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1.
We reply to Prof. Linkov comments on our article entitled “Explicit versus implicit front advancing schemes for the simulation of hydraulic fracture growth” (Int. J. Numer. Anal. Methods Geomech., 2019, 43 (6), 1300–1315). We present additional results indicating that both the implicit and explicit front advancement schemes are robust even in the case of a large stress contrast. 相似文献
2.
A universal particle velocity based algorithm for simulating hydraulic fractures, previously proposed for Newtonian fluids, is extended to the class of shear-thinning fluids. The scheme is not limited to any particular elasticity operator or crack propagation regime. The computations are based on two dependent variables: the crack opening and the reduced particle velocity. The application of the latter facilitates utilization of the local condition of Stefan type (speed equation) to trace the fracture front. The condition is given in a general explicit form which relates the crack propagation speed (and the crack length) to the solution tip asymptotics. The utilization of a modular structure, and the adaptive character of its basic blocks, result in a flexible numerical scheme. The computational accuracy of the proposed algorithm is validated against a number of analytical benchmark solutions. 相似文献
3.
《Geomechanics and Geoengineering》2013,8(3):153-177
An automatic time increment selection scheme for numerical analysis of long-term response of geomaterials is presented. The scheme is simple, rational and stable. Governed by a simple empirical expression, it can adaptively adjust the time increments depending on the strain rate-dependent temporal history of the material response. The proposed expression requires only a few parameters whose selection is a trivial task since they have a small effect on accuracy but have a significant effect on computational efficiency. This generalization has been made possible because of the enforcement of certain predefined control criteria to avoid extreme conditions. If any of the control criteria is satisfied, the computation is restarted by going a few time steps back to ensure the smoothness of the computed responses and time increments are again continuously adjusted through the governing equation provided. Performance of the automatic time increment selection scheme is investigated through finite element analyses of the long-term consolidation response of clay under different geotechnical profiles and loading conditions. Both elastic and elasto-viscoplastic constitutive relations are considered, including the consideration of the destructuration effects of geomaterials. Numerical results show that the performance of the automatic time increment selection scheme is reasonably excellent. While offering reasonable accuracy of the numerical solution, it can ensure temporal stability at optimal computational efficiency. In addition to the Euler implicit method, the automatic time increment selection scheme also performs well even when the explicit fourth-order Runge–Kutta method is employed for the integration of time derivatives. 相似文献
4.
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
5.
Susmita Majumdar D. R. C. Nair R. S. Saraswat A. Chandrasekar 《Journal of Earth System Science》1997,106(3):147-155
The explicit nonlinear normal mode initialization (ENMI) scheme is applied to a tropical barotropic limited area shallow water
model in spherical coordinates. The model is formulated by considering potential enstrophy conserving finite difference scheme.
It is seen from the results of this study that the ENMI scheme is fully capable of filtering out the spurious gravity wave
oscillations. The results are compared with those using an implicit nonlinear normal mode initialization (INMI). The latter
scheme gives equally satisfactory results, requiring less computational time than the explicit scheme. 相似文献
6.
计算地球流体力学的回顾、进展及展望 总被引：1，自引：0，他引：1
简要回顾了计算地球流体力学的发展历史,概括介绍了计算地球流体力学的研究进展及最新发展方向。针对线性发展方程的计算稳定性问题,介绍了判定线性发展方程初值问题的稳定性判别条件：CLF条件。对分析线性偏微分方程差分格式计算稳定性判据的Fourier方法、启发性稳定性分析方法,也做了简要的介绍。同时,重点介绍了判定线性发展方程初边值问题计算稳定性的GKS理论。在非线性发展方程的计算稳定性方面,重点介绍的主要内容包括：非线性发展方程的计算紊乱现象和计算不稳定的原因;克服非线性发展方程计算不稳定的方法;瞬时平方守恒型差分格式的构造;隐式和显式完全平方守恒格式的设计;强迫耗散非线性发展方程的计算稳定性问题。在计算地球流体力学的近期进展方面,重点介绍了非线性发展方程的计算稳定性与初值的关系,强迫耗散非线性发展方程显式准完全平方守恒格式的构造。对计算地球流体力学需要进一步研究的问题,也做了简要介绍。这些研究工作的介绍,无疑对推动计算地球流体力学的研究和大气海洋模式的研制具有一定的指导意义。 相似文献
7.
An implicit material point method (MPM), a variant of the finite element method (FEM), is presented in this paper. The key feature of MPM is that the spatial discretisation uses a set of material points, which are allowed to move freely through the background mesh. All history-dependent variables are tracked on the material points and these material points are used as integration points similar to the Gaussian points. A mapping and re-mapping algorithm is employed, to allow the state variables and other information to be mapped back and forth between the material points and background mesh nodes during an analysis. In contrast to an explicit time integration scheme utilised by most researchers, an implicit time integration scheme has been utilised here. The advantages of such an approach are twofold: firstly, it addresses the limitation of the time step size inherent in explicit integration schemes, thereby potentially saving significant computational costs for certain types of problems; secondly, it enables an improved algorithm accuracy, which is important for some constitutive behaviours, such as elasto-plasticity. The main purpose of this paper is to provide a unified MPM framework, in which both quasi-static and dynamic analyses can be solved, and to demonstrate the model behaviour. The implementation closely follows standard FEM approaches, where possible, to allow easy conversion of other FEM codes. Newton’s method is used to solve the equation of motion for both cases, while the formation of the mass matrix and the required updating of the kinematic variables are unique to the dynamic analysis. Comparisons with an Updated Lagrangian FEM and an explicit MPM code are made with respect to the algorithmic accuracy and time step size in a couple of representative examples, which helps to illustrate the relative performance and advantages of the implicit MPM. A geotechnical application is then considered, illustrating the capabilities of the proposed method when applied in the geotechnical field. 相似文献
8.
To improve the computational efficiency of the numerical manifold method for discontinuous deformation simulations, a spatial-domain coupled explicit-implicit time integration algorithm is proposed. A subdomain partition algorithm based on a super manifold element is developed for the numerical manifold method to simulate dynamic motions of blocky rock mass. In different subdomains, explicit or implicit time integration method is employed respectively based on its contact and motion status. These subdomains interact through assembling the corresponding explicit or implicit time integration-based matrices of different rock blocks. The computational efficiency of the discontinuity system under dynamic loading is improved by partially diagonalizing the global matrices. Two verification examples of a sliding block along an inclined plane under a horizontal acceleration excitation and a multiblock system acted on by dynamic forces are studied to examine the accuracy of the proposed numerical method, respectively. A highly fractured rock mass situated on an inclined slope subjected to seismic excitations is then studied to show the computational efficiency of the developed algorithm. The simulated results are in good agreement with those from the versions using purely implicit or explicit time integration algorithm for the numerical manifold method. The computational efficiency is shown to be higher using the proposed algorithm, which demonstrates its potential for application in dynamic analysis of highly fractured rock masses. 相似文献
9.
针对传统算法效率低的问题,将隐式双时间步法应用于求解二维浅水方程,建立了非结构网格下高效的有限体积模型。在应用双时间步法时,虚拟时间层中的定常问题采用高效的隐式LU-SGS（Lower-Upper Symmetric Gauss-Seidel）方法进行迭代求解。通过模拟计算4个典型算例以及与传统显式算法进行比较,对模型精度、效率及处理实际问题能力进行检验,分析了时间步长、内迭代次数对模型性能的影响。结果表明,双时间步法放宽了稳定性对时间步长的限制,时间步长可取到显式格式10倍以上,计算耗时减少了50%以上,模型具有良好精度与适应性,具有较好的推广应用价值。 相似文献
10.
This paper addresses the problem of explicit fractured media modelling in an operational case. On one side, realistic fracture models are mainly used for research purposes in order to investigate better the flow behaviour impacted by the complex multi-scale fracture network. Often, a very fine grid and hence an increased computation time are needed. On the other hand, an operational fractured reservoir is still generally modelled using an implicit fracture media representation. The upscaled petrophysical properties and dual media are defined on a coarse grid to limit the computational time of dynamic simulation. The challenge of this work is to demonstrate that an explicit fracture modelling is not reserved only for the research domain, but can be applied to an operational case study. The static model is constructed using a multiple point statistics approach in order to represent complex interaction patterns of fractures and faults observed at the analogue outcrop. The dynamic behaviour is simulated based on this spatial fracture network representation. 相似文献
11.
Dieter F. E. Stolle 《国际地质力学数值与分析法杂志》1991,15(6):399-416
This paper explores similarities and differences between initial stress and initial strain methods of analyses. The author takes the position that both methods, although perhaps conceptually different, are actually numerically the same. A simple approach for providing closed-form stability criteria for explicit and implicit time-marching procedures is described. For the case of associated, non-hardening viscoplasticity the approach provides criteria which are identical to those of Cormeau for explicit schemes. An implicit time-marching scheme which avoids the compliance matrix inversions at the constitutive level is also presented. Like many other implicit methods, this implicit time-marching scheme is unconditionally stable for θ≥½. The connection between initial strain plasticity and an explicit viscoplastic time-marching scheme is also addressed. 相似文献
12.
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
13.
在一维显式、二维隐式水动力联网数学模型的基础上,建立了一种一维、二维全隐河网海湾水动力联网数学模型。该一维河网模型采用Preissmann四点隐式格式,用节点水位控制法进行数值计算,二维海湾模型采用改进型双向隐式(DSI)法进行数值求解。在河口一维、二维连接处,水力因子通过接口断面法传递,无需重叠一个一维河段来传递水力因子,避免了口门处二维网格需取较小尺度的问题。模型在珠江三角洲河网及横门、洪奇沥口门海域做了检验,验证结果表明,建立的河网海湾水动力联网数学模型是可行的,可以用于河网、河口治理工程的数值研究。 相似文献
14.
Hypoplastic constitutive equation based on nonlinear tensor functions possesses a failure surface but no yield surface. In this paper, we consider the numerical integration and FE implementation of a simple hypoplastic constitutive equation. The accuracy of several integration methods, including implicit and explicit methods, is examined by performing a set of triaxial compression tests. Adaptive explicit schemes show the best performance. In addition, the stress drift away from the failure surface is corrected with a predictor-corrector scheme, which is verified by two boundary value problems, i.e. rigid footing tests and slope stability. 相似文献
15.
In this paper, we present a computational framework for the simulation of coupled flow and reservoir geomechanics. The physical
model is restricted to Biot’s theory of single-phase flow and linear poroelasticity, but is sufficiently general to be extended
to multiphase flow problems and inelastic behavior. The distinctive technical aspects of our approach are: (1) the space discretization
of the equations. The unknown variables are the pressure, the fluid velocity, and the rock displacements. We recognize that
these variables are of very different nature, and need to be discretized differently. We propose a mixed finite element space
discretization, which is stable, convergent, locally mass conservative, and employs a single computational grid. To ensure
stability and robustness, we perform an implicit time integration of the fluid flow equations. (2) The strategies for the
solution of the coupled system. We compare different solution strategies, including the fully coupled approach, the usual
(conditionally stable) iteratively coupled approach, and a less common unconditionally stable sequential scheme. We show that
the latter scheme corresponds to a modified block Jacobi method, which also enjoys improved convergence properties. This computational
model has been implemented in an object-oriented reservoir simulator, whose modular design allows for further extensions and
enhancements. We show several representative numerical simulations that illustrate the effectiveness of the approach. 相似文献
16.
A virtual multidimensional internal bond (VMIB) model developed to simulate the propagation of hydraulic fractures using the finite‐element method is formulated within the framework of the virtual internal bond theory (VIB) that considers a solid as randomized material particles in the micro scale, and derives the macro constitutive relation from the cohesive law between the material particles with an implicit fracture criterion. Hydraulic pressure is applied using a new scheme that enables simulation of hydraulically driven cracks. When the model is applied to study hydraulic fracture propagation in the presence of a natural fracture, the results show the method to be very effective. It shows that although the in situ stress ratio is the dominant factor governing the propagation direction, a natural fault can also strongly influence the hydraulic fracture behavior. This influence is conditioned by the shear stiffness of the fault and the distance to the original hydraulic fracture. The model results show that when the fault is strong in shear, its impact on hydraulic fracture trajectory is weak and the hydraulic fracture will likely penetrate the fault. For a weak fault, however, the fracture tends to be arrested at the natural fault. The distance between the fault and the hydraulic fracture is also important; the fault influence increases with decreasing distance. The VMIB does not require selection of a fracture criterion and remeshing when the fracture propagates. Therefore, it is advantageous for modeling fracture initiation and propagation in naturally fractured rock. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
17.
This work deals with sequential implicit schemes for incompressible and immiscible two-phase Darcy flows which are commonly used and well understood in the case of spatially homogeneous capillary pressure functions. To our knowledge, the stability of this type of splitting schemes solving sequentially a pressure equation followed by the saturation equation has not been investigated so far in the case of discontinuous capillary pressure curves at different rock type interfaces. It will be shown here to raise severe stability issues for which stabilization strategies are investigated in this work. To fix ideas, the spatial discretization is based on the Vertex Approximate Gradient (VAG) scheme accounting for unstructured polyhedral meshes combined with an Hybrid Upwinding (HU) of the transport term and an upwind positive approximation of the capillary and gravity fluxes. The sequential implicit schemes are built from the total velocity formulation of the two-phase flow model and only differ in the way the conservative VAG total velocity fluxes are approximated. The stability, accuracy and computational cost of the sequential implicit schemes studied in this work are tested on oil migration test cases in 1D, 2D and 3D basins with a large range of capillary pressure parameters for the drain and barrier rock types. It will be shown that usual splitting strategies fail to capture the right solutions for highly contrasted rock types and that it can be fixed by maintaining locally the pressure saturation coupling at different rock type interfaces in the definition of the conservative total velocity fluxes. The numerical investigation of the sequential schemes is also extended to the widely used finite volume Two-Point Flux Approximation spatial discretization.
相似文献18.
19.
非连续变形分析方法（DDA）是一种平行于有限元法的新型数值计算方法,该方法基于最小势能原理,把每个离散块体的变形、运动和块体之间的接触统一到平衡方程中进行隐式求解。然而,传统DDA方法在计算过程中需组装整体刚度矩阵并联立求解方程组,在用于大型岩土工程问题的三维数值模拟时占用内存较大、耗时较长、计算效率极低。因此,提出一种基于显式时间积分的三维球颗粒DDA方法。该方法在求解过程中不需要组装整体刚度矩阵,在求解加速度时,由于质量矩阵为对角矩阵,可存储为一维向量占用内存较少,且可分块逐自由度求解,效率较高,在接触判断上采用最大位移准则简化了接触算法,采用较小的时步,保证了计算的精确性;通过几个典型算例验证了该方法的准确性及计算效率。 相似文献