共查询到20条相似文献，搜索用时 31 毫秒
1.
We explore the ability of the greedy algorithm to serve as an effective tool for the construction of reduced-order models for the solution of fully saturated groundwater flow in the presence of randomly distributed transmissivities. The use of a reduced model is particularly appealing in the context of numerical Monte Carlo (MC) simulations that are typically performed, e.g., within environmental risk assessment protocols. In this context, model order reduction techniques enable one to construct a surrogate model to reduce the computational burden associated with the solution of the partial differential equation governing the evolution of the system. These techniques approximate the model solution with a linear combination of spatially distributed basis functions calculated from a small set of full model simulations. The number and the spatial behavior of these basis functions determine the computational efficiency of the reduced model and the accuracy of the approximated solution. The greedy algorithm provides a deterministic procedure to select the basis functions and build the reduced-order model. Starting from a single basis function, the algorithm enriches the set of basis functions until the largest error between the full and the reduced model solutions is lower than a predefined tolerance. The comparison between the standard MC and the reduced-order approach is performed through a two-dimensional steady-state groundwater flow scenario in the presence of a uniform (in the mean) hydraulic head gradient. The natural logarithm of the aquifer transmissivity is modeled as a second-order stationary Gaussian random field. The accuracy of the reduced basis model is assessed as a function of the correlation scale and variance of the log-transmissivity. We explore the performance of the reduced model in terms of the number of iterations of the greedy algorithm and selected metrics quantifying the discrepancy between the sample distributions of hydraulic heads computed with the full and the reduced model. Our results show that the reduced model is accurate and is highly efficient in the presence of a small variance and/or a large correlation length of the log-transmissivity field. The flow scenarios associated with large variances and small correlation lengths require an increased number of basis functions to accurately describe the collection of the MC solutions, thus reducing significantly the computational advantages associated with the reduced model. 相似文献
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3.
F. O. Alpak F. Gray N. Saxena J. Dietderich R. Hofmann S. Berg 《Computational Geosciences》2018,22(3):815-832
Digital rock physics (DRP) is a rapidly evolving technology targeting fast turnaround times for repeatable core analysis and multi-physics simulation of rock properties. We develop and validate a rapid and scalable distributed-parallel single-phase pore-scale flow simulator for permeability estimation on real 3D pore-scale micro-CT images using a novel variant of the lattice Boltzmann method (LBM). The LBM code implementation is designed to take maximum advantage of distributed computing on multiple general-purpose graphics processing units (GPGPUs). We describe and extensively test the distributed parallel implementation of an innovative LBM algorithm for simulating flow in pore-scale media based on the multiple-relaxation-time (MRT) model that utilizes a precise treatment of body force. While the individual components of the resulting simulator can be separately found in various references, our novel contributions are (1) the integration of all of the mathematical and high-performance computing components together with a highly optimized code implementation and (2) the delivery of quantitative results with the simulator in terms of robustness, accuracy, and computational efficiency for a variety of flow geometries including various types of real rock images. We report on extensive validations of the simulator in terms of accuracy and provide near-ideal distributed parallel scalability results on large pore-scale image volumes that were largely computationally inaccessible prior to our implementation. We validate the accuracy of the MRT-LBM simulator on model geometries with analytical solutions. Permeability estimation results are then provided on large 3D binary microstructures including a sphere pack and rocks from various sandstone and carbonate formations. We quantify the scalability behavior of the distributed parallel implementation of MRT-LBM as a function of model type/size and the number of utilized GPGPUs for a panoply of permeability estimation problems. 相似文献
4.
Problems in hydrology frequently have moving fronts and dynamic driving mechanisms such as wells. Since the location of important
features changes during a simulation, accurate modeling requires uniformly fine resolution or the ability to change resolution
during the simulation. We will describe an algorithm for refinement and unrefinement of tetrahedral/triangular meshes that
has been implemented in the adaptive hydrology (ADH) code. The codes including the refinement/unrefinement algorithms are
implemented in parallel to accommodate problems with large run time and memory requirements. In this paper, we describe the
parallel, adaptive grid algorithm used in ADH and show the resulting grids from some example problems. 相似文献
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6.
Hugo A. Loáiciga 《Mathematical Geosciences》2008,40(2):199-211
The equation of groundwater flow in marine island aquifers in which there is time-independent, spatially-variable recharge
and pumping is solved in closed form for rectangular, circular, and elliptical island geometries. The solution of the groundwater
flow equation is expressed in terms of the elevation of the phreatic surface within the flow domain. The depth of the seawater-freshwater
interface below mean sea level follows from the Dupuit–Ghyben–Herzberg relation. The method of solution presented in this
work relies on expanding the hydraulic head and forcing function (recharge and groundwater extraction) as Fourier series that
transforms the two-dimensional Poisson-type flow equations into second-order ordinary differential equations solvable using
classical theory. The important case of constant recharge (without groundwater extraction) leads to solutions in which the
hydraulic head is expressible as the product of a flow factor equal to the squared root of the ratio of recharge over hydraulic
conductivity times a geometric factor involving island shape parameters and flow boundary conditions. Estimability conditions
for the hydraulic conductivity are derived for the cases of constant recharge and spatially variable recharge with pumping. 相似文献
7.
沙丘背风侧气流及其沉积类型与意义 总被引：6，自引：2，他引：6
在腾格里沙漠东南缘对现代沙丘表面气流、沉积过程的野外观测结果表明,由于区域气流、沙丘形态及其相互作用等的不同使沙丘背风坡气流发生变化,在此发现三种背风坡次生气流 :分离流、附体未偏向流和附体偏向流。前者以弱的反向流为特征多发生在横向气流条件下坡度较陡的背风坡;后二者具有相对高的风速,其中附体流多发生在坡度缓和的背风坡,其方向在横向气流条件下保持原来的方向,而在斜向气流作用下发生偏转且其强度为原始风入射角的余弦函数。根据背风坡气流方向及强度,作者阐述了不同区域气流环境中沙丘背风坡沉积过程、层理类型及特征,探讨了交错层产状与区域气流方向之间的关系. 相似文献
8.
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
9.
AbstractCompaction driven fluid flow is inherently unstable such that an obstruction to upward fluid flow (i.e. a shock) may induce fluid-filled waves of porosity, propagated by dilational deformation due to an effective pressure gradient within the wave. Viscous porosity waves have attracted attention as a mechanism for melt transport, but are also a mechanism for both the transport and trapping of fluids released by diagenetic and metamorphic reactions. We introduce a mathematical formulation applicable to compaction driven flow for the entire range of rheological behaviors realized in the lithosphere. We then examine three first-order factors that influence the character of fluid flow: (1) thermally activated creep, (2) dependence of bulk viscosity on porosity, and (3) fluid flow in the limit of zero initial connected porosity. For normal geothermal gradients, thermally activated creep stabilizes horizontal waves, a geometry that was thought to be unstable on the basis of constant viscosity models. Implications of this stabilization are that: (1) the vertical length scale for compaction driven flow is generally constrained by the activation energy for viscous deformation rather than the viscous compaction length, and (2) lateral fluid flow in viscous regimes may occur on greater length scales than anticipated from earlier estimates of compaction length scales. In viscous rock, inverted geothermal gradients stabilize vertically elongated waves or vertical channels. Decreasing temperature toward the earth’s surface can induce an abrupt transition from viscous to elastic deformation-propagated fluid flow. Below the transition, fluid flow is accomplished by short wavelength, large amplitude waves; above the transition flow is by high velocity, low amplitude surges. The resulting transient flow patterns vary strongly in space and time. Solitary porosity waves may nucleate in viscous, viscoplastic, and viscoelastic rheologies. The amplitude of these waves is effectively unlimited for physically realistic models with dependence of bulk viscosity on porosity. In the limit of zero initial connected porosity, arguably the only model relevant for melt extraction, travelling waves are only possible in a viscoelastic matrix. Such waves are truly self-propagating in that the fluid and the wave phase velocities are identical; thus, if no chemical processes occur during propagation, the waves have the capacity to transmit geochemical signatures indefinitely. In addition to solitary waves, we find that periodic solutions to the compaction equations are common though previously unrecognized. The transition between the solutions depends on the pore volume carried by the wave and the Darcyian velocity of the background fluid flux. Periodic solutions are possible for all velocities, whereas solitary solutions require large volumes and low velocities. © Elsevier, Paris 相似文献
10.
《地学前缘(英文版)》2016,7(1)
In this study, Imperialistic Competitive Algorithm(ICA) is utilized for locating the critical failure surface and computing the factor of safety(FOS) in a slope stability analysis based on the limit equilibrium approach. The factor of safety relating to each trial slip surface is calculated using a simplified algorithm of the Morgenstern-Price method, which satisfies both the force and the moment equilibriums. General slip surface is considered non-circular in this study that is constituted by linking random straight lines.To explore the performance of the proposed algorithm, four benchmark test problems are analyzed. The results demonstrate that the present techniques can provide reliable, accurate and efficient solutions for locating the critical failure surface and relating FOS. Moreover, in contrast with previous studies the present algorithm could reach the lower value of FOS and reached more exact solutions. 相似文献
11.
Franti
ek Hrouda 《Tectonophysics》2002,347(4)
The anisotropy of magnetic susceptibility (AMS) is often controlled by both ferromagnetic (sensu lato) and paramagnetic minerals. The anisotropy of magnetic remanence (AMR) is solely controlled by ferromagnetic minerals. Jelínek (Trav. Geophys. 37 (1993)) introduced a tensor derived from the isothermal AMR whose normalized form equals the normalized susceptibility tensor provided that the ferromagnetic fraction is represented by multi-domain magnetite. The present paper shows the close correlation between these tensors for a collection of strongly magnetic specimens containing multi-domain magnetite. In addition, acceptable correlation between the tensors was also found for a collection of specimens containing single-domain magnetite. A new method is developed for the AMS resolution into ferromagnetic and paramagnetic components using the AMR. Some examples are presented of this resolution in mafic microgranular enclaves in granodiorite and in gneisses of the KTB borehole. 相似文献
12.
In geophysical applications, the interest in least-squares migration (LSM) as an imaging algorithm is increasing due to the demand for more accurate solutions and the development of high-performance computing. The computational engine of LSM in this work is the numerical solution of the 3D Helmholtz equation in the frequency domain. The Helmholtz solver is Bi-CGSTAB preconditioned with the shifted Laplace matrix-dependent multigrid method. In this paper, an efficient LSM algorithm is presented using several enhancements. First of all, a frequency decimation approach is introduced that makes use of redundant information present in the data. It leads to a speedup of LSM, whereas the impact on accuracy is kept minimal. Secondly, a new matrix storage format Very Compressed Row Storage (VCRS) is presented. It not only reduces the size of the stored matrix by a certain factor but also increases the efficiency of the matrix-vector computations. The effects of lossless and lossy compression with a proper choice of the compression parameters are positive. Thirdly, we accelerate the LSM engine by graphics cards (GPUs). A GPU is used as an accelerator, where the data is partially transferred to a GPU to execute a set of operations or as a replacement, where the complete data is stored in the GPU memory. We demonstrate that using the GPU as a replacement leads to higher speedups and allows us to solve larger problem sizes. Summarizing the effects of each improvement, the resulting speedup can be at least an order of magnitude compared to the original LSM method. 相似文献
13.
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
14.
High‐order ADE scheme for solving the fluid diffusion equation in non‐uniform grids and its application in coupled hydro‐mechanical simulation 
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下载免费PDF全文 To improve the stability and efficiency of explicit technique, one proposed method is to use an unconditionally stable alternating direction explicit (ADE) scheme. However, the standard ADE scheme is only moderately accurate and restricted to uniform grids. This paper derives a novel high‐order ADE scheme capable of solving the fluid diffusion equation in non‐uniform grids. The new scheme is derived by performing a fourth‐order finite difference approximation to the spatial derivatives of the diffusion equation in non‐uniform grid. The implicit Crank‐Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps, giving rise to a new high‐order ADE scheme. Because the new scheme can be potentially applied in coupled hydro‐mechanical (H‐M) simulation, the pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer program Fast Lagrangian Analysis of Continua. This coupling procedure is called the sequentially explicit coupling technique based on the fourth‐order ADE scheme (SEA‐4). Verifications of well‐known consolidation problems showed that the new ADE scheme and SEA‐4 can reduce computer runtime by 46% to 75% to that of Fast Lagrangian Analysis of Continua's basic scheme. At the same time, the techniques still maintained average percentage error of 1.6% to 3.5% for pore pressure and 0.2% to 1.5% for displacement solutions and were still accurate under typical grid non‐uniformities. This result suggests that the new high‐order ADE scheme can provide an efficient explicit technique for solving the flow equation of a coupled H‐M problem, which will be beneficial for large‐scale and long‐term H‐M problems in geoengineering. 相似文献
15.
We present solutions for the effective stress induced by gas flow through a porous solid into a borehole resulting from sudden pressure reduction. Tensile effective stress that exceeds the strength of the solid will lead to borehole failure. This has applications to the intentional creation of cavities, relevant to the efficient recovery of coalbed methane, and the avoidance of borehole stability problems in conventional gas production. 相似文献
16.
Motivated by the needs for creating fast and accurate models of complex geological scenarios, accuracy and efficiency of three stencils for the isotropic eikonal equation on rectangular grids are evaluated using a fast marching implementation. The stencils are derived by direct modelling of the wave front, resulting in new and valuable insight in terms of improved upwind and causality conditions. After introducing a method for generalising first-order upwind stencils to higher order, a new second-order diagonal stencil is presented. Similarly to the multistencil fast marching approach, the diagonal stencil makes use of nodes in the diagonal directions, whereas the traditional Godunov stencil uses solely edge-connected neighbours. The diagonal stencil uses nodes close to each other, reaching upwind, to get a more accurate estimate of the angle of incidence of the arriving wave front. Although the stencils are evaluated in a fast marching setting, they can be adapted to other efficient eikonal solvers. All first- and second-order stencils are evaluated in a range of tests. The first test case models a folded structure from the Zagros fold belt in Iran. The other test cases are constructed to investigate specific properties of the examined stencils. The numerical investigation considers convergence rates and CPU times for non-constant and constant speed first-arrival computations. In conclusion, the diagonal stencil is the most efficient and accurate of the three alternatives. 相似文献
17.
In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
18.
Uncertainty quantification is typically accomplished by simulating multiple geological realizations, which can be very expensive computationally if the flow process is complicated and the models are highly resolved. Upscaling procedures can be applied to reduce computational demands, though it is essential that the resulting coarse-model predictions correspond to reference fine-scale solutions. In this work, we develop an ensemble level upscaling (EnLU) procedure for compositional systems, which enables the efficient generation of multiple coarse models for use in uncertainty quantification. We apply a newly developed global compositional upscaling method to provide coarse-scale parameters and functions for selected realizations. This global upscaling entails transmissibility and relative permeability upscaling, along with the computation of a-factors to capture component fluxes. Additional features include near-well upscaling for all coarse parameters and functions, and iteration on the a-factors, which is shown to improve accuracy. In the EnLU framework, this global upscaling is applied for only a few selected realizations. For 90 % or more of the realizations, upscaled functions are assigned statistically based on quickly computed flow and permeability attributes. A sequential Gaussian co-simulation procedure is incorporated to provide coarse models that honor the spatial correlation structure of the upscaled properties. The resulting EnLU procedure is applied for multiple realizations of two-dimensional models, for both Gaussian and channelized permeability fields. Results demonstrate that EnLU provides P10, P50, and P90 results for phase and component production rates that are in close agreement with reference fine-scale results. Less accuracy is observed in realization-by-realization comparisons, though the models are still much more accurate than those generated using standard coarsening procedures. 相似文献
19.
依据地热资料研究天然气水合物稳定带厚度在东海海域的分布情况。东海在地质构造上位于新生代环太平洋构造带西部边缘岛弧的内侧,又是欧亚板块、太平洋板块和菲律宾海板块的相互作用带。依据国际热流委员会(IHFC)提供的东海地热数据,经过统计确定出该区域的热流分布,热流平均值为121·0mW/m2,最小值为73·0mW/m2,最大值为168·0mW/m2。同时利用天然气水合物温压模型计算了稳定带厚度,数据显示稳定带厚度平均值为92·2m,最小值为1·4m,最大值为190·6m,薄于其他已经发现的海洋天然气水合物稳定带厚度(约400m)。天然气水合物大部分分布在条件适宜的陆坡和岛坡上,冲绳海槽底部水合物稳定带厚度相对较薄。统计分析表明本区热流值与水合物稳定带厚度相关性很差,相关系数仅有0·12。这是由于天然气水合物所在海域水深较浅时,海底温度的变化迫使运算所应用的非线性方程影响因子迅速积累,从而导致相关系数降低。最后结合东海陆坡的地质条件,探讨了在天然气水合物存在的情况下,陆坡失稳的可能性及其造成的环境影响。 相似文献
20.
Duke U. Ophori 《Hydrogeology Journal》1998,6(2):193-203
Flow of groundwater with variable density and viscosity was simulated at the Atikokan Research Area (ARA) in northwestern
Ontario, Canada. An empirical viscosity–concentration equation was modified to include total-dissolved-solids (TDS) data from
the ARA. The resulting equation was used successfully to estimate reasonably accurate viscosity values over the expected range
of temperature and concentration, in comparison with experimental values derived for sodium chloride solutions. A three-dimensional
finite-element code, MOTIF, developed by Atomic Energy of Canada Limited, was used in the simulations. The inclusion of the
effects of depth-increasing temperature and TDS-dependent fluid-density distribution, while maintaining only a temperature-dependent
viscosity relationship in a simulation, resulted in a more penetrative flow against expected buoyancy effects (i.e., the physics
of the system was not honored). Accounting for concentration in the viscosity equation caused water to be less penetrative
and more in accordance with the expected physics of the system. A conclusion is that fluid concentration should be considered
simultaneously in calculating the density and viscosity of a fluid during modeling of variable-density flow in areas underlain
by fluids with high TDS. Results of simulations suggest that both flow directions and magnitudes should be employed simultaneously
during the calibration of a model. Large-scale groundwater movement in the ARA may be analyzed with carefully selected vertical
no-flow boundaries. By incorporating the geothermal temperature gradient, groundwater recharge increases by 12%; thus, this
gradient plays a significant role in groundwater flow at the ARA. Variability in the fluid concentration at the ARA neither
decreases nor increases recharge into the groundwater system. The hypothesis that an isolated continuous regional flow system
may exist at depth in the ARA is not supported by these simulations.
Received, September 1996 Revised, September 1997, February 1998 Accepted, February 1998 相似文献