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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
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对h型自适应自然单元法的自适应细化方案进行了初步研究。在ZZ误差分析的基础上实现了节点的自动加密,使得随着自适应细化的进行,求解误差减小,而且误差分布趋于均匀。在数值分析中,主要有两种误差来源--插值误差和积分误差。随着节点的加密,Delaunay三角形的尺寸随之减小,三角形内的应力场趋于线性分布,那么插值误差和积分误差也都会随之减小。因而,h型自适应分析可以同时减小上述两种误差而达到不断提高求解精度的目的。由于自然单元法求解依赖于求解域内离散节点的Voronoi结构,建议的细化方案中新节点的引入只需局部调整Delaunay结构,算法的实现极为容易,程序实现简单、高效。研究表明,建议的自适应方案是可行的,自然单元法特别适合进行h型自适应分析。 相似文献
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In this paper, we systematically analyze the pressure projection stabilization method for the Darcy and coupled Darcy–Stokes flow problems in multiple dimensions. Stability results for this stabilization method are established. For the Darcy flow, optimal error estimates in the divergence norm for velocity and suboptimal error estimates in the $L^{2}$ -norm for pressure are obtained, and a superconvergence result for the pressure is derived; a local postprocessing scheme is constructed to generate optimal error estimates in the L 2-norm for pressure. For the coupled Darcy–Stokes flow, error estimates of optimal order are obtained in terms of the energy norm of velocity and pressure. Numerical results are presented to check the theory developed. 相似文献
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郑州市龙湖成湖方案研究 总被引：4，自引：0，他引：4
人工湖建设可能引起地下水位的抬升,将对周边生态环境造成影响,如部分河岸区的浸没、土壤次生盐渍化、地下水质恶化、影响湖周高层建筑物的地基承载力等。在分析人工湖渗漏问题基础上, 提出了在不采取防渗措施和采取防渗措施两种不同情况下的成湖方案, 并进行了防渗方案的优选。用地下水数值模型MODFLOW和优化模型MODMAN对处于黄河冲积平原地区拟开挖人工湖进行了数值模拟及优化。结果表明,在龙湖运行时,只要人工湖的渗漏量控制在一定范围内,辅之于相应的湖体周边的降水措施,就可有效避免各种环境问题的出现。 相似文献
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在岩土工程分析中求解精度控制常常是必需的,在数值流形法中可以通过控制数学覆盖网格的稀疏和覆盖位移的阶数来达到精度的要求。提出了基于等几何分析的数值流形方法,定义了相应的数学覆盖的构造形式,推导了基于二次B样条的9节点数值流形方法分析格式;针对基于Lagrange插值函数的4节点数值流形方法提出了基于T样条思想的数学覆盖网格的局部加密方法。算例计算结果表明,相对于4节点的数值流形方法,基于非均匀有理B样条的9节点数值流形方法具有更高的精度;基于T样条思想的加密网格在保持计算精度的前提下降低了自由度的数量,表明T样条加密是一种自然的局部加密算法。 相似文献
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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.
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P. D. Sreekanth P. D. Sreedevi Shakeel Ahmed N. Geethanjali 《Environmental Earth Sciences》2011,62(6):1301-1310
Prediction of water level is an important task for groundwater planning and management when the water balance consistently
tends toward negative values. In Maheshwaram watershed situated in the Ranga Reddy District of Andhra Pradesh, groundwater
is overexploited, and groundwater resources management requires complete understanding of the dynamic nature of groundwater
flow. Yet, the dynamic nature of groundwater flow is continually changing in response to human and climatic stresses, and
the groundwater system is too intricate, involving many nonlinear and uncertain factors. Artificial neural network (ANN) models
are introduced into groundwater science as a powerful, flexible, statistical modeling technique to address complex pattern
recognition problems. This study presents the comparison of two methods, i.e., feed-forward neural network (FFNN) trained
with Levenberg–Marquardt (LM) algorithm compared with a fuzzy logic adaptive network-based fuzzy inference system (ANFIS)
model for better accuracy of the estimation of the groundwater levels of the Maheshwaram watershed. The statistical indices
used in the analysis were the root mean square error (RMSE), regression coefficient (R
2) and error variation (EV).The results show that FFNN-LM and ANFIS models provide better accuracy (RMSE = 4.45 and 4.94, respectively,
R
2 is 93% for both models) for estimating groundwater levels well in advance for the above location. 相似文献
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Unsaturated flow problems in porous media often described by Richards’ equation are of great importance in many engineering applications. In this contribution, we propose a new numerical flow approach based on isogeometric analysis (IGA) for modeling the unsaturated flow problems. The non-uniform rational B-spline (NURBS) basis is utilized for spatial discretization whereas the stable implicit backward Euler method for time discretization. The nonlinear Richards’ equation is iteratively solved with the aid of the Newton–Raphson scheme. Owing to some desirable features of an efficient numerical flow approach, major advantages of the present formulation involve: (a) numerical oscillation at the wetting front can be avoided or facilitated, simply by using either an h-refinement or a lumped mass matrix technique; (b) higher-order exactness can be obtained due to the nature of the IGA features; (c) the approach is straightforward to implement and it does not need any transformation, e.g., Kirchhoff transformation or filter algorithm; and (d) in contrast to the Picard iteration scheme, which forms linear convergences, the proposed approach can however yield quadratic convergences by using the Newton–Raphson method for solving resultant nonlinear equations. Numerical model validation is analyzed by solving a three-dimensional unsaturated flow problem in soil, and its derived results are verified against analytical solutions. Numerical applications are then studied by considering three extensive examples with simple and complex configurations to further show the accuracy and applicability of the present IGA. 相似文献
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Emil M. Constantinescu Adrian Sandu Gregory R. Carmichael 《Computational Geosciences》2008,12(2):133-151
We discuss an adaptive resolution system for modeling regional air pollution based on the chemical transport model STEM. The
grid adaptivity is implemented using the generic adaptive mesh refinement tool Paramesh, which enables the grid management
operations while harnessing the power of parallel computers. The computational algorithm is based on a decomposition of the
domain, with the solution in different subdomains being computed with different spatial resolutions. Various refinement criteria
that adaptively control the fine grid placement are analyzed to maximize the solution accuracy while maintaining an acceptable
computational cost. Numerical experiments in a large-scale parallel setting (~0.5 billion variables) confirm that adaptive
resolution, based on a well-chosen refinement criterion, leads to the decrease in spatial error with an acceptable increase
in computational time. Fully dynamic grid adaptivity for air quality models is relatively new. We extend previous work on
chemical and transport modeling by using dynamically adaptive grid resolution. Advantages and shortcomings of the present
approach are also discussed. 相似文献
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Numerical modeling of toxic nonaqueous phase liquid removal from contaminated groundwater systems: mesh effect and discretization error estimation 下载免费PDF全文
下载免费PDF全文 Numerical modeling has now become an indispensable tool for investigating the fundamental mechanisms of toxic nonaqueous phase liquid (NAPL) removal from contaminated groundwater systems. Because the domain of a contaminated groundwater system may involve irregular shapes in geometry, it is necessary to use general quadrilateral elements, in which two neighbor sides are no longer perpendicular to each other. This can cause numerical errors on the computational simulation results due to mesh discretization effect. After the dimensionless governing equations of NAPL dissolution problems are briefly described, the propagation theory of the mesh discretization error associated with a NAPL dissolution system is first presented for a rectangular domain and then extended to a trapezoidal domain. This leads to the establishment of the finger‐amplitude growing theory that is associated with both the corner effect that takes place just at the entrance of the flow in a trapezoidal domain and the mesh discretization effect that occurs in the whole NAPL dissolution system of the trapezoidal domain. This theory can be used to make the approximate error estimation of the corresponding computational simulation results. The related theoretical analysis and numerical results have demonstrated the following: (1) both the corner effect and the mesh discretization effect can be quantitatively viewed as a kind of small perturbation, which can grow in unstable NAPL dissolution systems, so that they can have some considerable effects on the computational results of such systems; (2) the proposed finger‐amplitude growing theory associated with the corner effect at the entrance of a trapezoidal domain is useful for correctly explaining why the finger at either the top or bottom boundary grows much faster than that within the interior of the trapezoidal domain; (3) the proposed finger‐amplitude growing theory associated with the mesh discretization error in the NAPL dissolution system of a trapezoidal domain can be used for quantitatively assessing the correctness of computational simulations of NAPL dissolution front instability problems in trapezoidal domains, so that we can ensure that the computational simulation results are controlled by the physics of the NAPL dissolution system, rather than by the numerical artifacts. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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M. A. Hicks 《国际地质力学数值与分析法杂志》2000,24(5):453-476
An adaptive mesh refinement algorithm has been developed for non‐linear computations in geomechanics, based on a smoothed stress–strain finite element formulation. This uses estimates of error in the incremental shear strain invariant to guide the regeneration of unstructured meshes at regular intervals during loading. Following each mesh‐update, no re‐analysis of previous increments with the new mesh is necessary. Algorithm performance has been investigated by analysing a passive earth pressure problem using a linear elastic‐perfectly plastic Mohr–Coulomb soil model. Perfectly drained behaviour has been considered, as have partially drained situations using hydromechanical coupling, while undrained behaviour has been approximated using time steps close to zero. In all cases, mesh adaptivity has been successful in capturing regions of high strain gradient. The results have been compared with analytical solutions. Accurate computations of limit load and shear band orientation have been obtained for a wide range of material dilation angles. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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This work presents the coupling of two locally conservative methods for elliptic problems: namely, the discontinuous Galerkin method and the mixed finite element method. The couplings can be defined with or without interface Lagrange multipliers. The formulations are shown to be equivalent. Optimal error estimates are given; penalty terms may or may not be included. In addition, the analysis for non-conforming grids is also discussed. 相似文献
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Benjamin Faigle Rainer Helmig Ivar Aavatsmark Bernd Flemisch 《Computational Geosciences》2014,18(5):625-636
A sequential solution procedure is used to simulate compositional two-phase flow in porous media. We employ a multiphysics concept that adapts the numerical complexity locally according to the underlying processes to increase efficiency. The framework is supplemented by a local refinement of the simulation grid. To calculate the fluxes on such grids, we employ a combination of the standard two-point flux approximation and a multipoint flux approximation where the grid is refined. This is then used to simulate a large-scale example related to underground CO2 storage. 相似文献
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认识深部裂隙岩体中的地下水渗流特征(流速、渗流路径等),是深部地质工程开发建设的重要前提。近年来,分布式光纤测温技术作为识别深部裂隙岩体地下水渗流特征的有效方法,在国外开展了大量的研究,但在国内鲜少见在实际场地开展的相关工作。本研究以我国首个地下实验室场址甘肃北山新场花岗岩岩体中的两个钻孔(BSQ02及BSQ03)为试验对象,开展基于分布式光纤测温(Fiber-Optic Distributed Temperature Sensing,FO-DTS)的现场温度-水力试验,实现了对钻孔地下水温度的高精度、连续性观测。通过分析现场试验获取的钻孔温度-深度剖面随时间的变化,推断BSQ02在试验过程中存在外源地下水的流入,然后结合钻孔柱状图对钻孔中的入流导水裂隙进行了定位;基于现场观测数据建立了钻孔的渗流-传热耦合数值模型,反演估算出钻孔中地下水平均流速为0.01 m·s-1,通过裂隙流入地下水温度小于钻孔中原地下水温度,两者之间的温度差为0.7 ℃,通过裂隙流入的地下水流速为1×10-5 m·s-1,获取了地下水的渗流特征。该项工作可为基于分布式光纤测温技术的裂隙介质地下水渗流规律研究提供借鉴与指导。 相似文献
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P. Salinas D. Pavlidis Z. Xie H. Osman C. C. Pain M. D. Jackson 《Computational Geosciences》2018,22(5):1389-1401
Flows of multiple fluid phases are common in many subsurface reservoirs. Numerical simulation of these flows can be challenging and computationally expensive. Dynamic adaptive mesh optimisation and related approaches, such as adaptive grid refinement can increase solution accuracy at reduced computational cost. However, in models or parts of the model domain, where the local Courant number is large, the solution may propagate beyond the region in which the mesh is refined, resulting in reduced solution accuracy, which can never be recovered. A methodology is presented here to modify the mesh within the non-linear solver. The method allows efficient application of dynamic mesh adaptivity techniques even with high Courant numbers. These high Courant numbers may not be desired but a consequence of the heterogeneity of the domain. Therefore, the method presented can be considered as a more robust and accurate version of the standard dynamic mesh adaptivity techniques. 相似文献
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We present the results of a study on a posteriori error control strategies for finite volume element approximations of second order elliptic differential equations. Finite volume methods ensure local mass conservation and, combined with some up-wind strategies, give monotone solutions. We adapt the local refinement techniques known from the finite element method to the finite volume discretizations of various boundary value problems for steady-state convection–diffusion–reaction equations. In this paper we derive and study a residual type error estimator and illustrate its practical performance on a series of computational tests in 2 and 3 dimensions. Our tests show that the discussed locally conservative approximation methods with a posteriori error control can be used successfully in numerical simulation of fluid flow and transport in porous media. 相似文献
18.
选择了5种机器学习模型,即k最近邻方法（KNN）、多元自回归样条方法（MARS）、支持向量机（SVM）、多项对数线性模型（MLM）和人工神经网络（ANN）,利用海拔、相对湿度、坡向、植被、风速、气温和坡度等因子订正ITPCAS和CMORPH两种常用的青藏高原日降水数据集。五折交叉验证表明,KNN的订正精度最高。在三个验证站点（唐古拉、西大滩和五道梁）的误差分析,以及对青藏高原年降水量的空间分析均表明,KNN对CMORPH的订正效果显著,对ITPCAS在局部区域有一定订正效果,ITPCAS及其订正值的降水空间分布准确度高于CMORPH的订正值。主成分分析法表明降水订正是气象和环境因子综合作用的结果。 相似文献
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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
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We consider adaptive discontinuous Galerkin (DG) methods for solving reactive transport problems in porous media. To guide
anisotropic and dynamic mesh adaptation, a posteriori error estimators based on solving local problems are established. These error estimators are efficient to compute and effective
to capture local phenomena, and they apply to all the four primal DG schemes, namely, symmetric interior penalty Galerkin,
nonsymmetric interior penalty Galerkin, incomplete interior penalty Galerkin, and the Oden–Babuška-Baumann version of DG.
Numerical results are provided to illustrate the effectiveness of the proposed error estimators. 相似文献