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1.
Accurate simulation of fluid pressures in layered reservoirs with strong permeability contrasts is a challenging problem. For this purpose, the Discontinuous Galerkin (DG) method has become increasingly popular. Unfortunately, standard linear solvers are usually too inefficient for the aforementioned application. To increase the efficiency of the conjugate gradient (CG) method for linear systems resulting from symmetric interior penalty (discontinuous) Galerkin (SIPG) discretizations, we cast an existing two-level preconditioner into the deflation framework. The main idea is to use coarse corrections based on the DG solution with polynomial degree p = 0. This paper provides a numerical comparison of the performance of the original preconditioner and the resulting deflation variant in terms of scalability and overall efficiency. Furthermore, it studies the influence of the SIPG penalty parameter, weighted averages in the SIPG formulation (SWIP), the smoother, damping of the smoother, and the strategy for solving the coarse systems. We have found that the penalty parameter can best be chosen diffusion-dependent. In that case, both two-level methods yield fast and scalable convergence. Whether preconditioning or deflation is to be favored depends on the choice of the smoother and on the damping of the smoother. Altogether, both two-level methods can contribute to cheaper and more accurate fluid pressure simulations. 相似文献
2.
A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure 总被引：1，自引：0，他引：1
Peter Bastian 《Computational Geosciences》2014,18(5):779-796
In this paper, we formulate and test numerically a fully-coupled discontinuous Galerkin (DG) method for incompressible two-phase flow with discontinuous capillary pressure. The spatial discretization uses the symmetric interior penalty DG formulation with weighted averages and is based on a wetting-phase potential/capillary potential formulation of the two-phase flow system. After discretizing in time with diagonally implicit Runge-Kutta schemes, the resulting systems of nonlinear algebraic equations are solved with Newton’s method and the arising systems of linear equations are solved efficiently and in parallel with an algebraic multigrid method. The new scheme is investigated for various test problems from the literature and is also compared to a cell-centered finite volume scheme in terms of accuracy and time to solution. We find that the method is accurate, robust, and efficient. In particular, no postprocessing of the DG velocity field is necessary in contrast to results reported by several authors for decoupled schemes. Moreover, the solver scales well in parallel and three-dimensional problems with up to nearly 100 million degrees of freedom per time step have been computed on 1,000 processors. 相似文献
3.
A new formulation of the element‐free Galerkin (EFG) method is developed for solving coupled hydro‐mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro‐mechanical problems. Examples are studied and compared with closed‐form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro‐mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
4.
A continuous/discontinuous Galerkin framework for modeling coupled subsurface and surface water flow
Clint Dawson 《Computational Geosciences》2008,12(4):451-472
We consider conjunctive surface-subsurface flow modeling, where surface water flow is described by the shallow water equations
and ground water flow by Richards’ equation for the vadose zone. Coupling between the models is based on the continuity of
flux and water pressure. Numerical approximation of the coupled model using the framework of discontinuous Galerkin (DG) methods
is formulated. In the subsurface, the local discontinuous Galerkin (LDG) method is used to approximate ground water velocity
and hydraulic head; a DG method is also used to approximate surface water velocity and elevation. This approach allows for
a weak coupling of the models and the use of different approximating spaces and/or meshes within each regime. A simplified
LDG method based on continuous approximations to water head is also described. Numerical results that investigate physical
and numerical aspects of surface–subsurface flow modeling are presented.
This work was supported by National Science Foundation grant DMS-0411413. 相似文献
5.
This work presents the coupling of two locally conservative methods for elliptic problems: namely, the discontinuous Galerkin method and the mixed finite element method. The couplings can be defined with or without interface Lagrange multipliers. The formulations are shown to be equivalent. Optimal error estimates are given; penalty terms may or may not be included. In addition, the analysis for non-conforming grids is also discussed. 相似文献
6.
Three Galerkin methods using discontinuous approximation spaces are introduced to solve elliptic problems. The underlying bilinear form for all three methods is the same and is nonsymmetric. In one case, a penalty is added to the form and in another, a constraint on jumps on each face of the triangulation. All three methods are locally conservative and the third one is not restricted. Optimal a priori hp error estimates are derived for all three procedures. 相似文献
7.
8.
Ettore Vidotto Rainer Helmig Martin Schneider Barbara Wohlmuth 《Computational Geosciences》2018,22(6):1487-1502
In this paper, we present a fast streamline-based numerical method for the two-phase flow equations in high-rate flooding scenarios for incompressible fluids in heterogeneous and anisotropic porous media. A fractional flow formulation is adopted and a discontinuous Galerkin method (DG) is employed to solve the pressure equation. Capillary effects can be neglected in high-rate flooding scenarios. This allows us to present an improved streamline approach in combination with the one-dimensional front tracking method to solve the transport equation. To handle the high computational costs of the DG approximation, domain decomposition is applied combined with an algebraic multigrid preconditioner to solve the linear system. Special care at the interior interfaces is required and the streamline tracer has to include a dynamic communication strategy. The method is validated in various two- and three-dimensional tests, where comparisons of the solutions in terms of approximation of flow front propagation with standard fully implicit finite-volume methods are provided. 相似文献
9.
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
10.
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
11.
This study introduces the prediction of probabilistic settlements with the uncertainty in the spatial variability of Young’s modulus to illustrate the preliminary development of a spectral stochastic meshless local Petrov–Galerkin (SSMLPG) method. Generalized polynomial chaos expansions of Young’s moduli and a two-dimensional meshfree weak–strong formulation in elasticity are combined to derive the SSMLPG formulation. Because of the local and truly meshless nature, the SSMLPG method is more computationally efficient than available stochastic numerical methods. Two examples further show that SSMLPG-based predictions remain sufficiently accurate even in case of scattered nodes. Therefore, the SSMLPG method can be a valuable alternative for solving stochastic boundary-value problems. 相似文献
12.
In this paper, we formulate a finite-element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation
model of poroelasticity. We approximate the flow variables by a mixed finite-element space and the displacement by a family
of discontinuous Galerkin methods. Theoretical convergence error estimates are derived and, in particular, are shown to be
independent of the constrained specific storage coefficient, c
o
. This suggests that our proposed algorithm is a potentially effective way to combat locking, or the nonphysical pressure
oscillations, which sometimes arise in numerical algorithms for poroelasticity. 相似文献
13.
Lukáš Ackerman Jiří Zachariáš Marta Pudilová 《International Journal of Earth Sciences》2007,96(4):623-638
Fluid inclusions, mineral thermometry and stable isotope data from two types of mineralogically and texturally contrasting
pegmatites, barren ones and lithium ones, from the Moldanubian Zone of the Bohemian Massif were studied in order to constrain
P–T conditions of their emplacement, subsolidus hydrothermal evolution and to estimate composition of the early exsolved fluid
and that of the parental melt. Despite the fact that the lithium pegmatites are abundant throughout the crystalline units
of the Bohemian Massif, data similar to this paper have not been published yet. The studied pegmatites are hosted by iron-rich
calcic skarn bodies. This specific setting allowed scavenging of calcium, fluorine and some other elements from the host rocks
into the pegmatitic melts and post-magmatic fluids. Such contamination process was important namely in the case of barren
pegmatites, as can be deduced from the variation in anorthite contents in plagioclase and from the presence of fluorite, hornblende
(with F content) or garnet in the contact zones of pegmatite dykes. Fluid inclusions were studied mostly in quartz, but also
in fluorite, titanite and apatite. Early aqueous–carbonic and late aqueous fluids were identified in both pegmatite types.
The P–T conditions of crystallization as well as the detailed composition of exsolved magmatic fluid, however, particularly differ.
The magmatic fluids associated with barren pegmatites correspond to H2O–CO2 low salinity fluids, composition of which evolved from 20 to 23 to <5 mol% CO2, and from 2 to 4–6 mol% NaCl eq. Sudden decrease in the CO2 content of the post-magmatic fluids (<5 mol% CO2) seems to coincide with the enrichment of the fluid in calcium (from the contamination process) and resulted in precipitation
of calcites (frequently found as trapped solid phases in fluid inclusions). The fluids associated with lithium pegmatites
are more complex (H2O–CO2/N2–H3BO3–NaCl). The CO2 content of early exsolved fluid is 26–20 mol% CO2 and remains the same in the next fluid generation. The main difference between the magmatic and the first post-magmatic fluids
is the presence of 7–9 wt% of H3BO3 (identified as daughter mineral sassolite) in the former. The second post-magmatic fluids are again CO2-poor (∼4 mol%) and more saline (∼4 mol% NaCl eq.). The composition of exsolved fluid was further used to constrain volatile
composition and content of the parental melts. Finally, P–T conditions of pegmatite crystallization are constrained: 600–640°C and 420–580 MPa for the barren pegmatites and 500–570°C
and 310–430 MPa for the lithium pegmatite. While the emplacement of the former occurred in thermal equilibrium with the Moldanubian
host rock environment, the emplacement of the later suggests substantial thermal disequilibrium. 相似文献
14.
B‐bar based algorithm applied to meshfree numerical schemes to solve unconfined seepage problems through porous media 下载免费PDF全文
下载免费PDF全文 The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous media. The Biot's equations are formulated in displacements (or u − w) assuming an elastic solid skeleton. The free surface location and its evolution in time are obtained by interpolation of pore water pressures throughout the domain. Shape functions based on the principle of local maximum entropy are chosen for the meshfree approximation schemes. In order to avoid the locking involved in the fluid phase of the porous media, a B‐bar based algorithm is devised to compute the average volumetric strain in a patch composed of various integration points. The efficiency of such an implementation for one phase problems is shown through the Benchmark problem, Cook's membrane loaded by a distributive shear load. The proposed methodology is firstly applied to various classical examples in unconfined steady seepage problems through earth dams, then to the dynamic consolidation of a soil column. The results obtained for both problems are quite satisfactory and demonstrate the feasibility of the proposed method in solving coupled problems in porous media. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
15.
Florian Frank Chen Liu Faruk O. Alpak Beatrice Riviere 《Computational Geosciences》2018,22(2):543-563
A numerical method is formulated for the solution of the advective Cahn–Hilliard (CH) equation with constant and degenerate mobility in three-dimensional porous media with non-vanishing velocity on the exterior boundary. The CH equation describes phase separation of an immiscible binary mixture at constant temperature in the presence of a conservation constraint and dissipation of free energy. Porous media / pore-scale problems specifically entail images of rocks in which the solid matrix and pore spaces are fully resolved. The interior penalty discontinuous Galerkin method is used for the spatial discretization of the CH equation in mixed form, while a semi-implicit convex–concave splitting is utilized for temporal discretization. The spatial approximation order is arbitrary, while it reduces to a finite volume scheme for the choice of element-wise constants. The resulting nonlinear systems of equations are reduced using the Schur complement and solved via inexact Newton’s method. The numerical scheme is first validated using numerical convergence tests and then applied to a number of fundamental problems for validation and numerical experimentation purposes including the case of degenerate mobility. First-order physical applicability and robustness of the numerical method are shown in a breakthrough scenario on a voxel set obtained from a micro-CT scan of a real sandstone rock sample. 相似文献
16.
Donald P. Hauber Kristin Saltonstall David A. White Craig S. Hood 《Estuaries and Coasts》2011,34(4):851-862
Multiple introductions are believed to play an important role in increasing genetic diversity and adaptability of invasive
species, but there are few well-documented examples. The common reed, Phragmites australis, has dramatically increased in tidal wetlands throughout the USA in the past century due primarily to the introduction of
a Eurasian lineage. In the Mississippi River “Balize” delta, P. australis is the dominant vegetation where monotypic stands of an introduced form blanket the outer marshes. The delta’s interior marshes,
on the other hand, are more vegetatively diverse, serving as important waterfowl foraging habitat. Recent encroachment by
various phenotypic forms of P. australis into the interior marshes led to this study examining genetic variation in these stands. Our results revealed four chloroplast
DNA haplotypes that also segregate based on microsatellite variation. Three of these are closely related and introduced, but
differ relative to time and likely mode of introduction. The “Delta” type (haplotype M1), which is unique to the region and
the most common lineage, displays considerable microsatellite diversity. The Eurasian introduced lineage of P. australis (haplotype M), which is invasive elsewhere in North America, is increasing its distribution in the delta. A novel haplotype,
AD, was also identified which is phenotypically and genetically similar to haplotype M. Despite the close relatedness, we
found no evidence for inter-haplotype gene exchange at the nuclear level, suggesting that intraspecific hybridization is not
a contributing factor to these invasions. The site provides a unique opportunity for researchers to understand the dynamics
of multiple P. australis invasions. 相似文献
17.
The seasonal variation of foliar δ13C values in Sabina przewalskii Kom. and Sabina chinensis (Lin.) Ant. was measured. The relationships between foliar δ13C values and branch δ13C values as well as environmental factors (monthly total precipitation, monthly average air temperature, monthly average soil
temperature, monthly total solar duration, relative humidity, atmospheric pressure, vapor pressure, wind speed and potential
evaporation) were investigated. The results showed that the foliar δ13C values were negatively correlated with air pressure, and positively correlated with air temperature, precipitation, vapor
pressure, potential evaporation, solar duration, wind speed and soil temperature. No significant relationship between δ13C values and relative humidity was detected. This demonstrates that the foliar δ13C of Sabina is a successful empirical indictor of these meteorological factors within the usual range of C3 whole-leaf δ13C values. Furthermore, the δ13C signature of leaf tissue is similar to that of wood tissue and the responses of δ13C values in S.
przewalskii Kom. to environmental factors are also relatively stronger than that of S. chinensis (Lin.) Ant. These results provided strong evidence that it is feasible to extract climatic information from tree-ring δ13C series and S.
przewalskii Kom. is a dendroclimatologically promising tree species. 相似文献
18.
裂隙岩体因含有发育程度不同的裂隙、节理和断层等不连续面,致其渗透性具有各向异性、不连续性等特点,因此传统的有限元法对分布密集的裂隙岩体渗流场求解有一定的难度。本文提出了采用无单元Glaerkin法求解有自由面裂隙渗流问题,并推导了无单元法求解渗流场的基本方程和积分格式,给出了应用罚函数法处理渗流边界条件和自由面处理方法。采用IDL语言编制了二维无单元法计算软件LIDAREFM。文中以北京怀柔桥梓镇某裂隙岩体边坡渗流场计算为例,研究了复杂裂隙共同作用下渗流场特性和自由面分布,讨论了不同开度、不同连通程度的裂隙对渗流场的影响。研究结果表明:无单元法可以较好地解决有密集裂隙的岩体渗流场的求解问题,实现了裂隙处结点任意加密以及积分网格的独立布置,避免了对有自由面和裂隙穿越的子域的重新处理,简化了渗流问题的求解过程。 相似文献
19.
接触摩擦问题的数值模拟 总被引：3，自引：1，他引：2
无网格伽辽金法(EFGM)可脱离单元的概念,特别适合岩体裂纹面的接触摩擦分析。基于EFGM,在裂纹面引入罚参数,通过迭代计算,得到裂纹面真实的应力状态,从而模拟闭合裂纹的粘接、滑移和张开行为,数值结果表明该方法是合理可行的。 相似文献