共查询到20条相似文献，搜索用时 31 毫秒
1.
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves the flow equation in a mixed formulation on a coarse grid by constructing multiscale basis functions. The resulting velocity field is mass-conservative on the fine grid. Our main goal is to obtain first-order convergence in terms of the mesh size which is independent of local contrast. This is achieved, first, by constructing some auxiliary spaces, which contain global information that cannot be localized, in general. This is built on our previous work on the generalized multiscale finite element method (GMsFEM). In the auxiliary space, multiscale basis functions corresponding to small (contrast-dependent) eigenvalues are selected. These basis functions represent the high-conductivity channels (which connect the boundaries of a coarse block). Next, we solve local problems to construct multiscale basis functions for the velocity field. These local problems are formulated in the oversampled domain, taking into account some constraints with respect to auxiliary spaces. The latter allows fast spatial decay of local solutions and, thus, allows taking smaller oversampled regions. The number of basis functions depends on small eigenvalues of the local spectral problems. Moreover, multiscale pressure basis functions are needed in constructing the velocity space. Our multiscale spaces have a minimal dimension, which is needed to avoid contrast dependence in the convergence. The method’s convergence requires an oversampling of several layers. We present an analysis of our approach. Our numerical results confirm that the convergence rate is first order with respect to the mesh size and independent of the contrast. 相似文献
2.
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
3.
Alexander Bihlo Colin G. Farquharson Ronald D. Haynes J Concepción Loredo-Osti 《Computational Geosciences》2017,21(1):117-129
Probabilistic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell’s equations as used in the magnetotelluric method. The domain is split into non-overlapping sub-domains and the solution on the sub-domain boundaries is obtained by evaluating the stochastic form of the exact solution of Maxwell’s equations by a Monte-Carlo approach. These sub-domains can be naturally chosen by splitting the sub-surface domain into regions of constant (or at least continuous) conductivity. The solution over each sub-domain is obtained by solving Maxwell’s equations in the strong form. The sub-domain solver used for this purpose is a meshless method resting on radial basis function-based finite differences. The method is demonstrated by solving a number of classical magnetotelluric problems, including the quarter-space problem, the block-in-half-space problem and the triangle-in-half-space problem. 相似文献
4.
Implementation of a Locally Conservative Numerical Subgrid Upscaling Scheme for Two-Phase Darcy Flow 总被引：1，自引：0，他引：1
Todd Arbogast 《Computational Geosciences》2002,6(3-4):453-481
We present a locally mass conservative scheme for the approximation of two-phase flow in a porous medium that allows us to obtain detailed fine scale solutions on relatively coarse meshes. The permeability is assumed to be resolvable on a fine numerical grid, but limits on computational power require that computations be performed on a coarse grid. We define a two-scale mixed finite element space and resulting method, and describe in detail the solution algorithm. It involves a coarse scale operator coupled to a subgrid scale operator localized in space to each coarse grid element. An influence function (numerical Greens function) technique allows us to solve these subgrid scale problems independently of the coarse grid approximation. The coarse grid problem is modified to take into account the subgrid scale solution and solved as a large linear system of equations posed over a coarse grid. Finally, the coarse scale solution is corrected on the subgrid scale, providing a fine grid representation of the solution. Numerical examples are presented, which show that near-well behavior and even extremely heterogeneous permeability barriers and streaks are upscaled well by the technique. 相似文献
5.
We review and perform comparison studies for three recent multiscale methods for solving elliptic problems in porous media
flow; the multiscale mixed finite-element method, the numerical subgrid upscaling method, and the multiscale finite-volume
method. These methods are based on a hierarchical strategy, where the global flow equations are solved on a coarsened mesh
only. However, for each method, the discrete formulation of the partial differential equations on the coarse mesh is designed
in a particular fashion to account for the impact of heterogeneous subgrid structures of the porous medium. The three multiscale
methods produce solutions that are mass conservative on the underlying fine mesh. The methods may therefore be viewed as efficient,
approximate fine-scale solvers, i.e., as an inexpensive alternative to solving the elliptic problem on the fine mesh. In addition,
the methods may be utilized as an alternative to upscaling, as they generate mass-conservative solutions on the coarse mesh.
We therefore choose to also compare the multiscale methods with a state-of-the-art upscaling method – the adaptive local–global
upscaling method, which may be viewed as a multiscale method when coupled with a mass-conservative downscaling procedure.
We investigate the properties of all four methods through a series of numerical experiments designed to reveal differences
with regard to accuracy and robustness. The numerical experiments reveal particular problems with some of the methods, and
these will be discussed in detail along with possible solutions. Next, we comment on implementational aspects and perform
a simple analysis and comparison of the computational costs associated with each of the methods. Finally, we apply the three
multiscale methods to a dynamic two-phase flow case and demonstrate that high efficiency and accurate results can be obtained
when the subgrid computations are made part of a preprocessing step and not updated, or updated infrequently, throughout the
simulation.
The research is funded by the Research Council of Norway under grant nos. 152732 and 158908. 相似文献
6.
地质雷达数值模拟中有损耗介质吸收边界条件的实现 总被引：5，自引：1，他引：4
利用时间域有限差分(FDTD)法将麦克斯韦方程进行离散化,可以对地质雷达进行数值模拟。利用完全匹配层(PML)作为吸收边界条件可以有效地吸收向外的电磁波,从而大大提高了计算效率。对于有损耗介质的情况,采用扩张坐标系下改正的麦克斯韦方程,只要扩张变量满足一定的关系,同样可有效地吸收向外的电磁波, 这种吸收边界条件称为通用完全匹配层。 相似文献
7.
Acoustic imaging and sensor modeling are processes that require repeated solution of the acoustic wave equation. Solution of the wave equation can be computationally expensive and memory intensive for large simulation domains. One scheme for speeding up solution of the wave equation is the operator-based upscaling method. The algorithm proceeds in two steps. First, the wave equation is solved for fine grid unknowns internal to coarse blocks assuming the coarse blocks do not need to communicate with neighboring blocks in parallel. Second, these fine grid solutions are used to form a new problem which is solved on the coarse grid. Accurate and efficient wave propagation schemes also must avoid artificial reflections off of the computational domain edges. One popular method for preventing artificial reflections is the nearly perfectly matched layer (NPML) method. In this paper, we discuss applying NPML to operator upscaling for the wave equation. We show that although we only apply NPML to the first step of this two step algorithm (directly affecting the fine grid unknowns only), we still see a significant reduction of reflections back into the domain. We describe three numerical experiments (one homogeneous medium experiment and two heterogeneous media examples) in which we validate that the solution of the wave equation exponentially decays in the NPML regions. Numerical experiments of acoustic wave propagation in two dimensions with a reasonable absorbing layer thickness resulted in a maximum pressure reflection of 3–8%. While the coarse grid acceleration is not explicitly damped in our algorithm, the tight coupling between the two steps of the algorithm results in only 0.1–1% of acceleration reflecting back into the computational domain. 相似文献
8.
Multiscale mixed/mimetic methods on corner-point grids 总被引：1，自引：0，他引：1
Multiscale simulation is a promising approach to facilitate direct simulation of large and complex grid models for highly
heterogeneous petroleum reservoirs. Unlike traditional simulation, approaches based on upscaling/downscaling, multiscale methods
seek to solve the full flow problem by incorporating subscale heterogeneities into local discrete approximation spaces. We
consider a multiscale formulation based on a hierarchical grid approach, where basis functions with subgrid resolution are
computed numerically to correctly and accurately account for subscale variations from an underlying (fine-scale) geomodel
when solving the global flow equations on a coarse grid. By using multiscale basis functions to discretise the global flow
equations on a (moderately sized) coarse grid, one can retain the efficiency of an upscaling method and, at the same time,
produce detailed and conservative velocity fields on the underlying fine grid. For pressure equations, the multiscale mixed
finite-element method (MsMFEM) has been shown to be a particularly versatile approach. In this paper, we extend the method
to corner-point grids, which is the industry standard for modelling complex reservoir geology. To implement MsMFEM, one needs
a discretisation method for solving local flow problems on the underlying fine grids. In principle, any stable and conservative
method can be used. Here, we use a mimetic discretisation, which is a generalisation of mixed finite elements that gives a
discrete inner product, allows for polyhedral elements, and can (easily) be extended to curved grid faces. The coarse grid
can, in principle, be any partition of the subgrid, where each coarse block is a connected collection of subgrid cells. However,
we argue that, when generating coarse grids, one should follow certain simple guidelines to achieve improved accuracy. We
discuss partitioning in both index space and physical space and suggest simple processing techniques. The versatility and
accuracy of the new multiscale mixed methodology is demonstrated on two corner-point models: a small Y-shaped sector model
and a complex model of a layered sedimentary bed. A variety of coarse grids, both violating and obeying the above mentioned
guidelines, are employed. The MsMFEM solutions are compared with a reference solution obtained by direct simulation on the
subgrid. 相似文献
9.
A new numerical method to solve the system of equations describing two phase flow in a Hele-Shaw cell is presented. It combines
a mixed finite element method, the method of subtraction of the singularity and a front tracking grid in a single computational
strategy. This choice of discretization techniques is well motivated by the difficulties present in the system of equations
and the physics of the problem. The new method was tested against analytical solutions and also by solving the Saffman–Taylor
viscous fingering problem for finite and infinite mobility ratios. In both cases convergence under mesh refinement is achieved
for the fingers developed from an initial sinusoidal interface. Finger splitting is observed for low values of the surface
tension and high mobility ratio. Different explanations, based in our results, are provided for this phenomenon.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
The problem of multiphase phase flow in heterogeneous subsurface porous media is one involving many uncertainties. In particular, the permeability of the medium is an important aspect of the model that is inherently uncertain. Properly quantifying these uncertainties is essential in order to make reliable probabilistic-based predictions and future decisions. In this work, a measure-theoretic framework is employed to quantify uncertainties in a two-phase subsurface flow model in high-contrast media. Given uncertain saturation data from observation wells, the stochastic inverse problem is solved numerically in order to obtain a probability measure on the space of unknown permeability parameters characterizing the two-phase flow. As solving the stochastic inverse problem requires a number of forward model solves, we also incorporate the use of a conservative version of the generalized multiscale finite element method for added efficiency. The parameter-space probability measure is used in order to make predictions of saturation values where measurements are not available, and to validate the effectiveness of the proposed approach in the context of fine and coarse model solves. A number of numerical examples are offered to illustrate the measure-theoretic methodology for solving the stochastic inverse problem using both fine and coarse solution schemes. 相似文献
11.
多尺度有限单元法求解非均质多孔介质中的三维地下水流问题 总被引：7，自引：0，他引：7
应用多尺度有限单元法模拟非均质多孔介质中的三维地下水流问题。与传统有限单元法相比，多尺度有限单元法的基函数具有能反映单元内参数变化的优点，所以这种方法能在大尺度上抓住解的小尺度特征获得较精确的解。在介绍多尺度有限单元法求解非均质多孔介质中三维地下水流问题的基本原理之后，对参数水平方向渐变垂直方向突变的非均质多孔介质中的三维地下水流和Borden实验场的三维地下水流分别用多尺度有限单元法和传统等参有限单元法进行了计算，结果表明在模拟高度非均质多孔介质中的三维地下水流问题时，多尺度有限单元法比传统有限单元法有效，既节省计算量又有较高的精度；在模拟非均质性弱的多孔介质中的三维地下水流问题时，多尺度有限单元法虽然也能在大尺度上获得较为精确的解，但效果不明显。 相似文献
12.
This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM‐XFEM is its ability to model discontinuities in the domain independently of the computational mesh. The proposed FM approach is a continuum‐based approach that is used to model the flow interaction between the porous matrix and existing fractures via a transfer function. Fracture geometry is defined using the level set method. Therefore, in contrast to the discrete fracture flow model, the fracture representation is not meshed along with the computational domain. Consequently, the method is able to determine the influence of fractures on fluid flow within a fractured domain without the complexity of meshing the fractures within the domain. The XFEM component of the scheme addresses the discontinuous displacement field within elements that are intersected by existing fractures. In XFEM, enrichment functions are added to the standard finite element approximation to adequately resolve discontinuous fields within the simulation domain. Numerical tests illustrate the ability of the method to adequately describe the displacement and fluid pressure fields within a fractured domain at significantly less computational expense than explicitly resolving the fracture within the finite element mesh. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
13.
An efficient finite–discrete element method applicable for the analysis of quasi‐static nonlinear soil–structure interaction problems involving large deformations in three‐dimensional space was presented in this paper. The present method differs from previous approaches in that the use of very fine mesh and small time steps was not needed to stabilize the calculation. The domain involving the large displacement was modeled using discrete elements, whereas the rest of the domain was modeled using finite elements. Forces acting on the discrete and finite elements were related by introducing interface elements at the boundary of the two domains. To improve the stability of the developed method, we used explicit time integration with different damping schemes applied to each domain to relax the system and to reach stability condition. With appropriate damping schemes, a relatively coarse finite element mesh can be used, resulting in significant savings in the computation time. The proposed algorithm was validated using three different benchmark problems, and the numerical results were compared with existing analytical and numerical solutions. The algorithm performance in solving practical soil–structure interaction problems was also investigated by simulating a large‐scale soft ground tunneling problem involving soil loss near an existing lining. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
14.
15.
Diffusion coefficients of dense gases in liquids can be measured by considering two-phase binary nonequilibrium fluid mixing in a closed cell with a fixed volume. This process is based on convection and diffusion in each phase. Numerical simulation of the mixing often requires accurate algorithms. In this paper, we design two efficient numerical methods for simulating the mixing of two-phase binary fluids in one-dimensional, highly permeable media. Mathematical model for isothermal compositional two-phase flow in porous media is established based on Darcy’s law, material balance, local thermodynamic equilibrium for the phases, and diffusion across the phases. The time-lag and operator-splitting techniques are used to decompose each convection–diffusion equation into two steps: diffusion step and convection step. The Mixed finite element (MFE) method is used for diffusion equation because it can achieve a high-order and stable approximation of both the scalar variable and the diffusive fluxes across grid–cell interfaces. We employ the characteristic finite element method with moving mesh to track the liquid–gas interface. Based on the above schemes, we propose two methods: single-domain and two-domain methods. The main difference between two methods is that the two-domain method utilizes the assumption of sharp interface between two fluid phases, while the single-domain method allows fractional saturation level. Two-domain method treats the gas domain and the liquid domain separately. Because liquid–gas interface moves with time, the two-domain method needs work with a moving mesh. On the other hand, the single-domain method allows the use of a fixed mesh. We derive the formulas to compute the diffusive flux for MFE in both methods. The single-domain method is extended to multiple dimensions. Numerical results indicate that both methods can accurately describe the evolution of the pressure and liquid level. 相似文献
16.
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17.
A multiscale method for the dynamic analysis of underground structures is proposed, which involves the concurrent discretization of the entire domain with both coarse‐scale and fine‐scale finite element meshes. The coarse‐scale mesh is employed to capture seismic response characteristics of the integral system, whereas the fine‐scale mesh describes in detail the dynamic response in positions of potential damage or interest. For both the coarse‐scale and fine‐scale meshes to overlap, a bridging scale term is introduced so that compatibility of dynamic behavior between the coarse‐ and fine‐scale models is enforced. Both material and contact nonlinearities are considered in the multiscale model. As an application, the model is used for large‐scale seismic response of a newly built long‐distance shield tunnel. Results show that this multiscale method does not have spurious wave reflections at the fine/coarse interface and does not need filtering procedures, which is an advantage compared with the displacement coupling method. Stress and deformation response in lining segments and their connecting bolts are investigated and analyzed within the fine‐scale model, and the capacity of critical structural components, such as bolts and joints is evaluated. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
18.
We present a variational multiscale mixed finite element method for the solution of Darcy flow in porous media, in which both
the permeability field and the source term display a multiscale character. The formulation is based on a multiscale split
of the solution into coarse and subgrid scales. This decomposition is invoked in a variational setting that leads to a rigorous
definition of a (global) coarse problem and a set of (local) subgrid problems. One of the key issues for the success of the
method is the proper definition of the boundary conditions for the localization of the subgrid problems. We identify a weak
compatibility condition that allows for subgrid communication across element interfaces, a feature that turns out to be essential
for obtaining high-quality solutions. We also remove the singularities due to concentrated sources from the coarse-scale problem
by introducing additional multiscale basis functions, based on a decomposition of fine-scale source terms into coarse and
deviatoric components. The method is locally conservative and employs a low-order approximation of pressure and velocity at
both scales. We illustrate the performance of the method on several synthetic cases and conclude that the method is able to
capture the global and local flow patterns accurately. 相似文献
19.
A local artificial boundary for transient seepage problems with unsteady boundary conditions in unbounded domains 
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下载免费PDF全文 Numerical analysis of transient seepage in unbounded domains with unsteady boundary conditions requires a more sophisticated artificial boundary approach to deal with the infinite character of the domain. To that end, a local artificial boundary is established by simplifying a global artificial boundary. The global artificial boundary conditions (ABCs) at the truncated boundary are derived from analytical solutions for one‐dimensional axisymmetric diffusion problems. By applying Laplace transforms and introducing some specially defined auxiliary variables, the global ABCs are simplified to local ABCs to significantly enhance the computational efficiency. The proposed local ABCs are implemented in a finite element computer program so that the solutions to various seepage problems can be calculated. The proposed approach is first verified by the computation of a one‐dimensional radial flow problem and then tentatively applied to more general two‐dimensional cylindrical problems and planar problems. The solutions obtained using the local ABCs are compared with those obtained using a large element mesh and using a previously proposed local boundary. This comparison demonstrates the satisfactory performance and obvious superiority of the newly established boundary to the other local boundary. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
20.
依据模拟钻井船在不同场地条件下贯入阻力的离心模型试验结果及具体工程实例,对利用耦合欧拉-拉格朗日（CEL）有限元方法模拟钻井船在黏土、砂土、黏土下覆砂土、砂土下覆黏土及成层土场地插桩过程时,影响贯入阻力计算结果的几个因素进行了研究。结果表明,对于不同土层场地条件,有限元模型中欧拉区域范围对贯入阻力几乎没有影响。为确保CEL数值结果的精度,有限元建模时靠近桩靴部分设置为细网格区域,以外区域设置为粗网格区域;对于不同土层场地条件,减小细网格尺寸及增大细网格范围可以减小贯入阻力的振荡情况;经比较总结,细网格尺寸建议取0.05倍桩靴直径,细网格范围建议取2倍桩靴直径。采用位移控制模拟钻井船插桩时,桩靴贯入速率对黏土场地的贯入阻力影响较小,对砂土下覆黏土场地的贯入阻力影响很大,对一般成层土场地的贯入阻力有一定影响。经比较总结,建议在研究钻井船在不同土层场地的计算贯入阻力时,有限元模型的桩靴贯入速率取0.2 m/s。 相似文献