共查询到20条相似文献，搜索用时 62 毫秒
1.
This paper deals with the computational aspects of nonaqueous phase liquid (NAPL) dissolution front instability in two-dimensional
fluid-saturated porous media of finite domains. After the governing equations of an NAPL dissolution system are briefly described,
a combination of the finite element and finite difference methods is proposed to solve these equations. In the proposed numerical
procedure, the finite difference method is used to discretize time, while the finite element method is used to discretize
space. Two benchmark problems, for which either analytical results or previous solutions are available, are used to verify
the proposed numerical procedure. The related simulation results from these two benchmark problems have demonstrated that
the proposed numerical procedure is useful and applicable for simulating the morphological evolution of NAPL dissolution fronts
in two-dimensional fluid-saturated porous media of finite domains. As an application, the proposed numerical procedure has
been used to simulate morphological evolution processes for three kinds of NAPL dissolution fronts in supercritical NAPL dissolution
systems. It has been recognized that: (1) if the Zhao number of an NAPL dissolution system is in the lower range of the supercritical
Zhao numbers, the fundamental mode is predominant; (2) if the Zhao number is in the middle range of the supercritical Zhao
numbers, the (normal) fingering mode is the predominant pattern of the NAPL dissolution front; and (3) if the Zhao number
is in the higher range of the supercritical Zhao numbers, the fractal mode is predominant for the NAPL dissolution front. 相似文献
2.
This paper deals with the theoretical aspects of nonaqueous phase liquid (NAPL)‐dissolution‐induced instability in two‐dimensional fluid‐saturated porous media including solute dispersion effects.After some weaknesses associated with the previous work are analyzed and overcome, a comprehensive dimensionless number, known as the Zhao number, is proposed to represent the main driving force and three controlling mechanisms of an NAPL‐dissolution system that has a finite domain. The linear stability analysis is carried out to derive the critical value of the comprehensive dimensionless number of the NAPL‐dissolution system in a limit case as the ratio of the equilibrium concentration to the density of the NAPL approaches zero. As a result, a theoretical criterion that can be used to assess the instability of planar NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media of finite domains has been established. Not only can the present theoretical results be used for the theoretical understanding of the effect of solute dispersion on the instability of an NAPL‐dissolution front in the fluid‐saturated porous medium of either a finite domain or an infinite domain, but also they can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
3.
Dirk Schaefer 《Environmental Earth Sciences》2012,67(8):2459-2467
Organic contaminants in aquifers are often present as non-aqueous phase liquids (NAPL), which are long-lasting sources for groundwater contamination. The existing NAPL mass is an important parameter for the persistence of the source, but its determination is difficult. One possible detection method is based on the ideal multicomponent dissolution theory, using aqueous concentrations downstream of a fully mixed NAPL source to calculate its mass. In this publication, the applicability of this method is tested for a source size of about 5 m, using numerical methods. In contrast to fully mixed source zones, on this scale the NAPL sources are not in contact with each other, do not mix and develop independently over time. Highly soluble NAPL components can be depleted or the NAPL phase can be completely exhausted locally, while in other portions of the source zone NAPL is still present with all its components. Hence, the interpretation of the resulting aqueous concentrations downstream using the ideal dissolution theory leads to erroneous NAPL masses of several orders of magnitude in the investigated scenarios. 相似文献
4.
An unconditionally stable, fully explicit and highly precise multiple timescale finite element modeling scheme is described for a fully coupled hydro-mechanical (FCHM) analysis of saturated poroelastic media. The finite element method (FEM) is used for the discretization of the FCHM differential equation in the space domain. Direct integration is performed based on the precise time step integration method (PTSIM) for the time derivatives. Two configurations for the proposed scheme are constructed (abbreviated as PTSIM-f1 and -f2, respectively). The stability and convergence of the PTSIM-f1 and -f2 are proved using a matrix-based spectral analysis in the time domain. It is demonstrated that the explicit scheme proposed in this paper is unconditionally stable and independent of the time-step size. The algorithmic error estimation results indicate that the numerical modeling performed using PTSIM-f1 and -f2 in the time domain match the computer precision. Theoretically, the algorithmic error is caused by only the mesh discretization. Therefore, the proposed modeling scheme is a semi-analytical scheme. The applicability and accuracy of the proposed scheme are examined using sample calculations. By comparing with the analytical solutions, it is indicated that the modeling results have significant advantages over the standard FEM in terms of precision and computational efficiency for large timescales. 相似文献
5.
Savithru Jayasinghe David L. Darmofal Nicholas K. Burgess Marshall C. Galbraith Steven R. Allmaras 《Computational Geosciences》2018,22(1):107-123
This paper presents a space-time adaptive framework for solving porous media flow problems, with specific application to reservoir simulation. A fully unstructured mesh discretization of space and time is used instead of a conventional time-marching approach. A space-time discontinuous Galerkin finite element method is employed to achieve a high-order discretization on the anisotropic, unstructured meshes. Anisotropic mesh adaptation is performed to reduce the error of a specified output of interest, by using a posteriori error estimates from the dual-weighted residual method to drive a metric-based mesh optimization algorithm. The space-time adaptive method is tested on a one-dimensional two-phase flow problem, and is found to be more efficient in terms of computational cost (degrees-of-freedom and total runtime) required to achieve a specified output error level, when compared to a conventional first-order time-marching finite volume method and the space-time discontinuous Galerkin method on structured meshes. 相似文献
6.
In natural rock masses, the shapes of three‐dimensional (3‐D) blocks cut by arbitrary fracture networks may be very complex. Owing to the geometric complexity and difficulty of mesh discretization of 3‐D blocks and fracture facets, explicit consideration of fracture networks in flow analysis of fractured porous medium (FPM) is very challenging. Using the numerical manifold method based on independent covers (NMMIC), an FPM flow model was proposed that can deal with very complex 3‐D fracture networks. In this paper, the convergence of NMMIC was first demonstrated. The theoretical basis of the arbitrary refinement of computational meshes was proven. Moreover, three peculiarities of NMMIC meshes, that is, arbitrary shape, arbitrary connection, and arbitrary refinement of independent covers, were concluded. Finally, some two‐dimensional (2‐D) tunnel flow examples were analyzed and the numerical results were compared with the analytical results. 3‐D examples with complex fracture distributions were also analyzed. In addition, the computational scale of the developed program was tested by increasing the number of computational elements. The results show that our model can accurately analyze the groundwater flow of rocks surrounding tunnels with complex fracture distributions. 相似文献
7.
Omid Ghaffaripour Golnaz A. Esgandani Arman Khoshghalb Babak Shahbodaghkhan 《国际地质力学数值与分析法杂志》2019,43(11):1919-1955
This paper presents the first application of an advanced meshfree method, ie, the edge-based smoothed point interpolation method (ESPIM), in simulation of the coupled hydro-mechanical behaviour of unsaturated porous media. In the proposed technique, the problem domain is spatially discretised using a triangular background mesh, and the polynomial point interpolation method combined with a simple node selection scheme is adopted for creating nodal shape functions. Smoothing domains are formed on top of the background mesh, and a constant smoothed strain, created by applying the smoothing operation over the smoothing domains, is assigned to each smoothing domain. The deformation and flow models are developed based on the equilibrium equation of the mixture, and linear momentum and mass balance equations of the fluid phases, respectively. The effective stress approach is followed to account for the coupling between the flow and deformation models. Further coupling among the phases is captured through a hysteretic soil water retention model that evolves with changes in void ratio. An advanced elastoplastic constitutive model within the context of the bounding surface plasticity theory is employed for predicting the nonlinear behaviour of soil skeleton. Time discretisation is performed by adopting a three-point discretisation method with growing time steps to avoid temporal instabilities. A modified Newton-Raphson framework is designed for dealing with nonlinearities of the discretised system of equations. The performance of the numerical model is examined through a number of numerical examples. The state-of-the-art computational scheme developed is useful for simulation of geotechnical engineering problems involving unsaturated soils. 相似文献
8.
饱和砂土局部变形带模拟的有限元数值实现 总被引：1，自引：0，他引：1
基于有限变形理论,推导了Newton-Raphson 迭代算法在k+1步增量表达的矩阵形式,实现了饱和砂土变形局部化的有限元数值计算,得到了饱和砂土发生局部化变形的准则。基于Galerkin 方法,得到了位移场和应力场的空间离散化矩阵方程;由土体局部变形带的连续性条件,引入第1切线算子,推导出了砂土等颗粒状媒介发生局部化变形的必要条件。基于此核心算法,编制了有限元计算程序,模拟了饱和砂土在不排水条件下平面压缩过程中剪切带的形成与发展;通过比较分析,研究了有限元网格粗细对于土体局部变形带的影响,结果表明,网格粗细的病态依赖只是微小的,它只与变形条带的宽度有关,对于土体所表现出来的其他力学特性没有影响。 相似文献
9.
10.
Coupled hydromechanical‐fracture simulations of nonplanar three‐dimensional hydraulic fracture propagation 
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下载免费PDF全文 This paper presents an algorithm and a fully coupled hydromechanical‐fracture formulation for the simulation of three‐dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3‐D fracture front at every fracture propagation step. A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time‐dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3‐D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented. 相似文献
11.
为了研究复杂地电模型的航空瞬变电磁法全波形响应特征,需要开发考虑发射波形的三维数值模拟算法。本研究基于非结构四面体网格和位移逆Krylov子空间(Shift-and-Invert Krylov,简称SAI Krylov)方法,采用基于电偶极子离散的场源处理方法模拟场源,在时间域进行计算实现了全波形航空瞬变电磁法矢量有限元三维数值模拟。使用均匀半空间模型在阶跃波、半正弦波、三角波和梯形波激发下的全波形解析解、VTEM实际激发波形的后推欧拉算法计算结果,检验了本研究开发的数值模拟算法的正确性。设计地表起伏异常体模型,计算和分析了航空瞬变电磁响应特征。开发的基于位移逆Krylov子空间的全波形航空瞬变电磁法三维数值模拟算法适合模拟复杂地电模型的响应,具有较高的计算精度。 相似文献
12.
13.
Coupled formulation and algorithms for the simulation of non‐planar three‐dimensional hydraulic fractures using the generalized finite element method 下载免费PDF全文
下载免费PDF全文 This paper presents a coupled hydro‐mechanical formulation for the simulation of non‐planar three‐dimensional hydraulic fractures. Deformation in the rock is modeled using linear elasticity, and the lubrication theory is adopted for the fluid flow in the fracture. The governing equations of the fluid flow and elasticity and the subsequent discretization are fully coupled. A Generalized/eXtended Finite Element Method (G/XFEM) is adopted for the discretization of the coupled system of equations. A Newton–Raphson method is used to solve the resulting system of nonlinear equations. A discretization strategy for the fluid flow problem on non‐planar three‐dimensional surfaces and a computationally efficient strategy for handling time integration combined with mesh adaptivity are also presented. Several three‐dimensional numerical verification examples are solved. The examples illustrate the generality and accuracy of the proposed coupled formulation and discretization strategies. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
14.
水文地质参数场的刻画是建立地下水流数值模拟模型的关键问题和难点问题。通常来讲,参数场合理性程度越高,模型拟合精度越高。本次研究将随机方法和参数空间分布表达进行结合,提出了趋势化随机参数场的构建方法。以渗透系数为研究对象,首先利用MCMC采样和样本数据特征确定水文地质参数的基本数据结构,进而根据样本空间分布特征对其进行趋势化处理,最终形成趋势化的渗透系数场。通过算例分析,利用趋势化处理后的渗透系数场能够大幅提高模拟精度,相比传统赋均值方法其误差可降至原来的1/3。在北京大兴跌隆起地区进行的实例应用说明,趋势化渗透系数场对提升岩性粒径较大(中砂以上)地区模拟精度效果显著,案例中粗砂区域渗透系数经趋势化处理后平均拟合误差由2.76 m下降至0.64 m;而对岩性以细砂及以下粒径为主的区域模拟精度提升并不明显。总体来说,该方法可为地下水流数值模型的优化提供借鉴,提升模型拟合精度,从而更加合理地刻画地下水流系统。 相似文献
15.
We consider the finite element (FE) approximation of the two dimensional shallow water equations (SWE) by considering discretizations in which both space and time are established using a stable FE method. Particularly, we consider the automatic variationally stable FE (AVS-FE) method, a type of discontinuous Petrov-Galerkin (DPG) method. The philosophy of the DPG method allows us to establish stable FE approximations as well as accurate a posteriori error estimators upon solution of a saddle point system of equations. The resulting error indicators allow us to employ mesh adaptive strategies and perform space-time mesh refinements, i.e., local time stepping. We establish a priori error estimates for the AVS-FE method and linearized SWE and perform numerical verifications to confirm corresponding asymptotic convergence behavior. In an effort to keep the computational cost low, we consider an alternative space-time approach in which the space-time domain is partitioned into finite sized space-time slices. Hence, we can perform adaptive mesh refinements on each individual slice to preset error tolerances as needed for a particular application. Numerical verifications comparing the two alternatives indicate the space-time slices are superior for simulations over long times, whereas the solutions are indistinguishable for short times. Multiple numerical verifications show the adaptive mesh refinement capabilities of the AVS-FE method, as well the application of the method to some commonly applied benchmarks for the SWE.
相似文献16.
The numerical error associated with finite-difference simulation of wave propagation in discontinuous media consists of two
components. The first component is a higher-order error that leads to grid dispersion; it can be controlled by higher-order
methods. The second component results from misalignment between numerical grids and material interfaces. We provide an explicit
estimate of the interface misalignment error for the second order in time and space staggered finite-difference scheme applied
to the acoustic wave equation. Our analysis, confirmed by numerical experiments, demonstrates that the interface error results
in a first-order time shift proportional to the distance between the interface and computational grids. A 2D experiment shows
that the interface error cannot be suppressed by higher-order methods and indicates that our 1D analysis gives a good prediction
about the behavior of the numerical solution in higher dimensions.
相似文献
17.
An embedded fracture modeling framework for simulation of hydraulic fracturing and shear stimulation 总被引：1，自引：0，他引：1
Jack H. Norbeck Mark W. McClure Jonathan W. Lo Roland N. Horne 《Computational Geosciences》2016,20(1):1-18
A numerical modeling framework is described that is able to calculate the coupled processes of fluid flow, geomechanics, and rock failure for application to general engineering problems related to reservoir stimulation, including hydraulic fracturing and shear stimulation. The numerical formulation employs the use of an embedded fracture modeling approach, which provides several advantages over more traditional methods in terms of computational complexity and efficiency. Specifically, the embedded fracture modeling strategy avoids the usual requirement that the discretization of the fracture domain conforms to the discretization of the rock volume surrounding the fractures. As fluid is exchanged between the two domains, conservation of mass is guaranteed through a coupling term that appears as a simple source term in the governing mass balance equations. In this manner, as new tensile fractures nucleate and propagate subject to mechanical effects, numerical complexities associated with the introduction of new fracture control volumes are largely negated. In addition, the ability to discretize the fractures and surrounding rock volume independently provides the freedom to choose an acceptable level of discretization for each domain separately. Three numerical examples were performed to demonstrate the utility of the embedded fracture model for application to problems involving fluid flow, mechanical deformation, and rock failure. The results of the numerical examples confirm that the embedded fracture model was able to capture accurately the complex and nonlinear evolution of reservoir permeability as new fractures propagate through the reservoir and as fractures fail in shear. 相似文献
18.
Piyang Liu Gary Douglas Couples Jun Yao Zhaoqin Huang Wenhui Song Jingsheng Ma 《Computational Geosciences》2018,22(5):1187-1201
The two-scale continuum model is widely used in simulating the reactive dissolution process and predicting the optimum injection rate for carbonate reservoir acidizing treatment. The numerical methods of this model are currently based on structured grids, which are not applicable for complicated geometries. In this study, a general numerical scheme for simulating a reactive flow problem on both structured and unstructured grids is presented based on the finite volume method (FVM). The convection and diffusion terms involved in the reactive flow model are discretized by using the upwind scheme and two-point flux approximation (TPFA), respectively. The location of the centroid node inside each control volume is moved by using an optimization algorithm to make the connections with the surrounding elements as orthogonal as possible, which systematically improves the accuracy of the TPFA scheme. Additionally, in order to avoid the computational complexity resulting from the discretization of the non-linear term, the mass balance equation is only discretized in the spatial domain to get a set of ordinary differential equations (ODEs). These ODEs are coupled with the reaction equations and then solved using the numerical algorithm on ODEs. The accuracy and efficiency of the proposed method are studied by comparing the results obtained from the proposed numerical method with previous experimental and numerical results. This comparison indicates that, compared with the previous methods, the proposed method predicts the wormhole structure more accurately. Finally, the presented method is used to check the effect of the domain geometry, and it is found that the geometry of the flow domain has no effect on the optimum injection velocity, but the radial domain requires a larger breakthrough volume than the linear domain when other parameters are fixed. 相似文献
19.
地下水数值模拟过程中,人工开采量大都被当作确定项处理。但实际情况是开采量往往缺乏准确的统计数据,尤其是农业灌溉开采量,在计算中具有更大的不确定性。传统的处理方法是将这些人工开采量概化为抽水量确定的开采井,显然不能反映实际情况。采用概率论及数理统计的方法,分析了概化后开采量的不确定性,得出开采量服从正态分布。以此为基础,运用蒙特卡罗方法,对开采量不确定条件下数值模拟的结果进行可靠性分析。结果表明：传统处理方法不能反映开采量不确定条件下数值模拟结果可靠性的变化情况,而采用随机模拟的方法,可以计算出不同的给定允许降深条件下,模拟结果的可靠性。 相似文献
20.
Luz Angélica Caudillo-Mata Eldad Haber Christoph Schwarzbach 《Computational Geosciences》2017,21(5-6):963-980
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static Maxwell’s equations in the frequency domain. We assume a coarse mesh nested within a fine mesh that accurately discretizes the problem. For each coarse cell, we independently solve a local version of the original Maxwell’s system subject to linear boundary conditions on an extended domain, which includes the coarse cell and a neighborhood of fine cells around it. The local Maxwell’s system is solved using the fine mesh contained in the extended domain and the mimetic finite volume method. Next, these local solutions (basis functions) together with a weak-continuity condition are used to construct a coarse-mesh version of the global problem. The basis functions can be used to obtain the fine-mesh details from the solution of the coarse-mesh problem. Our approach leads to a significant reduction in the size of the final system of equations and the computational time, while accurately approximating the behavior of the fine-mesh solutions. We demonstrate the performance of our method using two 3D synthetic models: one with a mineral deposit in a geologically complex medium and one with random isotropic heterogeneous media. Both models are discretized using an adaptive mesh refinement technique. 相似文献