共查询到20条相似文献，搜索用时 625 毫秒
1.
Evaluation and numerical modeling of seawater intrusion in the Gaza aquifer (Palestine) 总被引：3，自引：1，他引：3
A numerical assessment of seawater intrusion in Gaza, Palestine, has been achieved applying a 3-D variable density groundwater flow model. A two-stage finite difference simulation algorithm was used in steady state and transient models. SEAWAT computer code was used for simulating the spatial and temporal evolution of hydraulic heads and solute concentrations of groundwater. A regular finite difference grid with a 400 m2 cell in the horizontal plane, in addition to a 12-layer model were chosen. The model has been calibrated under steady state and transient conditions. Simulation results indicate that the proposed schemes successfully simulate the intrusion mechanism. Two pumpage schemes were designed to use the calibrated model for prediction of future changes in water levels and solute concentrations in the groundwater for a planning period of 17 years. The results show that seawater intrusion would worsen in the aquifer if the current rates of groundwater pumpage continue. The alternative, to eliminate pumpage in the intruded area, to moderate pumpage rates from water supply wells far from the seashore and to increase the aquifer replenishment by encouraging the implementation of suitable solutions like artificial recharge, may limit significantly seawater intrusion and reduce the current rate of decline of the water levels. 相似文献
2.
Implementation of a Locally Conservative Numerical Subgrid Upscaling Scheme for Two-Phase Darcy Flow 总被引：1，自引：0，他引：1
Todd Arbogast 《Computational Geosciences》2002,6(3-4):453-481
We present a locally mass conservative scheme for the approximation of two-phase flow in a porous medium that allows us to obtain detailed fine scale solutions on relatively coarse meshes. The permeability is assumed to be resolvable on a fine numerical grid, but limits on computational power require that computations be performed on a coarse grid. We define a two-scale mixed finite element space and resulting method, and describe in detail the solution algorithm. It involves a coarse scale operator coupled to a subgrid scale operator localized in space to each coarse grid element. An influence function (numerical Greens function) technique allows us to solve these subgrid scale problems independently of the coarse grid approximation. The coarse grid problem is modified to take into account the subgrid scale solution and solved as a large linear system of equations posed over a coarse grid. Finally, the coarse scale solution is corrected on the subgrid scale, providing a fine grid representation of the solution. Numerical examples are presented, which show that near-well behavior and even extremely heterogeneous permeability barriers and streaks are upscaled well by the technique. 相似文献
3.
A preliminary problem to solve in the set-up of a mathematical model simulating a geophysical process is the choice of a suitable discrete scheme to approximate the governing differential equations. This paper presents a simple technique to test finite difference schemes used in the modeling of geophysical processes occurring in a geological structure. This technique consists in generating analytical solutions similar to the ones characterizing a geophysical process, given general information on some relevant parameters. Useful information for the choice of the discrete scheme to employ in the mathematical model simulating the original geophysical process can be obtained from the comparison between the analytical solution and the approximated numerical solutions generated by means of different discrete schemes. Two classes of numerical examples approximating the differential equation that governs the steady state earth's heat flow have been treated using three different finite differences schemes. The first class of examples deals with media whose phenomenological parameters vary as continuous space functions; the second class, instead, deals with media whose phenomenological parameters vary as discontinuous space functions. The finite difference schemes that have been utilized are: Centered Finite Difference Scheme (CDS), Arithmetic Mean Scheme (AMS), and Harmonic Mean Scheme (HMS).The numerical simulations showed that: the CDS may yield physically inconsistent solutions if the lattice internodal distance is too large, but in case of phenomenological parameters varying as a continuous function, this pitfall can be avoided increasing the lattice node refinement. In case of phenomenological parameters varying as a discontinuous function, instead, the CDS may yield physically inconsistent solutions for any lattice-node refinement. The HMS produced good results for both classes of examples showing to be a scheme suitable to model situations like these. 相似文献
4.
G. Bernard-Michel C. Le Potier A. Beccantini S. Gounand M. Chraibi 《Computational Geosciences》2004,8(2):187-201
We present here results for the Andra Couplex 1 test case, obtained with the code Cast3m. This code is developped at the CEA (Commissariat l'nergie atomique) and is used mainly to solve problems of solid mechanics, fluid mechanics and heat transfers. Different types of discretization are available, among them finite element, finite volume and mixed hybrid finite element method. Cast3m is also a componant of the platteform Alliances (co-developped by Andra, CEA), which will be used by Andra for the safety calculation of an underground waste disposal in year 2004. We solve the Darcy equation for the water flow and a convection–diffusion transport equation for the Iodine 129 which escapes from a repository cave into the water. The water flow is calculated with a MHFE discretization. It is shown that this method provides sharp results even on relatively coarse grids. The convection–diffusion transport equation is discretized with FE (Finite Element), MHFE (Mixed Hybrid Finite Element) and FV (Finite Volume) methods. In our comparison, we point out the differences of these methods in term of accuracy, respect of the maximum principle and calculations cost. Neither the finite element nor the mixed hybrid finite element approach respects the maximum principle. This results in the presence of negative concentrations near the repository cave, whereas FV calculations respect the monotonicity. We show that mass lumping techniques suppress this problem but with strong restrictions on the grid. FE and MHFE approaches are more accurate than FV for the diffusion equation, but the overall results are equivalent since the advective terms are dominant in the far field and are discretized with centered schemes. We conclude by studying the influence of the grid: a very fine grid near the repository solves almost all the problems of monotonicity, without employing mass lumping techniques. We also observed a very important increase of the accuracy on a structured grid made up of rectangles. 相似文献
5.
The Weather Research and Forecasting model was used to test the sensitivity of Typhoon Haiyan (2013) to the use of a cumulus parameterization scheme, specifically the revised Kain–Fritsch (rKF) scheme, at high horizontal resolutions with grid spacing varying from 9 to 2 km. The rKF scheme simulated the typhoon in best agreement with the observation compared with other schemes, but some fundamental drawbacks relating the rKF scheme, e.g., neglecting the momentum adjustment and being less applicable to high-resolution modeling than multi-scaled schemes, could influence the results and were discussed. Initial results showed that the typhoon track simulations benefited little from the use of the rKF scheme or a fine resolution, partially because of the similar large-scale steering flows induced by the analyzed boundary conditions used in each simulation. The influences of using the rKF scheme on typhoon intensity, size, structure, and precipitation were dependent on the grid spacing, and the most apparent changes occurred near a grid length of 4 km. At 9–4-km grid spacings, using the rKF scheme produced typhoons much stronger with more rainfall and surface latent heat flux than did using no cumulus parameterization scheme. At 3- or 2-km grid spacing, using the rKF scheme caused little changes on typhoon intensity, and the changes in precipitation and surface latent heat flux were relatively small. These results suggested that the grid spacing of 2 km for simulations using no cumulus parameterization scheme or the grid spacing of 4 km for simulations using the rKF scheme facilitated reproducing the observed Typhoon Haiyan. 相似文献
6.
A finite volume-based numerical modeling framework using a hierarchical fracture representation (HFR) has been developed to compute flow-induced shear failure. To accurately capture the mechanics near fracture manifolds, discontinuous basis functions are employed which ensure continuity of the displacement gradient across fractures. With these special basis functions, traction and compressive forces on the fracture segment can be calculated without any additional constraints, which is extremely useful for estimating the irreversible displacement along the fracture (slip) based on a constitutive friction law. The method is further extended to include slip-dependent hydraulic aperture change and grid convergent results are obtained. Further, the change in hydraulic aperture is modeled using an asymptotic representation which respects the experimentally observed behavior of pore volume dilation due to shear slip. The model allows the initial rapid increase in hydraulic aperture due to shear slip and asymptotically approaches a finite value after repeated shearing of a fracture segment. This aperture increase is the only feedback for mechanics into the fluid flow for a linear elastic mechanics problem. The same model is also extended to include poroelastic relations between flow and mechanics solver. The grid convergence result in the case of poroelastic flow-mechanics coupling for flow-induced shear failure is also obtained. This proves the robustness of the numerical and analytical modeling of fracture and friction in the extended finite volume method (XFVM) set-up. Finally, a grid convergent result for seismic moment magnitude for single fracture and fracture network with random initial hydraulic and friction properties is also obtained. The b-value, which represents the slope of seismic moment occurrence frequency decay vs seismic moment magnitude, which is approximately constant in a semi-logarithmic plot, is estimated. The numerical method leads to converged b-values for both single fracture and fracture network simulations, as grid and time resolutions are increased. For the resulting linear system, a sequential approach is used, that is, first, the flow and then the mechanics problems are solved. The new modeling framework is very useful to predict seismicity, permeability, and flow evolution in geological reservoirs. This is demonstrated with numerical simulations of enhancing a geothermal system. 相似文献
7.
E. Bruce Pitman 《国际地质力学数值与分析法杂志》1993,17(6):385-400
The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second-order Godunov-type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations. The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell-tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher-order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual. 相似文献
8.
The generation of a numerical model must consider the separate issues of the governing equations, the numerical representation of those equations, the data structure that describes the model, the choice of programming language and finally the implementation and code management issues. These issues are considered as a whole in this paper and as a consequence, 10 golden rules for numerical modelling are proposed. By way of application, a saturated–unsaturated flow problem is modelled using the Richards equation and an innovative edge‐based finite volume method. The implementation uses a novel data structure. This is shown to have over 91% code re‐use and hence code written in this way is highly flexible and applicable to many different problems. By way of example, a compacted core earth filled dam problem has been solved. Finally, we conclude that this advanced programming method can significantly reduce code development time. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
9.
10.
海水入侵导致地下水变咸对青岛李哥庄地区经济发展产生了不利影响,急需开展治理该地区咸水体的工作。根据研究区已有的降雨、蒸发及水文地质等资料,结合现场调查和监测,利用地下水模拟软件Visual-MODFLOW中的SEAWAT模块建立了该地区的数值模型,并利用实测资料识别和验证了该模型参数,表明所建模型能反映李哥庄地区的实际水文地质条件。为了模拟研究区地下咸水体的恢复治理情况,提出了连续抽水、间歇式抽水和抽注水结合三种咸水恢复方案,并利用该模型对三种恢复方案进行了模拟优化。结果表明,抽取地下咸水只是咸水恢复的一个因素,周边淡水的驱替作用则是咸水恢复另一个的因素,抽注水结合恢复方案为三种方案中最优的方案。 相似文献
11.
This paper describes a nonlinear elasto-plastic simulation of freezing and thawing of rock. A mathematical formulation is described in which deformation, fluid flow and heat flow are fully coupled. A non-linear elasto-plastic constitutive relationship is presented and a two dimensional (plane stress) numerical modeling is performed based on the finite element method applied to thermo-poro-elastoplasticity. It is assumed that the Mohr-Coulomb's failure criterion is valid for yield locus and plastic potential. The numerical scheme employed in the code accommodates phase change of pore-water from liquid to solid (ice). The primary aim of this paper is to compare the temperature transfer and deformation prediction obtained from the numerical code with those obtained from the freezing and thawing experiments. It is found from the numerical simulation that a relatively good prediction can be made of temperature transfer and deformation behavior. The numerical code has also been applied to a hypothetical cavern problem to demonstrate its applicability. 相似文献
12.
声波散射数值模拟的两种新方案 总被引：4，自引：0，他引：4
孙建国 《吉林大学学报(地球科学版)》2006,36(5):863-868
声波散射的数值模拟问题一般用网格法或积分方程法解决。当模型的尺度很大时,两种方法都会遇到计算机资源不足所造成的困难。另外,在网格法中,场源的位置和场源附近的波场奇异性逼近精度都受网格点的控制,因此难以满足实际问题所提出的要求。针对这些问题,提出了两种处理声波散射问题的新方案。一种主要针对网格法,另外一种针对积分方程法。在针对网格法的方案中,通过模型分解和波场分裂,将原始的总场计算问题转化为散射场计算问题。由于背景场是由解析公式给出的,所以可以将场源放置在数值网格的任意位置,不一定非得在网格点上。基于同样的原因,场源附近的波场奇异性可以精确地算出。在针对积分方程法的方案中,通过引入拟线性近似,使得散射场的数值求解不必再借助于代数方程组,只要进行数值积分即可。所建立的数值计算方案具有普遍的适用性,其基本思想可以直接用于解决弹性波散射的数值模拟问题并用于反演密度和速度。 相似文献
13.
Jeremy Edward Kozdon Bradley T. Mallison Margot G. Gerritsen 《Computational Geosciences》2011,15(3):399-419
Truly multidimensional methods for hyperbolic equations use flow-based information to determine the computational stencil,
as opposed to applying one-dimensional methods dimension by dimension. By doing this, the numerical errors are less correlated
with the underlying computational grid. This can be important for reducing bias in flow problems that are inherently unstable
at simulation scale, such as in certain porous media problems. In this work, a monotone, multi-D framework for multiphase
flow and transport in porous media is developed. A local coupling of the fluxes is introduced through the use of interaction
regions, resulting in a compact stencil. A relaxed volume formulation of the coupled hyperbolic–elliptic system is used that
allows for nonzero residuals in the pressure equation to be handled robustly. This formulation ensures nonnegative masses
and saturations (volume fractions) that sum to one (Acs et al., SPE J 25(4):543–553, 1985). Though the focus of the paper is on immiscible flow, an extension of the methods to a class of more general scalar hyperbolic
equations is also presented. Several test problems demonstrate that the truly multi-D schemes reduce biasing due to the computational
grid. 相似文献
14.
We present Folder, a numerical toolbox for modelling deformation in layered media subject to layer parallel shortening or extension in two dimensions. The toolbox includes a range of features that ensure maximum flexibility to configure model geometry, define material parameters, specify numerical parameters, and choose the plotting options. Folder builds on an efficient finite element method model and implements state of the art iterative and time integration schemes. We describe the basic Folder features and present several case studies of single and multilayer stacks subject to layer parallel shortening and extension. Folder additionally comprises an application that illustrates various analytical solutions of growth rates calculated for the cases of layer parallel shortening and extension of a single layer with interfaces perturbed with a single sinusoidal waveform. We further derive two novel analytical expressions for the growth rate in the cases of layer parallel shortening and extension of a linear viscous layer embedded in a linear viscous medium of a finite thickness. These solutions help understand mechanical instabilities in layered rocks and provide a unique opportunity for benchmarking of numerical codes. We demonstrate how Folder can be used for benchmarking of numerical codes. We test the accuracy of single-layer folding simulations using various 1) spatial and temporal resolutions, 2) iterative algorithms for non-linear materials, and 3) time integration schemes. The accuracy of the numerical results is quantified by: 1) comparing them to analytical solutions, if available, or 2) running convergence tests. As a result, we provide a map of the most optimal choice of grid size, time step, and number of iterations to keep the results of the numerical simulations below a given error for a given time integration scheme. Folder is an open source MATLAB application and comes with a user-friendly graphical interface. Folder is suitable for both educational and research purposes. 相似文献
15.
R. Eymard T. Gallouët C. Guichard R. Herbin R. Masson 《Computational Geosciences》2014,18(3-4):285-296
We give here a comparative study on the mathematical analysis of two (classes of) discretization schemes for the computation of approximate solutions to incompressible two-phase flow problems in homogeneous porous media. The first scheme is the well-known finite volume scheme with a two-point flux approximation, classically used in industry. The second class contains the so-called approximate gradient schemes, which include finite elements with mass lumping, mixed finite elements, and mimetic finite differences. Both (classes of) schemes are nonconforming and can be expressed using discrete function and gradient reconstructions within a variational formulation. Each class has its specific advantages and drawbacks: monotony properties are natural with the two-point finite volume scheme, but meshes are restricted due to consistency issues; on the contrary, gradient schemes can be used on general meshes, but monotony properties are difficult to obtain. 相似文献
16.
17.
The general framework of the paper deals with the finite element modelling of thermomechanical problems involving viscous materials. The study focuses on the statement of constitutive equations describing the thermoviscoplastic behaviour of bituminous concrete, as well as on their implementation in a finite element program. After stating the general equations of the space- and time-continuous problem and the constitutive relations governing the viscoplastic component of the bituminous concrete behaviour, we deal with their integration over finite time steps, considering two different schemes. Eventually, two sets of numerical results are presented. The first one, an homogeneous triaxial test, is used to compare those schemes, whereas the second one consists of numerical simulations of real-size experiments performed on a road structure subjected to thermal and mechanical loadings. By comparing the numerical results with experimental ones, it allows us to test the finite element code on a more complex and realistic problem. Copyright © 1999 John Wiley & Sons Ltd. 相似文献
18.
Iterative methods for the solution of non‐linear finite element equations are generally based on variants of the Newton–Raphson method. When they are stable, full Newton–Raphson schemes usually converge rapidly but may be expensive for some types of problems (for example, when the tangent stiffness matrix is unsymmetric). Initial stiffness schemes, on the other hand, are extremely robust but may require large numbers of iterations for cases where the plastic zone is extensive. In most geomechanics applications it is generally preferable to use a tangent stiffness scheme, but there are situations in which initial stiffness schemes are very useful. These situations include problems where a nonassociated flow rule is used or where the zone of plastic yielding is highly localized. This paper surveys the performance of several single‐parameter techniques for accelerating the convergence of the initial stiffness scheme. Some simple but effective modifications to these procedures are also proposed. In particular, a modified version of Thomas' acceleration scheme is developed which has a good rate of convergence. Previously published results on the performance of various acceleration algorithms for initial stiffness iteration are rare and have been restricted to relatively simple yield criteria and simple problems. In this study, detailed numerical results are presented for the expansion of a thick cylinder, the collapse of a rigid strip footing, and the failure of a vertical cut. These analyses use the Mohr–Coulomb and Tresca yield criteria which are popular in soil mechanics. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
19.
A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
20.
We construct a new class of locally conservative numerical methods for two-phase immiscible flow in heterogeneous poroelastic media. Within the framework of the so-called iteratively coupled methods and fixed-stress split algorithm we develop mixed finite element methods for the flow and geomechanics subsystems which furnish locally conservative Darcy velocity and transient porosity input fields for the transport problem for the water saturation. Such hyperbolic equation is decomposed within an operator splitting technique based on a predictor–corrector scheme with the predictor step discretized by a higher-order non-oscillatory finite volume central scheme. The proposed scheme adopts an inhomogeneous dual mesh with variable cell size ruled by the local wave speed of propagation to compute numerical fluxes at cell edges. In the limit of small time steps the central scheme gives rise to a semidiscrete formulation for the water saturation capable of incorporating heterogeneous porosity fields and generalized flux functions including the water transport due to the solid phase velocity. Numerical simulations of a water-flooding problem in secondary oil recovery are presented for different realizations of the input random fields (permeability, Young modulus and initial porosity). Comparison between the accuracies of the proposed approach and the traditional one-way coupled hydro-geomechanical formulation are presented. The effects of the cross-correlation between the input random fields and compaction drive mechanism upon finger growth and breakthrough curves are also analyzed. A notable feature of the formulation proposed herein is the accurate prediction of the influence of geomechanical effects upon the unstable movement of the water front, whose evolution is dictated by rock heterogeneity and unfavorable viscosity ratio, without deteriorating the local conservative character of the numerical schemes. 相似文献