共查询到20条相似文献，搜索用时 31 毫秒
1.
M. D. Sharma 《Journal of Earth System Science》2005,114(4):411-419
Wave propagation is studied in a general anisotropic poroelastic solid saturated with a viscous fluid flowing through its
pores of anisotropic permeability. The extended version of Biot’s theory is used to derive a system of modified Christoffel
equations for the propagation of plane harmonic waves in such media. The non-trivial solution of this system is ensured by
a biquadratic equation whose roots represent the complex velocities of four attenuating quasi-waves in the medium. These complex
velocities define phase velocity and attenuation of each quasi-wave propagating along a given phase direction in three-dimensional
space. The solution itself defines the polarisations of the quasi-waves along with phase shift. The variations of polarisations
of quasi-waves with their phase direction, are computed for a realistic numerical model. 相似文献
2.
We develop a finite element discretization and multigrid solver for a Darcy–Stokes system of three-dimensional vuggy porous media, i.e., porous media with cavities. The finite element method uses low-order mixed finite elements in the Darcy
and Stokes domains and special transition elements near the Darcy–Stokes interface to allow for tangential discontinuities
implied by the Beavers–Joseph boundary condition. We design a multigrid method to solve the resulting saddle point linear
system. The intertwining of the Darcy and Stokes subdomains makes the resulting matrix highly ill-conditioned. The velocity
field is very irregular, and its discontinuous tangential component at the Darcy–Stokes interface makes it difficult to define
intergrid transfer operators. Our definition is based on mass conservation and the analysis of the orders of magnitude of
the solution. The coarser grid equations are defined using the Galerkin method. A new smoother of Uzawa type is developed
based on taking an optimal step in a good search direction. Our algorithm has a measured convergence factor independent of
the size of the system, at least when there are no disconnected vugs. We study the macroscopic effective permeability of a
vuggy medium, showing that the influence of vug orientation; shape; and, most importantly, interconnectivity determine the
macroscopic flow properties of the medium.
This work was supported by the U.S. National Science Foundation under grants DMS-0074310 and DMS-0417431. 相似文献
3.
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
4.
Jeremy Edward Kozdon Bradley T. Mallison Margot G. Gerritsen 《Computational Geosciences》2011,15(3):399-419
Truly multidimensional methods for hyperbolic equations use flow-based information to determine the computational stencil,
as opposed to applying one-dimensional methods dimension by dimension. By doing this, the numerical errors are less correlated
with the underlying computational grid. This can be important for reducing bias in flow problems that are inherently unstable
at simulation scale, such as in certain porous media problems. In this work, a monotone, multi-D framework for multiphase
flow and transport in porous media is developed. A local coupling of the fluxes is introduced through the use of interaction
regions, resulting in a compact stencil. A relaxed volume formulation of the coupled hyperbolic–elliptic system is used that
allows for nonzero residuals in the pressure equation to be handled robustly. This formulation ensures nonnegative masses
and saturations (volume fractions) that sum to one (Acs et al., SPE J 25(4):543–553, 1985). Though the focus of the paper is on immiscible flow, an extension of the methods to a class of more general scalar hyperbolic
equations is also presented. Several test problems demonstrate that the truly multi-D schemes reduce biasing due to the computational
grid. 相似文献
5.
The evolution of an active continental margin is simulated in two dimensions, using a finite difference thermomechanical code with half-staggered grid and marker-in-cell technique. The effect of mechanical properties, changing as a function of P and T, assigned to different crustal layers and mantle materials in the simple starting structure is discussed for a set of numerical models. For each model, representative P–T paths are displayed for selected markers. Both the intensity of subduction erosion and the size of the frontal accretionary wedge are strongly dependent on the rheology chosen for the overriding continental crust. Tectonically eroded upper and lower continental crust is carried down to form a broad orogenic wedge, intermingling with detached oceanic crust and sediments from the subducted plate and hydrated mantle material from the overriding plate. A small portion of the continental crust and trench sediments is carried further down into a narrow subduction channel, intermingling with oceanic crust and hydrated mantle material, and to some extent extruded to the rear of the orogenic wedge underplating the overriding continental crust. The exhumation rates for (ultra)high pressure rocks can exceed subduction and burial rates by a factor of 1.5–3, when forced return flow in the hanging wall portion of the self-organizing subduction channel is focused. The simulations suggest that a minimum rate of subduction is required for the formation of a subduction channel, because buoyancy forces may outweigh drag forces for slow subduction. For a weak upper continental crust, simulated by a high pore pressure coefficient in the brittle regime, the orogenic wedge and megascale melange reach a mid- to upper-crustal position within 10–20 Myr (after 400–600 km of subduction). For a strong upper crust, a continental lid persists over the entire time span covered by the simulation. The structural pattern is similar in all cases, with four zones from trench toward arc: (a) an accretionary complex of low-grade metamorphic sedimentary material; (b) a wedge of mainly continental crust, with medium-grade HP metamorphic overprint, wound up and stretched in a marble cake fashion to appear as nappes with alternating upper and lower crustal provenance, and minor oceanic or hydrated mantle interleaved material; (c) a megascale melange composed of high-pressure and ultrahigh-pressure metamorphic oceanic and continental crust, and hydrated mantle, all extruded from the subduction channel; (d) zone represents the upward tilted frontal part of the remaining upper plate lid in the case of a weak upper crust. The shape of the P–T paths and the time scales correspond to those typically recorded in orogenic belts. Comparison of the numerical results with the European Alps reveals some similarities in their gross structural and metamorphic pattern exposed after collision. A similar structure may be developed at depth beneath the forearc of the Andes, where the importance of subduction erosion is well documented, and where a strong upper crust forms a stable lid. 相似文献
6.
Thomas H. Robey 《Mathematical Geology》1995,27(6):709-729
Geostatistical techniques allow simulation of properties such as porosity or conductivity on a fine scale. Typically, porous media flow modeling is performed at a coarser scale. Upscaling properties from the fine scale to the coarser scale introduces potential errors which are constrained by the degree of homogeneity of the cell or element. Adaptive grid techniques can be used to minimize the heterogeneity in the individual cells or elements, thus minimizing potential upscaling errors. A geostatistical adaptive grid (GAG) algorithm based on local minimization of heterogeneity is introduced. Local minimization allows greater control over the type of distortion permitted. Comparisons are made with a general elastic grid adjustment (GEGA) algorithm based on global minimization of heterogeneity. Several sample problems are used to test and demonstrate the two approaches. 相似文献
7.
利用时间分裂的错格伪谱法模拟地震波在基于改进BISQ模型的双相介质中的传播 总被引：1，自引：0，他引：1
改进的BISQ(Biot-Squirt)模型中各参数具有明确的物理意义和可实现性,在不引入特征喷流长度的情况下可将Biot流动和喷射流动两种力学机制有机地结合起来;而高精度的地震波场数值模拟技术是研究双相介质地震波传播规律的重要手段。本文从本构方程、动力学方程和动力学达西定律出发,推导了基于改进BISQ模型的双相各向同性介质的一阶速度--应力方程组;采用时间分裂错格伪谱法求该方程组的数值解,模拟半空间及层状双相介质中的地震波场。数值模拟结果表明:①与传统方法相比,时间分裂错格伪谱法波场数值模拟的精度更高,压制网格频散效果更好;②在非黏滞相界情况下,慢纵波呈传播性,而在黏滞相界情况下,慢纵波呈扩散性,以静态模式出现在震源位置;③双相介质分界面处,各类波型复杂的反射透射规律可由数值模拟结果清晰展现。 相似文献
8.
The aim of the study is to increase the reliability of estimation of the acoustic parameters of a layered permeable formation using new software, based on two-velocity continuum equations for 2D numerical simulation of acoustic waves propagating in a borehole. The key method is the method of finite differences as applied to solving equations of the continuum filtration theory. The dissipative characteristics of Stoneley waves have been identified for the case of their propagation in a layered formation. These aspects should be taken into account when using Stoneley waves to estimate the permeability of geologic media. 相似文献
9.
Chan-Hee Park Christof Beyer Sebastian Bauer Olaf Kolditz 《Environmental Geology》2008,55(8):1755-1766
Precise and efficient numerical simulation of transport processes in subsurface systems is a prerequisite for many site investigation
or remediation studies. Random walk particle tracking (RWPT) methods have been introduced in the past to overcome numerical
difficulties when simulating propagation processes in porous media such as advection-dominated mass transport. Crucial for
the precision of RWPT methods is the accuracy of the numerically calculated ground water velocity field. In this paper, a
global node-based method for velocity calculation is used, which was originally proposed by Yeh (Water Resour Res 7:1216–1225,
1981). This method is improved in three ways: (1) extension to unstructured grids, (2) significant enhancement of computational
efficiency, and (3) extension to saturated (groundwater) as well as unsaturated systems (soil water). The novel RWPT method
is tested with numerical benchmark examples from the literature and used in two field scale applications of contaminant transport
in saturated and unsaturated ground water. To evaluate advective transport of the model, the accuracy of the velocity field
is demonstrated by comparing several published results of particle pathlines or streamlines. Given the chosen test problem,
the global node-based velocity estimation is found to be as accurate as the CK method (Cordes and Kinzelbach in Water Resour
Res 28(11):2903–2911, 1992) but less accurate than the mixed or mixed-hybrid finite element methods for flow in highly heterogeneous media. To evaluate
advective–diffusive transport, a transport problem studied by Hassan and Mohamed (J Hydrol 275(3–4):242–260, 2003) is investigated here and evaluated using different numbers of particles. The results indicate that the number of particles
required for the given problem is decreased using the proposed method by about two orders of magnitude without losing accuracy
of the concentration contours as compared to the published numbers. 相似文献
10.
倾斜层状地层中速度模型对于震源精确定位具有重要意义。基于水平层状地层两点间的快速射线追踪法,分析了应力波在倾斜地层中的传播路径及规律。结合网格搜索法,提出了针对倾斜地层的微震定位算法,并与传统的基于单一速度模型的定位算法进行对比分析;探索性地采用了颗粒流理论构建地层数值模型,通过颗粒间的相互作用模拟应力波传播进行定位算法有效性验证。研究结果表明：（1）对于倾斜地层,基于简化弹性波等速传播规律的定位算法精度较差,单一速度模型不能满足复杂介质的定位要求;（2）采用倾斜分层速度模型并改进应力波传播路径的计算方法能有效提高倾斜地层的震源定位精度,同时分析了地层倾角以及地层数对算法精度的影响,表明定位误差与倾角、地层数成正比;（3）通过减小网格搜索法的网格尺寸可在一定程度上提高定位精度,合理的尺寸大小和搜索策略有助于网格搜索法在实际工程中的应用。建立的倾斜地层震源定位及其验证方法可为进一步研究复杂地层定位监测技术提供重要的理论和技术支撑。 相似文献
11.
Dali Zhang Michael P. Lamoureux Gary F. Margrave Elena Cherkaev 《Computational Geosciences》2011,15(1):117-133
The article presents a numerical inversion method for estimation of quality Q factor and phase velocity in linear, viscoelastic, isotropic media using reconstruction of relaxation spectrum from measured
or computed complex velocity or modulus of the medium. Mathematically, the problem is formulated as an inverse problem for
reconstruction of relaxation spectrum in the analytic Stieltjes representation of the complex modulus using rational approximation.
A rational (Padé) approximation to the relaxation spec trum is derived from a constrained least squares minimization problem
with regularization. The recovered stress-strain relaxation spectrum is applied to numerical calculation of frequency-dependent
Q factor and frequency-dependent phase velocity for known analytical models of a standard linear viscoelastic solid (Zener)
model as well as a nearly constant-Q model which has a continuous spectrum. Numerical results for these analytic models show good agreement between theoretical
and predicted values and demonstrate the validity of the algorithm. The proposed method can be used for evaluating relaxation
mechanisms in seismic wavefield simulation of viscoelastic media. The constructed lower order Padé approximation can be used
for determination of the internal memory variables in time-domain finite difference numerical simulation of viscoelastic wave
propagation. 相似文献
12.
We continue the work that was initiated in (K. H. Karlsen, K.-A. Lie, and N. H. Risebro. A fast marching method for reservoir
simulation. Comp. Geo., 4(2) (2000)185–206) on a marching method for simulating two-phase incompressible immiscible flow of water and oil in a porous
medium. We first present an alternative derivation of the marching method that reveals a strong connection to modern streamline
methods. Then, through the study of three numerical test cases we present two deficiencies: (i) the original marching algorithm
does not always compute the correct solution of the underlying difference equations, and (ii) the method gives largely inaccurate
arrival times in the presence of large jumps within the upwind difference stencil. As a remedy of the first problem, we present
a new advancing-front method, which is faster than the original marching method and guarantees a correct solution of the underlying
discrete linear system. To cure the second problem, we present two adaptive strategies that avoid the use of finite-difference
stencils containing large jumps in the arrival times. The original marching method was introduced as a fast tool for simulating
two-phase flow scenarios in heterogeneous formations. The new advancing-front method has limited applicability in this respect,
but may rather be used as a fast and relatively accurate method for computing arrival times and derived quantities in heterogeneous
media. 相似文献
13.
The aim of this study was to determine at which parameters hydrothermal systems generate rich veins with bulk sphalerite contents
of 30% and local concentrations in vein cross sections up to 60–70% and more. Such contents were found in the vein bodies
of the Dzhimi deposit in the Sadon ore district, North Osetiya. For this purpose, we examined the thermodynamic models of
the formation of base-metal filling veins. Ore-bearing fluids are formed in the root part of the hydrothermal system by the
interaction of barren solutions with the host rocks (granites), which contain background contents of ore elements. The thermodynamic
simulations were conducted for the system H-O-K-Na-Ca-Mg-Al-Si-Fe-C-Cl-S-Zn-Pb-Cu, which is described by 54 minerals of constant
and variable composition and 78 aqueous species. The calculations for the mobilization zone were carried out for the temperature
range of 360–440°C (through 10°C) and pressures of 600–1200 bar (with a 100 bar step). At each of the indicated temperature
and pressure values, 100 waves (portions) of primary barren solution were subsequently passed through the granites. More than
20 complete models of the formation of filling veins (each model involving from 1000 to 1300 calculations) were constructed
for individual T-P points in the mobilization zone, which was modeled by a sequence of multiwave step flowing reactors with a step of 10°C from
350–420 to 100°C at a constant pressure within the range of 600–1100 bar. We studied the effect of different background contents
of Zn and Pb in granites on the efficiency of mobilization and ore formation and compared the relations in the naturally occurring
distribution of ore elements along the continuous cross sections through Pb-Zb veins with the results of thermodynamic simulation.
It was established that ore bodies with indicated bulk and local cross sectional contents of sphalerite could be formed in
a narrow range of conditions in the mobilization zone (410–440°C and 900–1200 bar) and elevated background contents of Zn
(more than 0.007 wt %) in the host granite. The maximum sphalerite contents (bulk and local in vein cross sections) are achieved
updip the model veins within the temperature range of 150–200°C.
Original Russian Text ? M.V. Borisov, D.A. Bychkov, Yu.V. Shvarov, 2006, published in Geokhimiya, 2006, No. 11, pp. 1218–1239. 相似文献
14.
We present the software program THERIA_G, which allows for numerical simulation of garnet growth in a given volume of rock
along any pressure–temperature–time (P–T–t) path. THERIA_G assumes thermodynamic equilibrium between the garnet rim and the rock matrix during growth and accounts for
component fractionation associated with garnet formation as well as for intracrystalline diffusion within garnet. In addition,
THERIA_G keeps track of changes in the equilibrium phase relations, which occur during garnet growth along the specified P–T–t trajectory. This is accomplished by the combination of two major modules: a Gibbs free energy minimization routine is used
to calculate equilibrium phase relations including the volume and composition of successive garnet growth increments as P and T and the effective bulk rock composition change. With the second module intragranular multi-component diffusion is modelled
for spherical garnet geometry. THERIA_G allows to simulate the formation of an entire garnet population, the nucleation and
growth history of which is specified via the garnet crystal size frequency distribution. Garnet growth simulations with THERIA_G
produce compositional profiles for the garnet porphyroblasts of each size class of a population and full information on equilibrium
phase assemblages for any point along the specified P–T–t trajectory. The results of garnet growth simulation can be used to infer the P–T–t path of metamorphism from the chemical zoning of garnet porphyroblasts. With a hypothetical example of garnet growth in a
pelitic rock we demonstrate that it is essential for the interpretation of the chemical zoning of garnet to account for the
combined effects of the thermodynamic conditions of garnet growth, the nucleation history and intracrystalline diffusion.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.
相似文献
| F. GaidiesEmail: |
15.
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
16.
A numerical technique, based on a mathematical programming algorithm, is presented for the solution of geotechnical problems where elastic-plastic material behaviour is considered. The proposed approach can be adopted for geotechnical media characterized by any suitable yield condition, accounting, if necessary, for workhardening behaviour. The loading process is subdivided into a series of steps applied to a finite element mesh with geometry and material properties constant along each step, but with possible changes between subsequent steps. As an application some typical geotechnical problems are analysed by means of the proposed algorithm and a comparison is made between the available in situ measurements and the numerical results. 相似文献
17.
用三维梁-颗粒模型BPM3D(beam-particlemodelinthreedimensions)对岩石类非均质脆性材料的力学性质和破坏过程进行了数值模拟。梁-颗粒模型是在离散单元法基础上,结合有限单元法中的网格模型提出的用于模拟岩石类材料损伤破坏过程的数值模型。在模型中,材料在细观层次上被离散为颗粒单元集合体,相邻颗粒单元由有限单元法中的弹脆性梁单元联结。梁单元的力学性质均按韦伯(Weibull)分布随机赋值,以模拟岩石类材料力学参数的空间变异性。材料内部裂纹通过断开梁单元来模拟。通过自动生成的非均质材料模型对岩石类材料的破坏机理进行研究。岩石类非均质脆性材料在单轴压缩状态下破坏过程细观数值模拟结果显示,岩石材料宏观破坏是由于其内部细观裂纹产生、扩展、贯通的结果。通过数值模拟结果之间的对比分析,揭示出岩石试样宏观破坏模式随细观层次上韦伯分布参数的变化而不同。与实际矿柱破坏形态的对比分析表明了模型的适用性。根据数值模拟结果对岩石类非均质材料的破坏机理进行了探讨。 相似文献
18.
The numerical error associated with finite-difference simulation of wave propagation in discontinuous media consists of two
components. The first component is a higher-order error that leads to grid dispersion; it can be controlled by higher-order
methods. The second component results from misalignment between numerical grids and material interfaces. We provide an explicit
estimate of the interface misalignment error for the second order in time and space staggered finite-difference scheme applied
to the acoustic wave equation. Our analysis, confirmed by numerical experiments, demonstrates that the interface error results
in a first-order time shift proportional to the distance between the interface and computational grids. A 2D experiment shows
that the interface error cannot be suppressed by higher-order methods and indicates that our 1D analysis gives a good prediction
about the behavior of the numerical solution in higher dimensions.
相似文献
19.
This paper focuses on a simple numerical code to investigate the wave propagation and damage effect in a concrete slab. First,
the derivations of governing equations and a cross-format central finite difference algorithm are presented. A self-written
FORTRAN code is thus developed. Then, the Johnson–Holmquist-Concrete constitutive model is introduced and implemented into this code. Finally, after the code is verified against LS-DYNA, the
mutual coupling of combined wave loadings and the induced compression damage in the concrete slab is explored in details.
Numerical results show that this code is effective and can conveniently simulate the responses of concrete slab under different
combinations of boundary loadings. 相似文献
20.
Chiara Biscarini 《Landslides》2010,7(2):117-124
This paper describes the application of detailed computational fluid dynamics (CFD) to simulate the formation and propagation
of waves generated by the impact of landslide material with water. The problem is schematised as a multiphase–multicomponent
fluid flow: compressible air, water and transported alluvial material. The landslide simulation is performed by means of a
hybrid approach: as a rigid solid body slipping down along an inclined slope until it starts penetrating the water body. The
CFD model solves the Navier–Stokes equations with the RNG k-ɛ turbulence closure scheme and the volume of fluid multiphase
method, which maintains the interface as a sharp front. The governing equations are solved using the commercial CFD code,
FLUENT. The computed results are compared with experimental data reported in the literature. The model is then applied to
simulate the 1958 Lituya bay Tsunami event with a 2D a simplified geometry and the results are compared to others found in
literature. 相似文献