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1.
An accurate finite‐volume Eulerian Lagrangian localized adjoint method (ELLAM) is presented for solving the one‐dimensional variable coefficients advection dispersion equation that governs transport of solute in porous medium. The method uses a moving grid to define the solution and test functions. Consequently, the need for spatial interpolation, or equivalently numerical integration, which is a major issue in conventional ELLAM formulations, is avoided. After reviewing the one‐dimensional method of ELLAM, we present our strategy and detailed calculations for both saturated and unsaturated porous medium. Numerical results for a constant‐coefficient problem and a variable‐coefficient problem are very close to analytical and fine‐grid solutions, respectively. The strength of the developed method is shown for a large range of CFL and grid Peclet numbers. Copyright 2004 John Wiley & Sons, Ltd.  相似文献   

2.
Accurate up-scaling is an essential part of creating a valid reservoir coarse scale dynamic model. In this article, unstructured discretization of spatial domain is accompanied by numerical permeability up-scaling in order to construct an accurate coarse scale model. A new technique for generating a course scale triangular mesh is presented in which the density of elements in key flow regions is kept high to capture accuracy. The fine scale permeability map is investigated using image processing techniques, especially steerable filters, and the results are converted into a high-resolution element size map. This element size map will be refined by the integration of other important factors such as well-position effects and used to construct a coarse triangular mesh. The combination of flux-continuous pressure approximation and mass conservative, total variation diminishing finite volume schemes have been considered to solve two phase flow equations on the control volume finite element mesh. Fine scale simulations results are compared with the coarse scale ones for a series of water flooding examples to investigate the efficiency and accuracy of the presented gridding methodology. This method is developed for 2D cases, but can be easily extended to 3D problems.  相似文献   

3.
本文结合拉格朗日观点的运动坐标与欧拉观点的固定坐标,分别求解对流—弥敌方程的对流效应和弥散效应,并在从固定坐标向运动坐标投影时利用了三次样条插值方法,使模型更为精确而简单。通过与特定情况下的理论解比较,说明模型是准确可靠的。通过与实验室室内试验结果的比较,模型的可靠性得到了进一步的验证。利用模型对淡水洗盐结合浅群井抽排咸水治理盐碱地过程的模拟分析,认为结合浅群井抽排可较大地提高淡水洗盐的效果。  相似文献   

4.
We discuss the numerical modeling of the infiltration of contaminated water into unsaturated porous media. A system with contaminant transport, dispersion, and adsorption is considered. The mathematical model for unsaturated flow is based on Richards nonlinear and degenerate equation. Nonlinear adsorption is represented by adsorption isotherms and kinetic rates. An accurate numerical method is constructed in 1D which can be a good candidate for the solution of inverse problems to determine model parameters in the adsorption part of the model. Our numerical solution is based on the method of lines (MOL method) where space discretization leads to the corresponding system of ODEs. We substantially use the numerical modeling of interfaces, separating fully saturated, partially saturated, and dry zones in the underground. Finally, in a series of numerical experiments and in comparisons with HYDRUS (?imunek et al., The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably/saturated media, version 2.0, Rep. IGWMC-TPS-70, 202 pp., Int. Groundwater Model. Cent., Colo. Sch of Mines, Golden, Colo), we demonstrate the effectiveness of our method.  相似文献   

5.
固体材料的应变局部化行为是导致结构破坏失效的重要因素之一,开展相关数值模拟分析对于结构安全性评估具有重要意义.然而由于材料的非均质和多尺度特性,采用传统数值方法进行求解时通常需要从最小特征尺度离散求解的结构,这将大幅度增加计算规模和成本.针对这一问题,本文提出了一种基于嵌入强间断模型的多尺度有限元方法.该方法从粗细两个尺度离散求解模型,首先在细尺度单元上引入嵌入强间断模型来描述单元间断特性,所附加的跳跃位移自由度则通过凝聚技术进行消除,从而保持细尺度单元刚度阵维度不变.其次,提出了一种增强多节点粗单元技术,其可根据局部化带与粗单元边界相交情况自适应动态地增加粗节点,新构造的增强数值基函数可以捕捉细尺度间断特性,完成物理信息从细单元到粗单元的准确传递以及宏观响应的快速分析;再次,在细尺度解的计算中,将细尺度解分解为降尺度解与单胞局部摄动解,从而消除弹塑性分析时单胞内部的不平衡力.最后,通过两个典型算例分析,并与完全采用细单元的嵌入有限元结果进行对比,验证了所提出算法的正确性与有效性.  相似文献   

6.
7.
Fluid flow and solute transport in a 3D rough-walled fracture–matrix system were simulated by directly solving the Navier–Stokes equations for fracture flow and solving the transport equation for the whole domain of fracture and matrix with considering matrix diffusion. The rough-walled fracture–matrix model was built from laser-scanned surface tomography of a real rock sample, by considering realistic features of surfaces roughness and asperity contacts. The numerical modeling results were compared with both analytical solutions based on simplified fracture surface geometry and numerical results by particle tracking based on the Reynolds equation. The aim is to investigate impacts of surface roughness on solute transport in natural fracture–matrix systems and to quantify the uncertainties in application of simplified models. The results show that fracture surface roughness significantly increases heterogeneity of velocity field in the rough-walled fractures, which consequently cause complex transport behavior, especially the dispersive distributions of solute concentration in the fracture and complex concentration profiles in the matrix. Such complex transport behaviors caused by surface roughness are important sources of uncertainty that needs to be considered for modeling of solute transport processes in fractured rocks. The presented direct numerical simulations of fluid flow and solute transport serve as efficient numerical experiments that provide reliable results for the analysis of effective transmissivity as well as effective dispersion coefficient in rough-walled fracture–matrix systems. Such analysis is helpful in model verifications, uncertainty quantifications and design of laboratorial experiments.  相似文献   

8.
This paper presents a systematic research for understanding mechanical shearing effects on the fluid flow and the solute transport behavior of rough fractures through a numerical simulation approach. The aperture fields were modeled based on a real rock fracture geometry and the normal displacement obtained from the shear-flow test. The fluid flow through the rough fracture under shear was simulated using a finite element code that solves the Reynolds equation, and the transport behavior through the rough fracture under shear was simulated calculating the advection–dispersion equation. The results show that the fracture apertures increase as the shear displacement increases, with a few major flow channels detected through the fracture. The shear-induced flow channels increase both flow connectivity and transport connectivity, which accelerate the movement of solutes in a particular direction and lead to early breakthrough of the contaminants. Adsorption, acting as a retardation term, has a decisive influence on the transport process. These results can give a basic knowledge of the hydromechanical and solute transport progress through fracture, and will be helpful to safety assessment for high-level radioactive waste disposal facilities.  相似文献   

9.
A Lagrangian perturbation approach has been applied to develop the method of moments for predicting mean and variance of solute flux through a three-dimensional nonstationary flow field. The flow nonstationarity may stem from medium nonstationarity, finite domain boundaries, and/or fluid pumping and injecting. The solute flux is described as a space–time process where time refers to the solute flux breakthrough and space refers to the transverse displacement distribution at the control plane. The analytically derived moment equations for solute transport in a nonstationary flow field are too complicated to solve analytically, a numerical finite difference method is implemented to obtain the solutions. This approach combines the stochastic model with the flexibility of the numerical method to boundary and initial conditions. This method is also compared with the numerical Monte Carlo method. The calculation results indicate the two methods match very well when the variance of log-conductivity is small, but the method of moment is more efficient in computation.  相似文献   

10.
Younes  A.  Ackerer  Ph.  Mose  R. 《Transport in Porous Media》1999,35(3):375-394
Case 5, Level 1 of the international HYDROCOIN groundwater flow modeling project is an example of idealized flow over a salt dome. The groundwater flow is strongly coupled to solute transport since density variations in this example are large (20%).Several independent teams simulated this problem using different models. Results obtained by different codes can be contradictory. We develop a new numerical model based on the mixed hybrid finite elements approximation for flow, which provides a good approximation of the velocity, and the discontinuous finite elements approximation to solve the advection equation, which gives a good approximation of concentration even when the dispersion tensor is very small. We use the new numerical model to simulate the salt dome flow problem.In this paper we study the effect of molecular diffusion and we compare linear and nonlinear dispersion equations. We show the importance of the discretization of the boundary condition on the extent of recirculation and the final salt distribution. We study also the salt dome flow problem with a more realistic dispersion (very small dispersion tensor). Our results are different to prior works with regard to the magnitude of recirculation and the final concentration distribution. In all cases, we obtain recirculation in the lower part of the domain, even for only dispersive fluxes at the boundary. When the dispersion tensor becomes very small, the magnitude of recirculation is small. Swept forward displacement could be reproduced by using finite difference method to compute the dispersive fluxes instead of mixed hybrid finite elements.  相似文献   

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