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1.
This paper describes a stochastic analysis of steady state flow in a bounded, partially saturated heterogeneous porous medium subject to distributed infiltration. The presence of boundary conditions leads to non-uniformity in the mean unsaturated flow, which in turn causes non-stationarity in the statistics of velocity fields. Motivated by this, our aim is to investigate the impact of boundary conditions on the behavior of field-scale unsaturated flow. Within the framework of spectral theory based on Fourier–Stieltjes representations for the perturbed quantities, the general expressions for the pressure head variance, variance of log unsaturated hydraulic conductivity and variance of the specific discharge are presented in the wave number domain. Closed-form expressions are developed for the simplified case of statistical isotropy of the log hydraulic conductivity field with a constant soil pore-size distribution parameter. These expressions allow us to investigate the impact of the boundary conditions, namely the vertical infiltration from the soil surface and a prescribed pressure head at a certain depth below the soil surface. It is found that the boundary conditions are critical in predicting uncertainty in bounded unsaturated flow. Our analytical expression for the pressure head variance in a one-dimensional, heterogeneous flow domain, developed using a nonstationary spectral representation approach [Li S-G, McLaughlin D. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour Res 1991;27(7):1589–605; Li S-G, McLaughlin D. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour Res 1995; 31(3):541–51], is precisely equivalent to the published result of Lu et al. [Lu Z, Zhang D. Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via Kirchhoff transformation. Adv Water Resour 2004;27:775–84]. 相似文献
2.
《Advances in water resources》2003,26(10):1041-1060
A new technique for generating coarse scale models of highly heterogeneous subsurface formations is developed and applied. The method uses generic global coarse scale simulations to determine the boundary conditions for the local calculation of upscaled properties (permeability or transmissibility). An iteration procedure assures consistency between the local and global calculations. Transport processes are simulated using a subgrid velocity reconstruction technique applied in conjunction with the local–global upscaling procedure. For highly heterogeneous (e.g., channelized) systems, the new method is shown to provide considerably more accurate coarse scale models for flow and transport, relative to reference fine scale results, than do existing local (and extended local) upscaling techniques. The applicability of the upscaled models for different global boundary conditions is also considered. 相似文献
3.
A methodology for transport upscaling of three-dimensional highly heterogeneous formations is developed and demonstrated. The overall approach requires a prior hydraulic conductivity upscaling using an interblock-centered full-tensor Laplacian-with-skin method followed by transport upscaling. The coarse scale transport equation includes a multi-rate mass transfer term to compensate for the loss of heterogeneity inherent to all upscaling processes. The upscaling procedures for flow and transport are described in detail and then applied to a three-dimensional highly heterogeneous synthetic example. The proposed approach not only reproduces flow and transport at the coarse scale, but it also reproduces the uncertainty associated with the predictions as measured by the ensemble variability of the breakthrough curves. 相似文献
4.
In this Comment on the recent work (Zhu and Ma, 2013) [11] by Zhu and Ma (ZM) we first show that all three local gray Lattice Boltzmann (GLB) schemes in the form (Zhu and Ma, 2013) [11]: GS (Chen and Zhu, 2008; Gao and Sharma, 1994) [1,4], WBS (Walsh et al., 2009) [12] and ZM, fail to get constant Darcy’s velocity in series of porous blocks. This inconsistency is because of their incorrect definition of the macroscopic velocity in the presence of the heterogeneous momentum exchange, while the original WBS model (Walsh et al., 2009) [12] does this properly. We improve the GS and ZM schemes for this and other related deficiencies. Second, we show that the “discontinuous velocity” they recover on the stratified interfaces with their WBS scheme is inherent, in different degrees, to all LBE Brinkman schemes, including ZM scheme. None of them guarantees the stress and the velocity continuity by their implicit interface conditions, even in the frame of the two-relaxation-times (TRT) collision operator where these two properties are assured in stratified Stokes flow, Ginzburg (2007) [5]. Third, the GLB schemes are presented in work (Zhu and Ma, 2013) [11] as the alternative ones to direct, Brinkman-force based (BF) schemes (Freed, 1998; Nie and Martys, 2007) [3,8]. Yet, we show that the BF-TRT scheme (Ginzburg, 2008) [6] gets the solutions of any of the improved GLB schemes for specific, viscosity-dependent choice of its one or two local relaxation rates. This provides the principal difference between the GLB and BF: while the BF may respect the linearity of the Stokes–Brinkman equation rigorously, the GLB-TRT cannot, unless it reduces to the BF via the inverse transform of the relaxation rates. Furthermore, we show that, in limited parameter space, “gray” schemes may run one another. From the practical point of view, permeability values obtained with the GLB are viscosity-dependent, unlike with the BF. Finally, the GLB shares with the BF a so-called anisotropy (Ginzburg, 2008; Nie and Martys, 2007) [6,8], that is, flow-direction-dependency in their effective viscosity corrections, related to the discretized spatial variation of the resistance forcing. 相似文献
5.
The purpose of this study is to quantify the dispersivity in the longitudinal direction by upscaling pore scale mixing over a network domain and to verify the dispersivity with that obtained through the more rigorous upscaling technique, the Brownian particle tracking model (BPTM). We model a porous medium with a network of pore-units that are comprised of pore bodies and bonds of finite volume. Such a pore-unit is assumed to be a mixing cell with the steady state flow condition for a single fluid. Dispersivity can be obtained by solving the mixing cell model (MCM) for the concentration in each pore-unit and by averaging the concentrations for a large number of pore units (as a function of time and space). A minimal size of network that ascertains an asymptotic value of dispersivity was determined and verified with large size pore networks. This numerically computed dispersivity is compared with the results from the BPTM for the same porous medium and flow conditions. We show that the dispersivity obtained from the MCM is equally reliable for the heterogeneous pore-networks and can be estimated as a function of pore size heterogeneity. For homogeneous networks with the MCM, the iteration time step plays an important role. On the other hand, for networks with the BPTM, the assumption of intra-bond velocity profile affects the results. 相似文献
6.
A new MODFLOW package (Nonlinear Flow Process; NLFP) simulating nonlinear flow following the Forchheimer equation was developed and implemented in MODLFOW‐2005. The method is based on an iterative modification of the conductance calculated and used by MODFLOW to obtain an effective Forchheimer conductance. The package is compatible with the different layer types, boundary conditions, and solvers as well as the wetting capability of MODFLOW. The correct implementation is demonstrated using four different benchmark scenarios for which analytical solutions are available. A scenario considering transient flow in a more realistic setting and a larger model domain with a higher number of cells demonstrates that NLFP performs well under more complex conditions, although it converges moderately slower than the standard MODFLOW depending on the nonlinearity of flow. Thus, this new tool opens a field of opportunities to groundwater flow simulation with MODFLOW, especially for core sample simulation or vuggy karstified aquifers as well as for nonlinear flow in the vicinity of pumping wells. 相似文献
7.
In this paper, we focus on strength properties of double porous materials having a Drucker-Prager solid phase at microscale. The porosity consists in two populations of micropores and mesopores saturated with different pressures. To this end, we consider a hollow sphere subjected to a uniform strain rate boundary conditions. For the microscale to mesoscale transition, we take advantage of available results by Maghous et al. (2009), while the meso to macro upscaling is performed by implementing a kinematical limit analysis approach using Eshelby-like trial velocity fields. This two-step homogenization procedure delivers analytical expression of the macroscopic criterion for the considered class of saturated double porous media. This generalizes and improves previous results established by Shen et al. (2014). The results are discussed in terms of the existence or not of effective stresses. Some illustrations are provided. 相似文献
8.
A Eulerian analytical method is developed for nonreactive solute transport in heterogeneous, dual-permeability media where the hydraulic conductivities in fracture and matrix domains are both assumed to be stochastic processes. The analytical solution for the mean concentration is given explicitly in Fourier and Laplace transforms. Instead of using the fast fourier transform method to numerically invert the solution to real space (Hu et al., 2002), we apply the general relationship between spatial moments and concentration (Naff, 1990; Hu et al., 1997) to obtain the analytical solutions for the spatial moments up to the second for a pulse input of the solute. Owing to its accuracy and efficiency, the analytical method can be used to check the semi-analytical and Monte Carlo numerical methods before they are applied to more complicated studies. The analytical method can be also used during screening studies to identify the most significant transport parameters for further analysis. In this study, the analytical results have been compared with those obtained from the semi-analytical method (Hu et al., 2002) and the comparison shows that the semi-analytical method is robust. It is clearly shown from the analytical solution that the three factors, local dispersion, conductivity variation in each domain and velocity convection flow difference in the two domains, play different roles on the solute plume spreading in longitudinal and transverse directions. The calculation results also indicate that when the log-conductivity variance in matrix is 10 times less than its counterpart in fractures, it will hardly influence the solute transport, whether the conductivity field is matrix is treated as a homogeneous or random field. 相似文献
9.
Optimization of groundwater and other subsurface resources requires analysis of multiple‐well systems. The usual modeling approach is to apply a linear flow equation (e.g., Darcy's law in confined aquifers). In such conditions, the composite response of a system of wells can be determined by summating responses of the individual wells (the principle of superposition). However, if the flow velocity increases, the nonlinear losses become important in the near‐well region and the principle of superposition is no longer valid. This article presents an alternative method for applying analytical solutions of non‐Darcy flow for a single‐ to multiple‐well systems. The method focuses on the response of the central injection well located in an array of equally spaced wells, as it is the well that exhibits the highest pressure change within the system. This critical well can be represented as a single well situated in the center of a closed square domain, the width of which is equal to the well spacing. It is hypothesized that a single well situated in a circular region of the equivalent plan area adequately represents such a system. A test case is presented and compared with a finite‐difference solution for the original problem, assuming that the flow is governed by the nonlinear Forchheimer equation. 相似文献
10.
This paper presents a new perturbation solution of the non-linear Boussinesq equation for one-dimensional tidal groundwater flow in a coastal unconfined aquifer. Built upon the work of Parlange et al. [Parlange, J.-Y., Stagnitti, F., Starr, J.L., Braddock, R.D., 1984. Free-surface flow in porous media and periodic solution of the shallow-flow approximation, J. Hydrol., 70, 251–263], the solution adopts a new perturbation parameter that is by definition less than unit, and thus is applicable to a wider range of physical conditions within the constraint of the Boussinesq approximation. This approach avoids a secular term in the third-order perturbation equation of Parlange et al. (1984), enabling the derivation of the third- and higher-order solutions. In comparison with a numerical (“exact”) solution, the new perturbation solution is shown to be slightly more accurate than that of Parlange et al. (1984) with the second-order approximation. The obtained third-order solution exhibits considerable improvement in accuracy. In relatively simple analytical forms, the present perturbation solution will help to understand better the non-linear characteristics of tidal water table fluctuations in as modeled by the non-linear Boussinesq equation coastal unconfined aquifers. 相似文献
11.
SPH simulation of free surface flow over a sharp-crested weir 总被引：1，自引：0，他引：1
In this paper the numerical simulation of a free surface flow over a sharp-crested weir is presented. Since in this case the usual shallow water assumptions are not satisfied, we propose to solve the problem using the full weakly compressible Navier–Stokes equations with the Tait equation of state for water. The numerical method used consists of the new meshless Smooth Particle Hydrodynamics (SPH) formulation proposed by Ferrari et al. (2009) [8], that accurately tracks the free surface profile and provides monotone pressure fields. Thus, the unsteady evolution of the complex moving material interface (free surface) can been properly solved. The simulations involving about half a million of fluid particles have been run in parallel on two of the most powerful High Performance Computing (HPC) facilities in Europe. The validation of the results has been carried out analysing the pressure field and comparing the free surface profiles obtained with the SPH scheme with experimental measurements available in literature [18]. A very good quantitative agreement has been obtained. 相似文献
12.
J. S. Frederiksen 《地球物理与天体物理流体动力学》2013,107(1-4):85-97
Abstract A new nonlinear stability criterion is derived for baroclinic flows over topography in spherical geometry. The stability of a wide class of exact three-dimensional nonlinear steady state solutions subject to arbitrary disturbances is established. The resonance condition, at the highest total wavenumber, for the steady state solutions and the stability criteria for baroclinic flow in the absence of topography provide the boundaries of the regions of stability in the presence of topography. The analogous results for flow on periodic or infinite beta planes incorporating non-orthogonal function large scale flows are also discussed. 相似文献
13.
We present a generic, semi-automated algorithm for generating non-uniform coarse grids for modeling subsurface flow. The method is applicable to arbitrary grids and does not impose smoothness constraints on the coarse grid. One therefore avoids conventional smoothing procedures that are commonly used to ensure that the grids obtained with standard coarsening procedures are not too rough. The coarsening algorithm is very simple and essentially involves only two parameters that specify the level of coarsening. Consequently the algorithm allows the user to specify the simulation grid dynamically to fit available computer resources, and, e.g., use the original geomodel as input for flow simulations. This is of great importance since coarse grid-generation is normally the most time-consuming part of an upscaling phase, and therefore the main obstacle that has prevented simulation workflows with user-defined resolution. We apply the coarsening algorithm to a series of two-phase flow problems on both structured (Cartesian) and unstructured grids. The numerical results demonstrate that one consistently obtains significantly more accurate results using the proposed non-uniform coarsening strategy than with corresponding uniform coarse grids with roughly the same number of cells. 相似文献
14.
The classical continuum model for the linear vertical vibrations of a suspension bridge (Bleich et al., 1950 [1]) is re-examined. The primary objective of the study is to extend the definitive analytical and numerical results of Irvine and Caughey (1974) [2], Irvine and Griffin (1976) [3] and Irvine (1980, 1981) [4], [5] for the natural frequencies, mode shapes, and modal participation factors for an extensible suspension cable, which depend on one dimensionless parameter related to the elasticity of the cable, to the case of a stiffened suspension bridge in which the response depends also on a second dimensionless parameter related to the stiffness of the girder. The continuum suspension bridge model is also used to understand the pattern of variation of mode shapes as a function of cable elasticity and girder stiffness, which has been shown by West et al. (1984) [6] to be considerably more complex than that for a suspension cable. Finally, the threshold amplitudes of free vibrations that would result in the incipient slackening of the hangers are determined. 相似文献
15.
Coupled groundwater–surface water (GW–SW) models are capable of simulating complex hydrological systems when used at fine resolutions. However, properly characterizing bulk GW–SW fluxes for either coarsely resolved integrated models or basin‐discretized surface water models remains a challenge. Loss of subgrid detail, while beneficially decreasing computational cost, leads to a decrease in model accuracy as scale effects become important. Ideally, coarse low‐resolution models should be informed by expected subgrid behaviour, reducing the impact of scale effects. Determining how to best represent these fine‐scale details in lower‐resolution models is important for improving the accuracy and appropriateness of these models. To investigate some of these scale effects, we here explore the relationships between area‐averaged hydraulic head and bulk GW–SW exchange fluxes (e.g. evapotranspiration and discharge), all of which are presumed to be controlled predominantly by subgrid topographic effects. These relationships may be useful for simply upscaling models without the complete loss of crucial fine‐resolution subgrid details. Using finely resolved simulation output from Modflow for a fine‐resolution simulation and post‐processed results generated to represent coarser resolutions, upscaled flux relationships (UFRs) are generated for multiple terrains; these UFRs define the relationships that exist between average hydraulic head and average fluxes in unconfined aquifer systems. It is found that, for steady‐flow regimes, similar one‐to‐one power law relationships consistently exist between area‐averaged hydraulic heads, exchange fluxes and saturated area for a variety of terrains. Additionally, when the averaged values are properly normalized, the generated steady‐state UFRs for a single terrain are independent of hydraulic conductivity and potential evapotranspiration rates and apparently insensitive to the presence of mild heterogeneity. While some hysteresis is apparent in the relationships under transient conditions, transient artefacts are shown to be minor under some circumstances, indicating that UFRs may be applied to both steady‐state and transient scenarios. Simpler tests performed under saturated and variably saturated conditions in a cross‐sectional model show similar trends, suggesting that the UFR representation is extendable to systems where the vadose zone plays a significant role. It is suggested that relatively simple UFRs such as these may find use as an alternative to direct point upscaling or multi‐resolution models for estimating GW–SW exchange fluxes in coarse‐scale models. They also appear to justify the functional form of some classical models of baseflow and evapotranspiration used in conceptual surface water models. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
16.
The equations of state (EOSs) of MgO produced by two independent scale-free methods, (1) the simultaneous elastic wave velocity and in situ synchrotron X-ray measurements (Kono et al., 2010; Li et al., 2006) and (2) the first-principles calculations (Wu et al., 2008), agree well with each other to at least 150 GPa and 2000 K. Furthermore, the EOS from first-principles calculations also agrees well with shock wave data, another pressure-scale-free data. These agreements strongly support that these EOSs provide reliable absolute pressure scales. Here we evaluate Au and Pt EOSs based on the EOS of Wu et al. (2008) using the simultaneously measured volume data of MgO, Au, and Pt from the literature. The primary pressure scales developed by Tange et al. (2009) and Yokoo et al. (2009) using only pressure-scale-free experimental data of MgO, Au, and Pt produce internal consistent pressure and agree with EOS of Wu et al. (2008). The Au EOS by Tsuchiya (2003) works well at room temperature but underestimates pressure at high temperature. The Au EOS by Fei et al. (2007) can well describe thermal pressure. The EOSs of Pt by Holmes et al. (1989) and Ono et al. (2011) work well at both room temperature and high temperature. The results also suggest that the discrepancy between bulk modulus of iron from experiments (Mao et al., 1990) and those from Earth’s core (Dziewonski and Anderson, 1981) is not originated from the overestimation of pressure by the EOS of Holmes et al. (1989). At high pressure and temperature, pressure uncertainty resulted from volume error becomes similarly important as the accuracy of the pressure scale. 相似文献
17.
The generation and further nonlinear dynamics of internal gravity wave (IGW) structures in a dissipative ionosphere in the presence of an inhomogeneous zonal wind (shear flow) have been studied. The effectiveness of the IGW amplification mechanism during the interaction with an inhomogeneous zonal wind is analyzed based on the corresponding model system of nonlinear dynamic equations constructed in (Aburjania et al., 2013). It has been indicated that IGWs effectively obtain the shear flow energy at the initial linear evolution stage and substantially (by an order of magnitude) increase their amplitude and, correspondingly, energy. The nonlinear self-localization mechanism starts operating with increasing amplitude, and the process terminates with the self-organization of nonlinear solitary strongly localized vortex structures. A new degree of system freedom and the disturbance evolution trend in a medium with a shear flow appear in such a way. Nonlinear IGW structures can be a purely monopoly vortex, a transverse vortex chain, and/or a longitudinal vortex path against the background of an inhomogeneous zonal wind, depending on the shear flow velocity profile. The accumulation of such vortices in the ionospheric medium can generate a strongly turbulent state. 相似文献
18.
This paper describes analytical solutions for assessing the axial dynamic response of the shaft of a pile subjected to vibratory loads, with particular reference to pile vibratory driving. Radial inhomogeneity arising from shear modulus degradation is accounted for by assuming continuous variations of the medium properties. This approach alleviates wave reflections from the interface between inner (nonlinear) and outer (linear) zones. Novel analytical solutions are presented for two cases describing the radial decrease of the soil modulus according to (a) a linear law and (b) a parabolic law. The results are evaluated over a wide range of parameters and compared with those obtained by a semi-analytical model derived from Michaelides et al. [14], [15] and by a radial discrete model simulating the pile and soil movements from integration of the laws of motion (Hipervib-II model) (Holeyman [8]). 相似文献
19.
Periodic variations in magma discharge rate and ground deformation have been commonly observed during lava dome eruptions. We performed a stability analysis of a conduit flow model by Barmin et al. [Barmin, A., Melnik, O., Sparks, R.S.J., 2002. Periodic behavior in lava dome eruptions. Earth and Planetary Science Letters 199 (1-2), 173–184], in which the periodic variations in magma flow rate and chamber pressure are reproduced as a result of the temporal and spatial changes of the magma viscosity controlled by the kinetics of crystallization. The model is reduced to a dynamical system where the time derivatives of the magma flow rate (dQ/dt) and the chamber pressure (dP/dt) are functions of Q and P evaluated at a shifted time t − t?. Here, the time delay t? represents the time for the viscosity of fluid particle to increase in a conduit. The dynamical system with time delay is approximated by a simple two-dimensional dynamical system of Q and P where t? is given as a parameter. The results of our linear stability analyses for these dynamical systems indicate that the transition from steady to periodic flow depends on nonlinearities in the steady state relation between Q and P. The steady state relation shows a sigmoidal curve in Q − P phase plane; its slope has negative values at intermediate flow rates. The steady state solutions become unstable, and hence P and Q oscillate periodically, when the negative slope of the steady state relation ([dP/dQ]S) exceeds a critical value; that is [dP/dQ]S < − t?γ/(2Vch), where Vch is the chamber volume and γ is an elastic constant which is related to the rigidity of chamber wall. We also found that the period and the pattern of oscillation of the conduit flow primarily depend on a quantity defined by LVch/r4, where L is the conduit length and r is the conduit radius. 相似文献
20.
Lawrence H. Tanner Sonia Calvari 《Journal of Volcanology and Geothermal Research》2004,137(4):329-340
The role of sector collapse in the generation of catastrophic volcanigenic tsunami has become well understood only recently, in part because of the problems in the preservation and recognition of tsunami deposits. Tinti et al. [Tinti, S., Bortolucci, E., Romagnoli, C., 2000. Computer simulations of tsunamis due to sector collapse at Stromboli, Italy. J. Volcanol. Geotherm. Res. 96, 103–128] modeled a tsunami produced by the c. 5,000 years BP collapse of the Sciara del Fuoco on the island volcano Stromboli. Although deposits associated with this event are generally lacking on the island, volcaniclastic breccias on the SE side of the island extending to an elevation above 120 m a.s.l. may have been generated by this tsunami. Deposits above 100 m are dominated by coarse breccias comprising disorganized, poorly sorted, nonbedded, angular to subangular lava blocks in a matrix of finer pyroclastic debris. These breccias are interpreted as a water-induced mass flow, possibly a noncohesive debris flow, generated as colluvial material on steep slopes was remobilized by the return flow of the tsunami wave, the run-up of which reached an elevation exceeding 120 m a.s.l. Finer breccias of subrounded to rounded lava blocks cropping out at 15 m a.s.l. are similar to modern high-energy beach deposits and are interpreted as beach material redeposited by the advancing tsunami wave. The location of these deposits matches the predicted location of the maximum tsunami wave amplitude as calculated by modeling studies of Tinti et al. [Tinti, S., Bortolucci, E., Romagnoli, C., 2000. Computer simulations of tsunamis due to sector collapse at Stromboli, Italy. J. Volcanol. Geotherm. Res. 96, 103–128]. Whereas the identification and modeling of paleo-tsunami events is typically based on the observation of the sedimentary deposits of the tsunami run-up, return flow may be equally or more important in controlling patterns of sedimentation. 相似文献