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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
2.
Microscopic studies using advanced experimental techniques have provided better insight into the fracture mechanisms in cement‐based materials. A clear understanding of fracture mechanisms is critical for the development of rigorous computational models for analysing fracture. Fracture analysis is usually carried out by finite element method. Accuracy of FE analysis depends upon the choice of mesh and for the predictions to be reliable, discretization errors are to be minimized. In cohesive crack approach, the non‐linearity is limited to the boundary conditions along the geometric discontinuity while the bulk of the material retains its elastic nature. The paper presents a mesh‐adaptive strategy based on ZZ error estimator to model discrete crack propagation in cement‐based materials. Examples of simulations have demonstrated the potential of the mesh‐adaptive technique in modelling the evolution of the localized strain profiles as well as failure of concrete test specimen. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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研究了三维渗流的自适应有限元法,建立了集成网格自动剖分、渗流有限元分析、网格调整、后处理等四大模块的四面体单元h型自适应系统。给出的算例证实了系统的有效性和优越性。 相似文献
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在有限元数值计算平台上,建立了一套基于后验误差评估和Delaunay三角剖分的网格自适应方案,针对饱和砂土静力受压和地震液化的特性进行模拟。验证了超收敛单元片回归（SPR）误差评估中原用于四边形单元的双线性回归函数在用于三角形单元网格时的适用性和可靠性;在饱和砂土动、静力算例中,网格自适应计算获得的变形、应变、超孔压比等的变化规律与常规有限元结果趋势一致。随着网格的再生成,参考点的位移和全域的平均相对误差逼近精确值。对于初始网格,讨论了合理的自适应程度并应用于地震液化的自适应数值模拟中,也对Delaunay三角剖分实施了一些改进。最终证明该自适应方案在提高计算效率的同时,亦可以保证计算所需的精准度。 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
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We present a method for solving steady‐state flow with a free surface in porous media. This method is based on a finite volume approach and is halfway between a fixed and an adaptive mesh method, taking advantage of both approaches: computational efficiency and localization accuracy. Most of the mesh remains fixed during the iterative process, while the cells in contact with the free surface (free surface cells) are being reshaped. Based on this idea, we developed two methods. In the first one, only the volumes of the free surface cells are adapted. In the second one, the computational nodes of the free surface cells are relocated exactly at the free surface. Both adaptations are designed for a better application of the free surface boundary conditions. Implementation details are given on a regular finite volume mesh for the case of homogeneous and heterogeneous rectangular dams in 2D and 3D. Accuracy and convergence properties of the proposed approach are demonstrated by comparison with an analytical solution and with existing references. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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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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电各向异性在自然界中普遍存在,特别是沉积盆地中的部分岩层经过压实变质作用,表现出很强的各向异性导电性,采用基于各向同性模型对实测资料进行正反演解释必然会造成困难甚至结果的错误,只有基于各向异性理论的正反演解释才更为合理准确。本文通过自适应有限元对大地电磁各向异性进行正演计算,分别模拟水平、垂直和倾斜各向异性介质在不同偏转角和主轴电阻率下的响应结果。结果表明：自适应有限元能够在后验误差的控制下得到合理的网格,使计算结果更加接近解析解;在各向异性介质中,大地电磁TE极化模式的视电阻率和阻抗相位与垂直于层面的电阻率无关;二维电各向异性结构中,大地电磁TM极化模式响应结果总是由主轴上的电阻率在y轴方向上的分量所决定。 相似文献
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Summary Sources of error are investigated for a two-dimensional finite difference computer program designed to model strata deformation. The program calculates the displacements of a mesh of mass points, by the iterative solution of equations of equilibrium for the stresses acting on each mass point. The effect of errors on both displacement estimates and stress estimates is considered.Round-off errors are discussed analytically, while the effect of choosing too coarse a mesh density is demonstrated by comparison of two runs of the program with identical material properties, but different mesh densities. The influence of boundary conditions and the result of incomplete relaxation of the finite difference equations is estimated by comparison with Kirsch's analytical solution for a thin plate of finite width with a circular hole under unidimensional load.As a result of the analysis, estimators for stresses and displacements are derived, which make allowance for some of the sources of error; suitable boundary conditions for first and subsequent runs of the program are proposed; and a convergence criterion for the iterative process is suggested. These results are then applied to simulations of mining situations, together with various refinements of the basic model, such as separation and slip between adjacent strata, and an allowance for failure of material. 相似文献
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Magnolia Mamaghani Guillaume Enchéry Claire Chainais-Hillairet 《Computational Geosciences》2011,15(1):17-34
Steam-assisted gravity drainage (SAGD) is an enhanced oil recovery process for heavy oils and bitumens. Numerical simulations of this thermal process allow us to estimate the retrievable volume of oil and to evaluate the benefits of the project. As there exists a thin flow interface (compared to the reservoir dimensions), SAGD simulations are sensitive to the grid size. Thus, to obtain precise forecasts of oil production, very small-sized cells have to be used, which leads to prohibitive CPU times. To reduce these computation times, one can use an adaptive mesh refinement technique, which will only refine the grid in the interface area and use coarser cells outside. To this end, in this work, we introduce new refinement criteria, which are based on the work achieved in Kröner and Ohlberger (Math Comput 69(229):25–39, 2000) on a posteriori error estimators for finite volume schemes for hyperbolic equations. Through numerical experiments, we show that they enable us to decrease in a significant way the number of cells (and then CPU times) while maintaining a good accuracy in the results. 相似文献
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Diogo L. Cecílio Philippe R. B. Devloo Sônia M. Gomes Erick S.R. Santos 《国际地质力学数值与分析法杂志》2019,43(4):814-828
A finite element formulation is proposed and implemented for analysing the stability of excavated wells using the DiMaggio-Sandler constitutive elastoplastic model with a typical carbonate reservoir configuration. The quality of the finite element approximation is ensured by applying smooth curved elements adapted to the wellbore geometry, and h − p adaptive finite element meshes in the plastic zone. General purpose procedures are defined to transfer the elastoplastic deformation history to newly created integration points. A breakout damage criterion is proposed based on the second invariant of the deviatoric plastic deformation tensor. This damage criterion is used to apply a mesh movement algorithm to represent material collapse. The automatic successive application of the breakout damage criterion results in elliptical realistically looking geometries obtained in experiments reported in the literature. 相似文献
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由于地质体和矿体的形态非常复杂，使用长方体网格离散建立正演模型时可能和真实情况有很大差别，因此计算结果可靠性差。本文提出一种基于约束Delaunay网格剖分的方法对地质体进行离散并进行重力建模，在模型边界等复杂区域使用网格自适应加密技术，将三维地质体离散为有限个四面体；并详细推导出针对四面体网格的重力正演公式，实现了基于约束Delaunay网格剖分技术的三维重力数值模拟；最后，针对一个合成数据模型，将计算解与解析解对比。结果表明，细化网格的模拟结果比粗糙网格更好，满足数值模拟的精度要求。将该方法应用到金川矿区实际地质体建模中，根据局部需要，建立各处网格密度不均匀的三维模型，并计算该模型的地表重力场，而后对比模拟数据与实测数据，结果表明Delaunay网格建模方法具有很强的适用性，能够模拟复杂的地质体重力异常。 相似文献
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Robert Kirby 《Computational Geosciences》2003,7(3):197-214
In this paper, residual-based a posteriori error bounds are derived for the mixed finite element method applied to a model second order elliptic problem. A global upper bound for the error in the scalar variable is established, as well as a local lower bound. In addition, due to the fact that the scalar and vector variables are approximated to equal order accuracy, the dual problem may be modified to give an upper bound for the vector variable. Some comments on estimating more general error quantities are also made. The estimate effectively guides adaptive refinement for a smooth problem with a boundary layer, as well as detects the need to refine near a singularity. 相似文献
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We present a numerical scheme for reactive contaminant transport with nonequilibrium sorption in porous media. The mass conservative scheme is based on Euler implicit, mixed finite elements, and Newton method. We consider the case of a Freundlich-type sorption. In this case, the sorption isotherm is not Lipschitz but just Hölder continuous. To deal with this, we perform a regularization step. The convergence of the scheme is analyzed. An explicit order of convergence depending only on the regularization parameter, the time step, and the mesh size is derived. We give also a sufficient condition for the quadratic convergence of the Newton method. Finally, relevant numerical results are presented. 相似文献
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Numerical challenges occur in the simulation of groundwater flow problems because of complex boundary conditions, varying material properties, presence of sources or sinks in the flow domain, or a combination of these. In this paper, we apply adaptive isogeometric finite element analysis using locally refined (LR) B‐splines to address these types of problems. The fundamentals behind isogeometric analysis and LR B‐splines are briefly presented. Galerkin's method is applied to the standard weak formulation of the governing equation to derive the linear system of equations. A posteriori error estimates are calculated to identify which B‐splines should be locally refined. The error estimates are calculated based on recovery of the L2‐projected solution. The adaptive analysis method is first illustrated by performing simulation of benchmark problems with analytical solutions. Numerical applications to two‐dimensional groundwater flow problems are then presented. The problems studied are flow around an impervious corner, flow around a cutoff wall, and flow in a heterogeneous medium. The convergence rates obtained with adaptive analysis using local refinement were, in general, observed to be of optimal order in contrast to simulations with uniform refinement. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
17.
Pedro Victor Serra Mascarenhas Ricardo Mendonça de Moraes André Luís Brasil Cavalcante 《国际地质力学数值与分析法杂志》2019,43(11):1956-1977
We propose an extension of the shifted Grünwald-Letnikov method to solve fractional partial differential equations in the Caputo sense with arbitrary fractional order derivative α and with an advective term. The method uses the relation between Caputo and Riemann-Liouville definitions, the shifted Grünwald-Letnikov, and the traditional backward and forward finite difference method. The stability of the method is investigated for the implicit and explicit scheme with homogeneous boundary conditions, and a stability criterion is found for the advective-dispersive equation. An application of the method is used to solve contaminant diffusion and advective-dispersive problems. The numerical solution for the fractional diffusion and fractional advection-dispersion is compared with their respective analytical solutions for different time and space grid refinements. The diffusion simulation exhibited a good fit between the analytical and numerical solutions, with the explicit scheme going from stable to unstable as the time and space refinement changes. The fractional advection-dispersion application produced small deviations from the analytical solution. These deviations, however, are analogous to the numerical dispersions encountered in conventional finite difference solutions of the advection-dispersion equation. The new method is also compared with the traditional L2 method. Notably, an example that involves asymmetrical fractional conditions, a fractional diffusivity that depends on time, and a source term show how the methods compare. Overall, this study assesses the quality and easiness of use of the numerical method. 相似文献
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Finite Element (FE) pseudo-static analysis can provide a good compromise between simplified methods of dynamic analysis and time domain analysis. The pseudo-static FE approach can accurately model the in situ, stresses prior to seismic loading (when it follows a static analysis simulating the construction sequence) is relatively simple and not as computationally expensive as the time domain approach. However this method should be used with caution as the results can be sensitive to the choice of the mesh dimensions. In this paper two simple examples of pseudo-static finite element analysis are examined parametrically, a homogeneous slope and a cantilever retaining wall, exploring the sensitivity of the pseudo-static analysis results on the adopted mesh size. The mesh dependence was found to be more pronounced for problems with high critical seismic coefficients values (e.g. gentle slopes or small walls), as in these cases a generalised layer failure mechanism is developed simultaneously with the slope or wall mechanism. In general the mesh width was found not to affect notably the predicted value of critical seismic coefficient but to have a major impact on the predicted movements. 相似文献
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The present paper proposes a new family of multiscale finite volume methods. These methods usually deal with a dual mesh resolution, where the pressure field is solved on a coarse mesh, while the saturation fields, which may have discontinuities, are solved on a finer reservoir grid, on which petrophysical heterogeneities are defined. Unfortunately, the efficiency of dual mesh methods is strongly related to the definition of up-gridding and down-gridding steps, allowing defining accurately pressure and saturation fields on both fine and coarse meshes and the ability of the approach to be parallelized. In the new dual mesh formulation we developed, the pressure is solved on a coarse grid using a new hybrid formulation of the parabolic problem. This type of multiscale method for pressure equation called multiscale hybrid-mixed method (MHMM) has been recently proposed for finite elements and mixed-finite element approach (Harder et al. 2013). We extend here the MH-mixed method to a finite volume discretization, in order to deal with large multiphase reservoir models. The pressure solution is obtained by solving a hybrid form of the pressure problem on the coarse mesh, for which unknowns are fluxes defined on the coarse mesh faces. Basis flux functions are defined through the resolution of a local finite volume problem, which accounts for local heterogeneity, whereas pressure continuity between cells is weakly imposed through flux basis functions, regarded as Lagrange multipliers. Such an approach is conservative both on the coarse and local scales and can be easily parallelized, which is an advantage compared to other existing finite volume multiscale approaches. It has also a high flexibility to refine the coarse discretization just by refinement of the lagrange multiplier space defined on the coarse faces without changing nor the coarse nor the fine meshes. This refinement can also be done adaptively w.r.t. a posteriori error estimators. The method is applied to single phase (well-testing) and multiphase flow in heterogeneous porous media. 相似文献
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复杂区域自适应三角形网格全自动生成方法 总被引：10，自引：4，他引：10
为了使用自适应有限单元法求解岩土工程问题，本文在行被法的基础上，提出了一种适用于多介质复杂区域的三角形网格全自动生成方法。文中给出三个工程算例． 相似文献