, a traditional method of LGR without feedback, and a new shared node method with feedback. Discrepancies from the solution obtained with the uniform fine grid are investigated. For the models tested, the traditional one-way coupled approaches produced discrepancies in head up to 6.8% and discrepancies in cell-to-cell fluxes up to 7.1%, while the new method has head and cell-to-cell flux discrepancies of 0.089% and 0.14%, respectively. Additional results highlight the accuracy, flexibility, and CPU time trade-off of these methods and demonstrate how the new method can be successfully implemented to model surface water-ground water interactions. 相似文献
6.
M. Giudici F. Delay G. de Marsily G. Parravicini G. Ponzini A. Rosazza 《Stochastic Hydrology and Hydraulics》1998,12(3):191-204
The Differential System Method (DSM) permits identification of the physical parameters of finite-difference groundwater flow
models in a confined aquifer when piezometric head and source terms are known at each point of the finite-difference lattice
for at least two independent flow situations for which the hydraulic gradients are not parallel. Since piezometric head data
are usually few and sparse, interpolation of the measured data onto a regular grid can be performed with geostatistical techniques.
We apply kriging to the sparse data of a synthetic aquifer to evaluate the stability of the DSM with respect to uncorrelated
measurement errors and interpolation errors. The numerical results show that the DSM is stable. 相似文献
7.
M. Giudici F. Delay G. de Marsily G. Parravicini G. Ponzini A. Rosazza 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(3):191-204
The Differential System Method (DSM) permits identification of the physical parameters of finite-difference groundwater flow
models in a confined aquifer when piezometric head and source terms are known at each point of the finite-difference lattice
for at least two independent flow situations for which the hydraulic gradients are not parallel. Since piezometric head data
are usually few and sparse, interpolation of the measured data onto a regular grid can be performed with geostatistical techniques.
We apply kriging to the sparse data of a synthetic aquifer to evaluate the stability of the DSM with respect to uncorrelated
measurement errors and interpolation errors. The numerical results show that the DSM is stable. 相似文献
8.
This work studies costs and benefits of utilizing local-grid refinement (LGR) as implemented in MODFLOW-LGR to simulate groundwater flow in a buried tunnel valley interacting with a regional aquifer. Two alternative LGR methods were used: the shared-node (SN) method and the ghost-node (GN) method. To conserve flows the SN method requires correction of sources and sinks in cells at the refined/coarse-grid interface. We found that the optimal correction method is case dependent and difficult to identify in practice. However, the results showed little difference and suggest that identifying the optimal method was of minor importance in our case. The GN method does not require corrections at the models' interface, and it uses a simpler head interpolation scheme than the SN method. The simpler scheme is faster but less accurate so that more iterations may be necessary. However, the GN method solved our flow problem more efficiently than the SN method. The MODFLOW-LGR results were compared with the results obtained using a globally coarse (GC) grid. The LGR simulations required one to two orders of magnitude longer run times than the GC model. However, the improvements of the numerical resolution around the buried valley substantially increased the accuracy of simulated heads and flows compared with the GC simulation. Accuracy further increased locally around the valley flanks when improving the geological resolution using the refined grid. Finally, comparing MODFLOW-LGR simulation with a globally refined (GR) grid showed that the refinement proportion of the model should not exceed 10% to 15% in order to secure method efficiency. 相似文献
9.
The ground water flow model MODFLOW inherently implements a nongeneralized integrated finite-difference (IFD) numerical scheme. The IFD numerical scheme allows for construction of finite-difference model grids with curvilinear (piecewise linear) rows. The resulting grid comprises model cells in the shape of trapezoids and is distorted in comparison to a traditional MODFLOW finite-difference grid. A version of MODFLOW-88 (herein referred to as MODFLOW IFD) with the code adapted to make the one-dimensional DELR and DELC arrays two dimensional, so that equivalent conductance between distorted grid cells can be calculated, is described. MODFLOW IFD is used to inspect the sensitivity of the numerical head and velocity solutions to the level of distortion in trapezoidal grid cells within a converging radial flow domain. A test problem designed for the analysis implements a grid oriented such that flow is parallel to columns with converging widths. The sensitivity analysis demonstrates MODFLOW IFD's capacity to numerically derive a head solution and resulting intercell volumetric flow when the internal calculation of equivalent conductance accounts for the distortion of the grid cells. The sensitivity of the velocity solution to grid cell distortion indicates criteria for distorted grid design. In the radial flow test problem described, the numerical head solution is not sensitive to grid cell distortion. The accuracy of the velocity solution is sensitive to cell distortion with error <1% if the angle between the nonparallel sides of trapezoidal cells is <12.5 degrees. The error of the velocity solution is related to the degree to which the spatial discretization of a curve is approximated with piecewise linear segments. Curvilinear finite-difference grid construction adds versatility to spatial discretization of the flow domain. MODFLOW-88's inherent IFD numerical scheme and the test problem results imply that more recent versions of MODFLOW 2000, with minor modifications, have the potential to make use of a curvilinear grid. 相似文献
10.
The identification of groundwater parameters in heterogeneous systems is a major challenge in groundwater modeling. Flexible parameterization methods are needed to assess the complexity of the spatial distributions of these parameters in real aquifers. In this article, we introduce an adaptative parameterization to identify the distribution of hydraulic conductivity within the large‐scale (4400 km2) Upper Rhine aquifer. The method is based on adaptative multiscale triangulation (AMT) coupled with an inverse problem procedure that identifies the parameters' distributions by reducing the error between measured and simulated heads. The AMT method has the advantage of combining both zonation and interpolation approaches. The AMT method uses area‐based interpolation rather than an interpolation based on stochastic features. The method is applied to a standard 2D groundwater model that takes into account the interactions between the aquifer and surface water bodies, groundwater recharge, and pumping wells. The simulation period covers 204 months, from January 1986 to December 2002. Recordings at 109 piezometers are used for model calibration. The simulated heads are globally quite accurate and reproduce the main dynamics of the system. The local hydraulic conductivities resulting from the AMT method agree qualitatively with existing local experimental observations across the Rhine aquifer. 相似文献
11.
Widely used numerical models of solute transport processes in subsurface aquifers are limited to nonlocally refined rectangular, or logically rectangular, structured grids. This presents an unsuitable option to efficient numerical simulations maintaining an acceptable level of accuracy. Optimal selection of locally refined cells for efficient solute transport models is challenging to the current generation of numerical models. We present a novel and relatively simple to implement algorithm addressing these shortcomings. This method operates in four steps involving travel times simulations, a grid coarsening stage followed by a selective local grid refinement based on a cell-wise indicator, and a final postprocessing step. The refinement index is the sum of weighted logarithmic distributions of scaled forward and backward travel times. We calculate representative flow and transport properties at the two scales of the composite grid with a flow-based upscaling technique. We present two test problems to demonstrate the performances of this new gridding algorithm. We obtain the most important speedups for composite grids generated with the highest indicator thresholds. When hydrodynamic dispersion effects increase, we obtain less important speedups. An important outcome of this work is that grid design depends on nature and strength of the underlying flow and solute transport processes. Therefore, we suggest developing solute transport workflows integrating this grid generation algorithm as an integral component to build comprehensive and efficient groundwater models. 相似文献
12.
The staggered grid finite-difference method is a powerful tool in seismology and is commonly used to study earthquake source
dynamics. In the staggered grid finite-difference method stress and particle velocity components are calculated at different
grid points, and a faulting problem is a mixed boundary problem, therefore different implementations of fault boundary conditions
have been proposed. Viriuex and Madariaga (1982) chose the shear stress grid as the fault surface, however, this method has
several problems: (1) Fault slip leakage outside the fault, and (2) the stress bump beyond the crack tip caused by S waves
is not well resolved. Madariaga et al. (1998) solved the latter problem via thick fault implementation, but the former problem remains and causes a new issue;
displacement discontinuity across the slip is not well modeled because of the artificial thickness of the fault. In the present
study we improve the implementation of the fault boundary conditions in the staggered grid finite-difference method by using
a fictitious surface to satisfy the fault boundary conditions. In our implementation, velocity (or displacement) grids are
set on the fault plane, stress grids are shifted half grid spacing from the fault and stress on the fictitious surface in
the rupture zone is given such that the interpolated stress on the fault is equal to the frictional stress. Within the area
which does not rupture, stress on the fictitious surface is given a condition of no discontinuity of the velocity (or displacement).
Fault normal displacement (or velocity) is given such that the normal stress on the fault is continuous across the fault.
Artificial viscous damping is introduced on the fault to avoid vibration caused by onset of the slip. Our implementation has
five advantages over previous versions: (1) No leakage of the slip prior to rupture and (2) a zero thickness fault, (3) stress
on the fault is reliably calculated, (4) our implementation is suitable for the study of fault constitutive laws, as slip
is defined as the difference between displacement on the plane of z = + 0 and that of z = − 0, and (5) cessation of slip is achieved correctly. 相似文献
13.
Regional finite-difference models tend to have large cell sizes, often on the order of 1–2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW–MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models. 相似文献
14.
《Advances in water resources》2007,30(4):1027-1045
Streamline methods have shown to be effective for reservoir simulation. For a regular grid, it is common to use the semi-analytical Pollock’s method to obtain streamlines and time-of-flight coordinates (TOF). The usual way of handling irregular grids is by trilinear transformation of each grid cell to a unit cube together with a linear flux interpolation scaled by the Jacobian. The flux interpolation allows for fast integration of streamlines, but is inaccurate even for uniform flow. To improve the tracing accuracy, we introduce a new interpolation method, which we call corner-velocity interpolation. Instead of interpolating the velocity field based on discrete fluxes at cell edges, the new method interpolates directly from reconstructed point velocities given at the corner points in the grid. This allows for reproduction of uniform flow, and eliminates the influence of cell geometries on the velocity field. Using several numerical examples, we demonstrate that the new method is more accurate than the standard tracing methods. 相似文献
15.
This work examines the simulation of stream–aquifer interactions as grids are refined vertically and horizontally and suggests that traditional methods for calculating conductance can produce inappropriate values when the grid size is changed. Instead, different grid resolutions require different estimated values. Grid refinement strategies considered include global refinement of the entire model and local refinement of part of the stream. Three methods of calculating the conductance of the Cauchy boundary conditions are investigated. Single- and multi-layer models with narrow and wide streams produced stream leakages that differ by as much as 122% as the grid is refined. Similar results occur for globally and locally refined grids, but the latter required as little as one-quarter the computer execution time and memory and thus are useful for addressing some scale issues of stream–aquifer interactions. Results suggest that existing grid-size criteria for simulating stream–aquifer interactions are useful for one-layer models, but inadequate for three-dimensional models. The grid dependence of the conductance terms suggests that values for refined models using, for example, finite difference or finite-element methods, cannot be determined from previous coarse-grid models or field measurements. Our examples demonstrate the need for a method of obtaining conductances that can be translated to different grid resolutions and provide definitive test cases for investigating alternative conductance formulations. 相似文献
16.
Two-way embedding algorithms: a review 总被引：3，自引：2，他引：1
Local mesh refinement features have now been added to a number of numerical ocean models. In its crudest form, a high-resolution grid is embedded (or nested) in a coarse-resolution grid, which covers the entire domain, and the two grids interact. The aim of this paper is to review existing two-way grid embedding algorithms. The basic algorithms and specificities related to ocean modelling are first described. Then, we address several important issues: conservation properties, design of interpolation/restriction operators, and noise control techniques. 相似文献
17.
Surface elevations represented in MODFLOW head-dependent packages are usually derived from digital elevation models (DEMs) that are available at much high resolution. Conventional grid refinement techniques to simulate the model at DEM resolution increases computational time, input file size, and in many cases are not feasible for regional applications. This research aims at utilizing the increasingly available high resolution DEMs for effective simulation of evapotranspiration (ET) in MODFLOW as an alternative to grid refinement techniques. The source code of the evapotranspiration package is modified by considering for a fixed MODFLOW grid resolution and for different DEM resolutions, the effect of variability in elevation data on ET estimates. Piezometric head at each DEM cell location is corrected by considering the gradient along row and column directions. Applicability of the research is tested for the lower Rio Grande (LRG) Basin in southern New Mexico. The DEM at 10 m resolution is aggregated to resampled DEM grid resolutions which are integer multiples of MODFLOW grid resolution. Cumulative outflows and ET rates are compared at different coarse resolution grids. Results of the analysis conclude that variability in depth-to-groundwater within the MODFLOW cell is a major contributing parameter to ET outflows in shallow groundwater regions. DEM aggregation methods for the LRG Basin have resulted in decreased volumetric outflow due to the formation of a smoothing error, which lowered the position of water table to a level below the extinction depth. 相似文献
18.
Tidal boundary conditions in SEAWAT 总被引：3，自引：0，他引：3
SEAWAT, a U.S. Geological Survey groundwater flow and transport code, is increasingly used to model the effects of tidal motion on coastal aquifers. Different options are available to simulate tidal boundaries but no guidelines exist nor have comparisons been made to identify the most effective approach. We test seven methods to simulate a sloping beach and a tidal flat. The ocean is represented in one of the three ways: directly using a high hydraulic conductivity (high-K) zone and indirect simulation via specified head boundaries using either the General Head Boundary (GHB) or the new Periodic Boundary Condition (PBC) package. All beach models simulate similar water fluxes across the upland boundary and across the sediment-water interface although the ratio of intertidal to subtidal flow is different at low tide. Simulating a seepage face results in larger intertidal fluxes and influences near-shore heads and salinity. Major differences in flow occur in the tidal flat simulations. Because SEAWAT does not simulate unsaturated flow the water table only rises via flow through the saturated zone. This results in delayed propagation of the rising tidal signal inland. Inundation of the tidal flat is delayed as is flow into the aquifer across the flat. This is severe in the high-K and PBC models but mild in the GHB models. Results indicate that any of the tidal boundary options are fine if the ocean-aquifer interface is steep. However, as the slope of that interface decreases, the high-K and PBC approaches perform poorly and the GHB boundary is preferable. 相似文献
19.
基于应力、速度混合变量弹性波方程及任意四边形网格差分算子,给出了交错计算应力及速度的非规则网格弹性波应力一速度差分法该方法融合了有限元法能适应复杂形状边界及差分法无需计算刚度阵的特点,具有较高的计算精度,所需计算机存储空间较少,计算效率也很高．基于积分平衡方程引入了任意形状自由表面的边界条件,且通过局部滤波改善了自由表面边界条件的稳定性,使得该方法可应用于考虑地表形状影响的地震波数值模拟 相似文献
20.
《Advances in water resources》1999,22(7):697-710
Flownets are useful tools for the visualization of groundwater flow fields. Using orthogonal flownets as grids for transport modeling is an effective way to control numerical dispersion, especially transverse to the direction of flow. Therefore tools for automatic generation of flownets may be seen both as postprocessors for groundwater flow simulations and preprocessors for contaminant transport models. Existing methods to generate streamline-oriented grids suffer from drawbacks such as the inability to include sources in the interior of the grid. In this paper, we introduce a new method for the generation of streamline-oriented grids which handles wells in the grid interior, and which produces orthogonal grids for anisotropic systems. Streamlines are generated from an accurate velocity field obtained from the solution of the mixed-hybrid finite element method for flow, while pseudopotentials, which are orthogonal to the streamlines, are obtained by a standard finite element solution of the pseudopotential equation. A comprehensive methodology for the generation of orthogonal grids, including the location of stagnation points and dividing streamlines, is introduced. The effectiveness of the method is illustrated by means of examples. A related paper presents a compatible formulation of the solution for reactive transport, while a second related paper gives a detailed quantitative assessment of the various forms of modelled mixing and their effect on the accuracy of simulations of the biodegradation of groundwater contaminants. 相似文献