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1.
This paper is a prequel to that of Marchand et al. (Comput Geosci 16:691–708, 2012), where an efficient and accurate hybrid-mixed finite element approximation for a system of time-dependent nonlinear conservation equations has been formulated, implemented, and tested, which are general enough to represent most of the existing formulations for two-component liquid–gas flow in porous medium with phase exchange, also allowing for any (dis)appearance of one of the phases. Temperature variation is neglected, but capillary effects are included by extended Darcy’s law, and Fickian diffusion is taken into account. The efficiency and stability of the numerical method of Lake (1989) relies on an equivalent reformulation of the otherwise commonly used model in terms of new principal variables and subsequent static (flash) equations allowing more generally for any (dis)appearance of one of the phases without the need of variable switching or unphysical quantities. In particular, the formulation in terms of complementarity conditions allows for an efficient and stable solution by the semismooth Newton’s method. 相似文献
2.
In this article, an approach for the efficient numerical solution of multi-species reactive transport problems in porous media
is described. The objective of this approach is to reformulate the given system of partial and ordinary differential equations
(PDEs, ODEs) and algebraic equations (AEs), describing local equilibrium, in such a way that the couplings and nonlinearities
are concentrated in a rather small number of equations, leading to the decoupling of some linear partial differential equations
from the nonlinear system. Thus, the system is handled in the spirit of a global implicit approach (one step method) avoiding
operator splitting techniques, solved by Newton’s method as the basic algorithmic ingredient. The reduction of the problem
size helps to limit the large computational costs of numerical simulations of such problems. If the model contains equilibrium
precipitation-dissolution reactions of minerals, then these are considered as complementarity conditions and rewritten as
semismooth equations, and the whole nonlinear system is solved by the semismooth Newton method. 相似文献
3.
4.
A multi-lithology diffusive stratigraphic model is considered, which simulates at large scales in space and time the infill
of sedimentary basins governed by the interaction between tectonics displacements, eustatic variations, sediment supply, and
sediment transport laws. The model accounts for the mass conservation of each sediment lithology resulting in a mixed parabolic,
hyperbolic system of partial differential equations (PDEs) for the lithology concentrations and the sediment thickness. It
also takes into account a limit on the rock alteration velocity modeled as a unilaterality constraint. To obtain a robust,
fast, and accurate simulation, fully and semi-implicit finite volume discre tization schemes are derived for which the existence
of stable solutions is proved. Then, the set of nonlinear equations is solved using a Newton algorithm adapted to the unilaterality
constraint, and preconditioning strategies are defined for the solution of the linear system at each Newton iteration. They
are based on an algebraic approximate decoupling of the sediment thickness and the concentration variables as well as on a
proper preconditioning of each variable. These algorithms are studied and compared in terms of robustness, scalability, and
efficiency on two real basin test cases. 相似文献
5.
6.
Surendra P. Verma 《Journal of Earth System Science》2000,109(1):79-88
This paper presents error propagation equations for modeling of radiogenic isotopes during mixing of two components or end-members.
These equations can be used to estimate errors on an isotopic ratio in the mixture of two components, as a function of the
analytical errors or the total errors of geological field sampling and analytical errors. Two typical cases (“Small errors”
and “Large errors”) are illustrated for mixing of Sr isotopes. Similar examples can be formulated for the other radiogenic
isotopic ratios. Actual isotopic data for sediment and basalt samples from the Cocos plate are also included to further illustrate
the use of these equations. The isotopic compositions of the predicted mixtures can be used to constrain the origin of magmas
in the central part of the Mexican Volcanic Belt. These examples show the need of high quality experimental data for them
to be useful in geochemical modeling of magmatic processes. 相似文献
7.
Clint N. Dawson Héctor Klíe Mary F. Wheeler Carol S. Woodward 《Computational Geosciences》1997,1(3-4):215-249
A new parallel solution technique is developed for the fully implicit three‐dimensional two‐phase flow model. An expandedcell‐centered finite difference scheme which allows for a full permeability tensor is employed for the spatial discretization, and backwardEuler is used for the time discretization. The discrete systems are solved using a novel inexact Newton method that reuses the Krylov information generated by the GMRES linear iterative solver. Fast nonlinear convergence can be achieved by composing inexact Newton steps with quasi‐Newton steps restricted to the underlying Krylov subspace. Furthermore, robustness and efficiency are achieved with a line‐search backtracking globalization strategy for the nonlinear systems and a preconditioner for each coupled linear system to be solved. This inexact Newton method also makes use of forcing terms suggested by Eisenstat and Walker which prevent oversolving of the Jacobian systems. The preconditioner is a new two‐stage method which involves a decoupling strategy plus the separate solutions of both nonwetting‐phase pressure and saturation equations. Numerical results show that these nonlinear and linear solvers are very effective. 相似文献
8.
The simulation of sedimentary basins aims at reconstructing its historical evolution in order to provide quantitative predictions
about phenomena leading to hydrocarbon accumulations. The kernel of this simulation is the numerical solution of a complex
system of partial differential equations of mixed parabolic–hyperbolic type. A discretisation and linearisation of this system
leads to large ill-conditioned nonsymmetric linear systems with three unknowns per mesh element. The preconditioning which
we will present for these systems consists in three stages: (i) a local decoupling of the equations which (in addition) aims
at concentrating the elliptic part of the system in the “pressure block”; (ii) an efficient preconditioning of the pressure
block using AMG; (iii) the “recoupling” of the equations. In all our numerical tests on real case studies we observed a reduction
of the CPU-time for the linear solver (up to a factor 4.3 with respect to the current preconditioner ILU(0)) and almost no
degradation with respect to physical and numerical parameters.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection–diffusion
PDEs coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each
grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper, a global
solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies
the Newton–Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated
in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that
one be able to solve chemical equilibrium problems (and compute derivatives) without having to know the solution method. An
additional advantage of the Newton–Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times
vector product. The proposed method is tested on the MoMaS reactive transport benchmark. 相似文献
10.
Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential
equation arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations.
The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained
minimization problem. We utilize the augmented Lagrangian method and transform the minimization problem into a coupled system
of nonlinear algebraic equations, which is solved efficiently with the nonlinear conjugate gradient method. Numerical experiments
are presented and discussed.
This work was partially supported by the Research Council of Norway (NFR), under grant 128224/431. 相似文献
11.
The structure of a circumstellar envelope around a young binary T Tauri star is considered. The supersonic orbital motion
of the system components in the envelope gas leads to the formation of bow shocks around the star. Two- and three-dimensional
numerical modeling indicates an important role of these shocks in the formation of the structure of the circumbinary envelope.
In particular, for systems with circular orbits, the size of the central region of the envelope that is not filled with matter
(the “gap”) is essentially determined by the parameters of the bow shocks. These modeling results are supported by comparisons
of the obtained estimates for the gap parameters with observations. 相似文献
12.
热液系统流体输运－化学反应耦合动力学综述 总被引：2，自引：0，他引：2
输运－反应模式通过连续质量守恒方程进行描述，它表示为主要组分的Ｎ＋Ｍ个耦合的非线性偏微分方程。这些方程可以通过有限差分或有限元等数值方法进行求解。利用准静态近似法，涉及平流、分子扩散和水动力弥散作用的地球化学系统的演化在时间上通过一系列静止状态模拟出来。模拟实际地质系统的动力学实验对输运－反应耦合动力学的应用具有十分重要的影响。 相似文献
13.
Landslide Hazard Zonation using Remote Sensing and GIS: a case study of Dikrong river basin, Arunachal Pradesh, India 总被引：3，自引：0，他引：3
Landslides are among the most costly and damaging natural hazards in mountainous regions, triggered mainly under the influence
of earthquakes and/or rainfall. In the present study, Landslide Hazard Zonation (LHZ) of Dikrong river basin of Arunachal
Pradesh was carried out using Remote Sensing and Geographic Information System (GIS). Various thematic layers namely slope,
photo-lineament buffer, thrust buffer, relative relief map, geology and land use / land cover map were generated using remote
sensing data and GIS. The weighting-rating system based on the relative importance of various causative factors as derived
from remotely sensed data and other thematic maps were used for the LHZ. The different classes of thematic layers were assigned
the corresponding rating value as attribute information in the GIS and an “attribute map” was generated for each data layer.
Each class within a thematic layer was assigned an ordinal rating from 0 to 9. Summation of these attribute maps were then
multiplied by the corresponding weights to yield the Landslide Hazard Index (LHI) for each cell. Using trial and error method
the weight-rating values have been re-adjusted. The LHI threshold values used were: 142, 165, 189 and 216. A LHZ map was prepared
showing the five zones, namely “very low hazard”, “low hazard”, “moderate hazard”, “high hazard” and “very high hazard” by
using the “slicing” operation. 相似文献
14.
Helge Holden Kenneth Hvistendahl Karlsen Knut-Andreas Lie 《Computational Geosciences》2000,4(4):287-322
We present an accurate numerical method for a large class of scalar, strongly degenerate convection–diffusion equations. Important subclasses are hyperbolic conservation laws, porous medium type equations, two-phase reservoir flow equations, and strongly degenerate equations coming from the recent theory of sedimentation–consolidation processes. The method is based on splitting the convective and the diffusive terms. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlinear diffusion part is solved by an implicit–explicit finite difference scheme. In addition, one version of the implemented operator splitting method has a mechanism built in for detecting and correcting unphysical entropy loss, which may occur when the time step is large. This mechanism helps us gain a large time step ability for practical computations. A detailed convergence analysis of the operator splitting method was given in Part I. Here we present numerical experiments with the method for examples modelling secondary oil recovery and sedimentation–consolidation processes. We demonstrate that the splitting method resolves sharp gradients accurately, may use large time steps, has first order convergence, exhibits small grid orientation effects, has small mass balance errors, and is rather efficient. 相似文献
15.
Hydrochemical framework of the aquifer in and around East Kolkata Wetlands,West Bengal,India 总被引：1，自引：0，他引：1
The area lies between Hugli river in the northwest and Bidyadhari river in the east and includes the East Kolkata Wetlands.
The East Kolkata Wetlands is included in the List of Wetlands of International Importance (“Ramsar List”), as per the Convention
on Wetlands signed in Ramsar, Iran, in 1971. This wetland has been declared as a Ramsar site on the 19th August 2002 (Ramsar
site no. 1208) and therefore has acquired an international status. The area is a part of the lower deltaic plain of the Bhagirathi–Ganga
river system and is generally flat in nature. The sub-surface geology of the area is completely blanketed by the Quaternary
fluviatile sediments comprising a succession of clay, silty clay, sand and sand mixed with occasional gravel. The Quaternary
aquifer is sandwiched between two clay sequences. The confined aquifer is made up of moderately well sorted sand and reflects
fluviatile environment of deposition. The regional groundwater flow direction is from east to west. Detailed geochemical investigations
of 40 groundwater samples along with statistical analysis (for example, correlation and principal component analysis) on these
chemical data reveal: (i) four types of groundwater quality, for example, good, poor, very poor and water unsuitable for drinking
purpose, (ii) four hydrochemical facies which may be assigned to three broad types such as “fresh”, “blended”, and “brackish”
waters, (iii) the evolution of the “blended” water is possibly due to hydraulic mixing of “fresh” and “brackish” waters within
the aquifer matrix and/or in well mixing, and (iv) absence of Na–Cl facies indicates continuous flushing of the aquifer. 相似文献
16.
The variational technique of data assimilation using adjoint equations has been illustrated using a nonlinear oceanographic
shallow water model. The technique consists of minimizing a cost function representing the misfit between the model and the
data subject to the model equations acting as constraints. The problem has been transformed into an unconstrained one by the
use of Lagrange multipliers. Particular emphasis has been laid on finite difference formulation of the algorithm. Several
numerical experiments have been conducted using simulated data obtained from a control run of the model. Implications of this
technique for assimilating asynoptic satellite altimeter data into ocean models have been discussed. 相似文献
17.
There is growing recognition among political ecologists of the need to examine shifting natural resource regimes and their
effects on livelihoods in “First World” places. This emerging literature has variously examined the “Third World within,”
the persistence of “subsistence activities” in the “First World,” and the “reterritorialization” of land tenure and access.
However, much of this work has tended to focus on traditional extractive industries in the American West, indigenous claims
to lands and resources in the U.S. and Canada, and non-timber resources on public lands. In contrast, we use a case study
of African-American sweetgrass basket-makers, associated with the Gullah culture, in South Carolina’s lowcountry to examine
the ways in which ongoing amenity-driven residential development is fundamentally reshaping resource access on private lands.
Historically, basket-makers harvested the materials (primarily sweetgrass or Mulenbergia filipes) needed for their culturally
important art form from accessible, rural, and privately held tracts of land in close proximity to their communities, but
development pressures and changes in resident interpretation of property rights has decreased access to basket-making resources.
The case is particularly illuminating, as it examines the emergence of ‘conservation subdivisions’ in the region and raises
important questions about what “rural uses” and users are being conserved through responses to exurban, suburban, and urban
development in formerly rural areas. 相似文献
18.
19.
N. A. Gnatus’ M. D. Khutorskoy V. K. Khmelevskoi 《Moscow University Geology Bulletin》2011,66(3):151-157
The geological-geophysical, methological, and economic aspects of extraction and utilization of petrothermal resources (“hot
dry rock thermal”) for thermal and electric energy production were considered. Heat collectors are hydraulic fracturing zones
of natural or artificially made cracks in the crystalline rocks of the basement; these rocks have higher temperature and can
be a kind of “thermal cauldron.” Detection of such “collectors” can be carried out by geophysical methods. When pumped out
of wells and warmed to 100–300°C, waters function as a heat transfer for thermal energy supply and electric energy generation.
If the technical problem of the rapid drilling of 6–10 km wells could be solved, then petrothermal energy will become competitive
with the traditional types of energy production and supply. 相似文献
20.
Konstantin Brenner Mayya Groza Laurent Jeannin Roland Masson Jeanne Pellerin 《Computational Geosciences》2017,21(5-6):1075-1094
Fully implicit time-space discretizations applied to the two-phase Darcy flow problem leads to the systems of nonlinear equations, which are traditionally solved by some variant of Newton’s method. The efficiency of the resulting algorithms heavily depends on the choice of the primary unknowns since Newton’s method is not invariant with respect to a nonlinear change of variable. In this regard, the role of capillary pressure/saturation relation is paramount because the choice of primary unknowns is restricted by its shape. We propose an elegant mathematical framework for two-phase flow in heterogeneous porous media resulting in a family of formulations, which apply to general monotone capillary pressure/saturation relations and handle the saturation jumps at rocktype interfaces. The presented approach is applied to the hybrid dimensional model of two-phase water-gas Darcy flow in fractured porous media for which the fractures are modelled as interfaces of co-dimension one. The problem is discretized using an extension of vertex approximate gradient scheme. As for the phase pressure formulation, the discrete model requires only two unknowns by degree of freedom. 相似文献