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1.
Joachim Berdal Haga Harald Osnes Hans Petter Langtangen 《Computational Geosciences》2012,16(3):723-734
Large-scale simulations of coupled flow in deformable porous media require iterative methods for solving the systems of linear
algebraic equations. Construction of efficient iterative methods is particularly challenging in problems with large jumps
in material properties, which is often the case in realistic geological applications, such as basin evolution at regional
scales. The success of iterative methods for such problems depends strongly on finding effective preconditioners with good
parallel scaling properties, which is the topic of the present paper. We present a parallel preconditioner for Biot’s equations
of coupled elasticity and fluid flow in porous media. The preconditioner is based on an approximation of the exact inverse
of the two-by-two block system arising from a finite element discretisation. The approximation relies on a highly scalable
approximation of the global Schur complement of the coefficient matrix, combined with generally available state-of-the-art
multilevel preconditioners for the individual blocks. This preconditioner is shown to be robust on problems with highly heterogeneous
material parameters. We investigate the weak and strong parallel scaling of this preconditioner on up to 512 processors and
demonstrate its ability on a realistic basin-scale problem in poroelasticity with over eight million tetrahedral elements. 相似文献
2.
The focus of this work is efficient solution methods for mixed finite element models of variably saturated fluid flow through
deformable porous media. In particular, we examine preconditioning techniques to accelerate the convergence of implicit Newton–Krylov
solvers. We highlight an approach in which preconditioners are built from block-factorizations of the coupled system. The
key result of the work is the identification of effective preconditioners for the various sub-problems that appear within
the block decomposition. We use numerical examples drawn from both linear and nonlinear hydromechanical models to test the
robustness and scalability of the proposed methods. Results demonstrate that an algebraic multigrid variant of the block preconditioner
leads to mesh-independent convergence, good parallel efficiency, and insensitivity to the material parameters of the medium. 相似文献
3.
Soil–structure interaction problems are commonly encountered in geotechnical practice and remarkably characterized with significant material stiffness contrast. When solving the soil–structure interaction problems, the employed Krylov subspace iterative method may converge slowly or even fail, indicating that the adopted preconditioning method may not suit for such problems. The inexact block diagonal preconditioners proposed recently have been shown effective for the soil–structure interaction problems; however, they haven't been exploited to full capabilities. By using the same partition strategy according to the structure elements and soil elements, the partitioned block symmetric successive over‐relaxation preconditioners or partitioned block constraint preconditioners are proposed. Based on two pile‐group foundation problems and a tunnel problem, the proposed preconditioners are evaluated and compared with the available preconditioners for the consolidation analysis and the drained analysis, respectively. In spite of one additional solve associated with the structure block and multiplications with off‐diagonal blocks in the preconditioning step, numerical results reveal that the proposed preconditioners obviously possess better performance than the recently developed inexact block preconditioners. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
4.
In this paper we present a study of the performance of sparse iterative solvers regarding the resolution of three-dimensional and non-linear problems encountered in soil/structure interaction. It is composed of two parts. In the first one, we present briefly iterative methods and preconditioners used in this study, then we analyse their performance on three soil/structure interaction problems: a shallow foundation under a vertical loading, a single pile subjected to a lateral loading and the construction of a lined tunnel in a soft soil. Tests are performed assuming an elastic–perfectly plastic constitutive law for the soil material with a non-associated Mohr–Coulomb flow rule. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
5.
Soil–structure interaction problems are commonly encountered in engineering practice, and the resulting linear systems of equations are difficult to solve due to the significant material stiffness contrast. In this study, a novel partitioned block preconditioner in conjunction with the Krylov subspace iterative method symmetric quasiminimal residual is proposed to solve such linear equations. The performance of these investigated preconditioners is evaluated and compared on both the CPU architecture and the hybrid CPU–graphics processing units (GPU) computing environment. On the hybrid CPU–GPU computing platform, the capability of GPU in parallel implementation and high-intensity floating point operations is exploited to accelerate the iterative solutions, and particular attention is paid to the matrix–vector multiplications involved in the iterative process. Based on a pile-group foundation example and a tunneling example, numerical results show that the partitioned block preconditioners investigated are very efficient for the soil–structure interaction problems. However, their comparative performances may apparently depend on the computer architecture. When the CPU computer architecture is used, the novel partitioned block symmetric successive over-relaxation preconditioner appears to be the most efficient, but when the hybrid CPU–GPU computer architecture is adopted, it is shown that the inexact block diagonal preconditioners embedded with simple diagonal approximation to the soil block outperform the others. 相似文献
6.
Multiscale methods can in many cases be viewed as special types of domain decomposition preconditioners. The localisation
approximations introduced within the multiscale framework are dependent upon both the heterogeneity of the reservoir and the
structure of the computational grid. While previous works on multiscale control volume methods have focused on heterogeneous
elliptic problems on regular Cartesian grids, we have tested the multiscale control volume formulations on two-dimensional
elliptic problems involving heterogeneous media and irregular grid structures. Our study shows that the tangential flow approximation
commonly used within multiscale methods is not suited for problems involving rough grids. We present a more robust mass conservative
domain decomposition preconditioner for simulating flow in heterogeneous porous media on general grids. 相似文献
7.
Parallel computers are potentially very attractive for the implementation of large size geomechanical models. One of the main difficulties of parallelization, however, relies on the efficient solution of the frequently ill‐conditioned algebraic system arising from the linearization of the discretized equilibrium equations. While very efficient preconditioners have been developed for sequential computers, not much work has been devoted to parallel solution algorithms in geomechanics. The present study investigates the state‐of‐the‐art performance of the factorized sparse approximate inverse (FSAI) as a preconditioner for the iterative solution of ill‐conditioned geomechanical problems. Pre‐and post‐filtration strategies are experimented with to increase the FSAI efficiency. Numerical results show that FSAI exhibits a promising potential for parallel geomechanical models mainly because of its almost ideal scalability. With the present formulation, however, at least 4 or 8 processors are required in the selected test cases to outperform one of the most efficient sequential algorithms available for FE geomechanics, i.e. the multilevel incomplete factorization (MIF). Further research is needed to improve the FSAI efficiency with a more effective selection of the preconditioner non‐zero pattern. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
8.
Grid adaptive methods combined with domain adaptation are discussed for two-dimensional seepage flow problems with free boundaries through porous media. Examples of grid and domain adaptive methods are presented to demonstrate several ways to predict grids and shapes of free boundaries using an iterative scheme. Finally, the combined adaptive methods are applied to obtain smooth non-oscillatory shape of a free boundary of seepage flow through non-homogeneous porous media. 相似文献
9.
The finite element (FE) simulation of large‐scale soil–structure interaction problems (e.g. piled‐raft, tunnelling, and excavation) typically involves structural and geomaterials with significant differences in stiffness and permeability. The symmetric quasi‐minimal residual solver coupled with recently developed generalized Jacobi, modified symmetric successive over‐relaxation (MSSOR), or standard incomplete LU factorization (ILU) preconditioners can be ineffective for this class of problems. Inexact block diagonal preconditioners that are inexpensive approximations of the theoretical form are systematically evaluated for mitigating the coupled adverse effects because of such heterogeneous material properties (stiffness and permeability) and because of the percentage of the structural component in the system in piled‐raft foundations. Such mitigation led the proposed preconditioners to offer a significant saving in runtime (up to more than 10 times faster) in comparison with generalized Jacobi, modified symmetric successive over‐relaxation, and ILU preconditioners in simulating piled‐raft foundations. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
10.
Constraint preconditioners have proved very efficient for the solution of ill-conditioned finite element (FE) coupled consolidation
problems in a sequential computing environment. Their implementation on parallel computers, however, is not straightforward
because of their inherent sequentiality. The present paper describes a novel parallel inexact constraint preconditioner (ParICP)
for the efficient solution of linear algebraic systems arising from the FE discretization of the coupled poro-elasticity equations.
The ParICP implementation is based on the use of the block factorized sparse approximate inverse incomplete Cholesky preconditioner,
which is a very recent and effective development for the parallel preconditioning of symmetric positive definite matrices.
The ParICP performance is experimented with in real 3D coupled consolidation problems, proving a scalable and efficient implementation
of the constraint preconditioning for high-performance computing. ParICP appears to be a very robust algorithm for solving
ill-conditioned large-size coupled models in a parallel computing environment. 相似文献
11.
A fully coupled element‐free Galerkin model for hydro‐mechanical analysis of advancement of fluid‐driven fractures in porous media 
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下载免费PDF全文 Hydraulic fracturing (HF) of underground formations has widely been used in different fields of engineering. Despite the technological advances in techniques of in situ HF, the industry uses semi‐analytical tools to design HF treatment. This is due to the complex interaction among various mechanisms involved in this process, so that for thorough simulations of HF operations a fully coupled numerical model is required. In this study, using element‐free Galerkin (EFG) mesh‐less method, a new formulation for numerical modeling of hydraulic fracture propagation in porous media is developed. This numerical approach, which is based on the simultaneous solution of equilibrium and continuity equations, considers the hydro‐mechanical coupling between the crack and its surrounding porous medium. Therefore, the developed EFG model is capable of simulating fluid leak‐off and fluid lag phenomena. To create the discrete equation system, the Galerkin technique is applied, and the essential boundary conditions are imposed via penalty method. Then, the resultant constrained integral equations are discretized in space using EFG shape functions. For temporal discretization, a fully implicit scheme is employed. The final set of algebraic equations that forms a non‐linear equation system is solved using the direct iterative procedure. Modeling of cracks is performed on the basis of linear elastic fracture mechanics, and for this purpose, the so‐called diffraction method is employed. For verification of the model, a number of problems are solved. According to the obtained results, the developed EFG computer program can successfully be applied for simulating the complex process of hydraulic fracture propagation in porous media. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
12.
Iteratively coupled solution strategies for a four‐field mixed finite element method for poroelasticity 下载免费PDF全文
下载免费PDF全文 In this paper, we consider numerical algorithms for modeling of the time‐dependent coupling between the fluid flow and deformation in elastic porous media. Here, we employ a four‐field formulation which uses the total stress, displacement, flux, and pressure as its primary variables and satisfies Darcy's law and linear elasticity in mixed weak form. We present four different iteratively coupled methods, known as drained, undrained, fixed‐strain, and fixed‐stress splits, in which the diffusion operator is separated from the elasticity operator and the two subproblems are solved in a staggered way while ensuring convergence of the solution at each time step. A‐priori convergence results for each iterative coupling which differs from those found when using a traditional two‐field or three‐field formulation are presented. We also present some numerical results to support the convergence estimates and to show the accuracy and efficiency of the algorithms. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
13.
The problem of finite element simulation of incompressible fluid flow in porous medium is considered. The porous medium is characterized by the X‐ray microtomography technique in three dimensions. The finite calculus‐based stabilization technique is reviewed to implement the equal order finite element interpolation functions for both velocity and pressure. A noble preconditioner, the nodal block diagonal preconditioner, is considered whose performance is thoroughly investigated. Combining this preconditioner with a standard iterative solver during the computational homogenization procedure, it is possible to carry out the large‐scale fluid flow simulation for estimating permeability of the porous medium with reasonable accuracy and reliability. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
14.
In this paper, a three‐dimensional smooth particle hydrodynamics (SPH) simulator for modeling grain scale fluid flow in porous media is presented. The versatility of the SPH method has driven its use in increasingly complex areas of flow analysis, including the characterization of flow through permeable rock for both groundwater and petroleum reservoir research. SPH provides the means to model complex multi‐phase flows through such media; however, acceptance of the methodology has been hampered by the apparent lack of actual verification within the literature, particulary in the three‐dimensional case. In this paper, the accuracy of SPH is addressed via a comparison to the previously recognized benchmarks of authors such as Sangani and Acrivos (Int. J. Multiphase Flow 1982; 8 (4): 343–360), Zick and Homsy (J. Fluid Mech. 1982; 115 :13–26) and Larson and Higdon (Phys. Fluids A 1989; 1 (1):38–46) for the well‐defined classical problems of flow through idealized two‐ and three‐dimensional porous media. The accuracy of results for such low Reynolds number flows is highly dependent on the implementation of no‐slip boundary conditions. A new, robust and numerically efficient, method for implementing such boundaries in SPH is presented. Simulation results for friction coefficient and permeability are shown to agree well with the available benchmarks. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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16.
In this paper, we present a numerical model for simulating two-phase (oil–water and air–water) incompressible and immiscible flow in porous media. The mathematical model which is based on a fractional flow formulation is formed of two nonlinear partial differential equations: a mean pressure equation and a water saturation equation. These two equations can be solved in a sequential manner. Two numerical methods are used to discretize the equations of the two-phase flow model: mixed hybrid finite elements are used to treat the pressure equation, h-based Richards' equation and the diffusion term in the saturation equation, the advection term in the saturation equation is treated with the discontinuous finite elements. We propose a better way to calculate the nonlinear coefficients contained in our equations on each element of the discretized domain. In heterogeneous porous media, the saturation becomes discontinuous at the interface between two porous media. We show in this paper how to use the capillary pressure–saturation relationship in order to handle the saturation jump in the mixed hybrid finite element method. The two-phase flow simulator is verified against analytical solutions for some flow problems treated by other authors. 相似文献
17.
Conventional modelling of transport problems for porous media usually assumes that the Darcy flow velocities are steady. In certain practical situations, the flow velocity can exhibit time‐dependency, either due to the transient character of the flow process or time dependency in the boundary conditions associated with potential flow. In this paper, we consider certain one‐ and three‐dimensional problems of the advective transport of a chemical species in a fluid‐saturated porous region. In particular, the advective flow velocity is governed by the piezo‐conduction equation that takes into account the compressibilities of the pore fluid and the porous skeleton. Time‐ and/or mesh‐refining adaptive schemes used in the computational modelling are developed on the basis of a Fourier analysis, which can lead to accurate and optimal solutions for the advective transport problem with time‐ and space‐dependent advective flow velocity distributions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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19.
George Zyvoloski 《国际地质力学数值与分析法杂志》1983,7(1):75-86
Two finite element algorithms suitable for long term simulation of geothermal reservoirs are presented. Both methods use a diagonal mass matrix and a Newton iteration scheme. The first scheme solves the 2N unsymmetric algebraic equations resulting from the finite element discretization of the equations governing the flow of heat and mass in porous media by using a banded equation solver. The second method, suitable for problems in which the transmissibility terms are small compared to the accumulation terms, reduces the set of N equations for the Newton corrections to a symmetric system. Comparison with finite difference schemes indicates that the proposed algorithms are competitive with existing methods. 相似文献
20.
A finite element method for modeling coupled flow and deformation in porous fractured media 下载免费PDF全文
下载免费PDF全文 Ahmad Pouya 《国际地质力学数值与分析法杂志》2015,39(16):1836-1852
Modeling the flow in highly fractured porous media by finite element method (FEM) has met two difficulties: mesh generation for fractured domains and a rigorous formulation of the flow problem accounting for fracture/matrix, fracture/fracture, and fracture/boundary fluid mass exchanges. Based on the recent theoretical progress for mass balance conditions in multifractured porous bodies, the governing equations for coupled flow and deformation in these bodies are first established in this paper. A weak formulation for this problem is then established allowing to build a FEM. Taking benefit from recent development of mesh‐generating tools for fractured media, this weak formulation has been implemented in a numerical code and applied to some typical problems of hydromechanical coupling in fractured porous media. It is shown that in this way, the FEM that has proved its efficiency to model hydromechanical phenomena in porous media is extended with all its performances (calculation time, couplings, and nonlinearities) to fractured porous media. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献