共查询到20条相似文献，搜索用时 125 毫秒
1.
《Advances in water resources》1999,22(7):711-728
Coupling advection-dominated transport to reactive processes leads to additional requirements and limitations for numerical simulation beyond those for non-reactive transport. Particularly, both monotonicity avoiding the occurence of negative concentrations, and high-order accuracy suppressing artificial diffusion, are necessary to study accurately the reactive interactions of compounds transported in groundwater. These requirements are met by non-linear Eulerian methods. Two cell-centered Finite Volume schemes are presented for the simulation of advection-dominated reactive transport. The first scheme is based on rectangular grids, whereas the second scheme requires streamline-oriented grids the generation of which is explained in an accompanying paper. Although excellent results for conservative transport are obtained by the scheme for rectangular grids, some artificial transverse mixing occurs in the case of multi-component transport. This may lead to erroneous reaction rates if the compounds interact. The transport scheme for streamline-oriented grids, on the other hand, avoids artificial transverse mixing. A quantitative comparison is given by two test cases. A conservative tracer simulation for a five-spot configuration in a heterogeneous aquifer shows a high coincidence of the breakthrough curves obtained for the two methods, whereas a test case of two reacting compounds shows significant differences. In this test case, a rate of convergence with respect to the overall reaction rates lower than first-order is calculated for the rectangular grid. 相似文献
2.
《Advances in water resources》2004,27(4):323-334
A forward particle tracking Eulerian Lagrangian localized adjoint method (ELLAM) is applied to the multicomponent reactive transport problem using a split operator approach. Two split operator algorithms are compared, the Strang algorithm and the sequential non-iterative algorithm (SNIA). The reaction equations are integrated using a coupled predictor corrector algorithm with adaptive time stepping. Reaction time steps are adjusted at the inflow boundary to reflect the actual time of transport inside the solution domain.Results show that split operator ELLAM formulations are competitive with direct or fully coupled ELLAM solutions for reactive transport problems. The SNIA algorithm is more accurate than the Strang splitting algorithm when large time steps are used. The reaction algorithm employed dominates computational effort in runs with large time step sizes. To illustrate the use of the method in practical problems, the model is fitted to aerobic aniline degradation data from laboratory scale column experiments. Model inversion is achieved using non-linear regression with a shuffled complex evolution optimization algorithm and parameter uncertainty is assessed using a Bayesian uncertainty analysis procedure. 相似文献
3.
With a depth-averaged numerical model, the tidally induced Lagrangian residual current in a model bay was studied. To correctly reflect the long-term mass transport, it is appropriate to use the Lagrangian residual velocity (LRV) rather than the Eulerian residual velocity (ERV) or the Eulerian residual transport velocity (ETV) to describe the residual current. The parameter κ, which is defined as the ratio of the typical tidal amplitude at the open boundary to the mean water depth, is considered to be the indicator of the nonlinear effect in the system. It is found that the feasibility of making the mass transport velocity (MTV) approximate the LRV is strongly dependent on κ. The error between the MTV and the LRV tends to increase with a growing κ. An additional error will come from the various initial tidal phases due to the Lagrangian drift velocity (LDV) when κ is no longer small. According to the residual vorticity equation based on the MTV, the Coriolis effect is found to influence the residual vorticity mainly through the curl of the tidal stress. A significant difference in the flow pattern indicates that the LRV is sensitive to the bottom friction in different forms. 相似文献
4.
Michela De Dominicis Giovanni Leuzzi Paolo Monti Nadia Pinardi Pierre-Marie Poulain 《Ocean Dynamics》2012,62(9):1381-1398
Ocean transport and dispersion processes are at the present time simulated using Lagrangian stochastic models coupled with Eulerian circulation models that are supplying analyses and forecasts of the ocean currents at unprecedented time and space resolution. Using the Lagrangian approach, each particle displacement is described by an average motion and a fluctuating part. The first one represents the advection associated with the Eulerian current field of the circulation models while the second one describes the sub-grid scale diffusion. The focus of this study is to quantify the sub-grid scale diffusion of the Lagrangian models written in terms of a horizontal eddy diffusivity. Using a large database of drifters released in different regions of the Mediterranean Sea, the Lagrangian sub-grid scale diffusion has been computed, by considering different regimes when averaging statistical quantities. In addition, the real drifters have been simulated using a trajectory model forced by OGCM currents, focusing on how the Lagrangian properties are reproduced by the simulated trajectories. 相似文献
5.
Marco Bianchi Hui-Hai Liu Jens T. Birkholzer 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(5):1081-1091
Laboratory experiments in rock samples collected from clay-rich formations indicate that the effective molecular diffusion coefficient (D) is a heterogeneous and anisotropic property. Since laboratory measurements of D are representative of a very small volume, upscaling is necessary in order to incorporate these data in large-scale numerical models of diffusive transport. In this work we address the problem of the estimating the equivalent diffusion coefficient (D eq ), in terms of total diffusive flux, in a three-dimensional domain characterized by a heterogeneous and anisotropic spatial distribution of D. D eq was estimated from the results of steady-state diffusive transport simulations through several realizations of the D field. The ensemble averages of D eq from fields with different degrees of heterogeneity and anisotropy were then compared with estimates from analytical upscaling expressions based on stochastic as well as power-averaging approaches. These expressions are largely based on similar expressions developed for calculating the effective hydraulic conductivity in heterogeneous and anisotropic domains. Comparisons showed that stochastic expressions provide accurate estimates of D eq only for fields characterized by low heterogeneity. Within the range of heterogeneity and anisotropy considered, our results showed that a power-averaging expression is very accurate in predicting D eq especially when the parameter p i is estimated through fitting of the numerical results. Nonetheless, the relationship between this parameter and the anisotropy ratio is linear. 相似文献
6.
We review the analysis of the dynamics of reactive transport in disordered media, emphasizing the nature of the chemical reactions and the role of small-scale fluctuations induced by the structure of the porous medium. We are motivated by results and interpretations of laboratory-scale experiments, for which detailed characterization of the system is possible. Modeling approaches based on continuum and particle tracking (PT) schemes are examined critically, highlighting how fluctuations are incorporated. The continuum approach spans a large literature. Traditional formats of reactive transport equations, such as the advection–dispersion–reaction equation (ADRE), are based on a series of assumptions related mainly to scale separation and relative magnitude of time scales involved in the reactive transport setting. These assumptions as well as further developments are assessed in depth. PT methods offer an alternative means of accounting for pore-scale dynamics, wherein space–time transitions are drawn from appropriate probability distributions that have been tested to account for anomalous transport. While PT methods have been employed for many years to describe conservative transport, their application to laboratory-scale reactive transport problems in the context of both Fickian and non-Fickian regimes is relatively recent. We concentrate on experimental observations of different types of reactions in disordered media: (1) the dynamics of a bimolecular reactive transport (A + B → C) in passive (non-reactive) media, and (2) a multi-step chemical reaction, as exemplified in the process of dedolomitization involving both dissolution and precipitation. The fluctuations in a number of the key variables controlling the processes prove to have a dominant role; elucidation of this role forms the basis of the present study and the comparison of methods. 相似文献
7.
8.
This paper presents a stochastic model for multicomponent competitive monovalent cation exchange in hierarchical porous media. Reactive transport in porous media is highly sensitive to heterogeneities in physical and chemical properties, such as hydraulic conductivity (K), and cation exchange capacity (CEC). We use a conceptual model for multimodal reactive mineral facies and develop a Eulerian-based stochastic theory to analyze the transport of multiple cations in heterogeneous media with a hierarchical organization of reactive minerals. Numerical examples investigate the retardation factors and dispersivities in a chemical system made of three monovalent cations (Na+, K+, and Cs+). The results demonstrate how heterogeneity influences the transport of competitive monovalent cations, and highlight the importance of correlations between K and CEC. Further sensitivity analyses are presented investigating how the dispersion and retardation of each cation are affected by the means, variances, and integral scales of K and CEC. The volume fraction of organic matter is shown to be another important parameter. The Eulerian stochastic framework presented in this work clarifies the importance of each system parameters on the migration of cation plumes in formations with hierarchical organization of facies types. Our stochastic approach could be used as an alternative to numerical simulations for 3D reactive transport in hierarchical porous media, which become prohibitively expensive for the multicomponent applications considered in this work. 相似文献
9.
10.
The focus of this paper is on the analysis of the influence of particles’ velocity distribution and their concentration on the sediment transport rate in bed-load from the Lagrangian perspective.Such aims are addressed by use of the relevant Lagrangian model of spherical saltating particles in which turbulence plays a significant role.The Monte Carlo approach is employed in the simulations to obtain the velocity and concentration of the saltating particles.Numerical simulations using two saltating particle models:(1) with;and(2) without particle-particle collisions are carried out.Based on the numerical results,we address the hypothesis that instead of averaged characteristics,the distributions of particles’ velocity and sediment concentration should be taken into account in the calculation of sediment transport rate.Moreover,our results also show that the interaction between particles during their collisions is the key for better understanding of the physics of sediment transport.All results are compared with well-known experimental formulae i.e.Meyer-Peter and Muller and Fernandez Luque and van Beek. 相似文献
11.
Station Helgoland Roads in the south-eastern North Sea (German Bight) hosts one of the richest long-term time series of marine
observations. Hydrodynamic transport simulations can help understand variability in the local data brought about by intermittent
changes of water masses. The objective of our study is to estimate to which extent the outcome of such transport simulations
depends on the choice of a specific hydrodynamic model. Our basic experiment consists of 3,377 Lagrangian simulations in time-reversed
mode initialized every 7 h within the period Feb 2002–Oct 2004. Fifty-day backward simulations were performed based on hourly
current fields from four different hydrodynamic models that are all well established but differ with regard to spatial resolution,
dimensionality (2D or 3D), the origin of atmospheric forcing data, treatment of boundary conditions, presence or absence of
baroclinic terms, and the numerical scheme. The particle-tracking algorithm is 2D; fields from 3D models were averaged vertically.
Drift simulations were evaluated quantitatively in terms of the fraction of released particles that crossed each cell of a
network of receptor regions centred at the island of Helgoland. We found substantial systematic differences between drift
simulations based on each of the four hydrodynamic models. Sensitivity studies with regard to spatial resolution and the effects
of baroclinic processes suggest that differences in model output cannot unambiguously be assigned to certain model properties
or restrictions. Therefore, multi-model simulations are needed for a proper identification of uncertainties in long-term Lagrangian
drift simulations. 相似文献
12.
Jan Erik H. Weber Kai H. Christensen Cléa Denamiel 《Continental Shelf Research》2009,29(11-12):1448-1453
A new theoretical approach for the wave-induced setup over a sloping beach is presented that takes into consideration the explicit variations of the surface waves due to bottom slope and viscosity. In this way, the wave forcing of the mean Lagrangian volume fluxes is calculated without assuming that the local depth is constant. The analysis is valid in the region outside the surf zone and is based on the shallow-water assumption. A novel approach for separating the viscous damping of the waves from the frictional damping of the mean flow is introduced, where the mean Eulerian velocity is applied in the bottom stress for the mean fluxes. In the case where the onshore Lagrangian mean transport is zero, a new formula is derived for the Eulerian mean free surface slope, in which the effects of bottom slope, viscous wave damping and frictional bottom drag on the mean flow are clearly identified. The analysis suggests that viscous damping of the waves and frictional dissipation of the Eulerian near-bed return flow could lead to setup outside the surf zone. 相似文献
13.
R.C. Acharya M.I.J. van Dijke K.S. Sorbie S.E.A.T.M. Van der Zee A. Leijnse 《Advances in water resources》2007
We present a 3D network model with particle tracking to upscale 3D Brownian motion of non-reactive tracer particles subjected to a velocity field in the network bonds, representing both local diffusion and convection. At the intersections of the bonds (nodes) various jump conditions are implemented. Within the bonds, two different velocity profiles are used. At the network scale the longitudinal dispersion of the particles is quantified through the coefficient DL, for which we evaluate a number of methods already known in the literature. Additionally, we introduce a new method for derivation of DL based on the first-arrival times distribution (FTD). To validate our particle tracking method, we simulate Taylor’s classical experiments in a single tube. Subsequently, we carry out network simulations for a wide range of the characteristic Péclet number Pe? to assess the various methods for obtaining DL. Using the new method, additional simulations have been carried out to evaluate the choice of nodal jump conditions and velocity profile, in combination with varying network heterogeneity. In general, we conclude that the presented network model with particle tracking is a robust tool to obtain the macroscopic longitudinal dispersion coefficient. The new method to determine DL from the FTD statistics works for the full range of Pe?, provided that for large Pe? a sufficiently large number of particles is used. Nodal jump conditions should include molecular diffusion and allow jumps in the upstream direction, and a parabolic velocity profile in the tubes must be implemented. Then, good agreement with experimental evidence is found for the full range of Pe?, including increased DL for increased porous medium heterogeneity. 相似文献
14.
We present a new streamline-based numerical method for simulating reactive solute transport in porous media. The key innovation of the method is that both longitudinal and transverse dispersion are incorporated accurately without numerical dispersion. Dispersion is approximated in a flow-oriented grid using a combination of a one-dimensional finite difference scheme and a meshless approximation. In contrast to previous hybrid alternatives to incorporate dispersion in streamline-based simulations, the proposed scheme does not require a grid and, hence, it does not introduce numerical dispersion. In addition, the proposed scheme eliminates numerical oscillations and negative concentration values even when the dispersion tensor includes the off-diagonal coefficients and the flow field is non-uniform. We demonstrate that for a set of two- and three-dimensional benchmark problems, the new proposed streamline-based formulation compares favorably to two state of the art finite volume and hybrid Eulerian–Lagrangian solvers. 相似文献
15.
Guangliang Liu Zhe Liu Huiwang Gao Zengxiang Gao Shizuo Feng 《Ocean Dynamics》2012,62(10-12):1443-1456
The Eulerian residual transport velocity and the first-order Lagrangian residual velocity for weakly nonlinear systems have been used extensively in the past to depict inter-tidal mass transport. However, these could not explain the observed net surface sediment transport pattern in Jiaozhou Bay (JZB), located on the western Yellow Sea. JZB is characterized by strong tidal motion, complex topography and an irregular coastline, which are features of typical nonlinear systems. The Lagrangian residual velocity, which is applicable to general nonlinear systems, was simulated with the water parcel tracking method. The results indicate that the composition of the Lagrangian residual velocity at different tidal phases coincides well with the observed net surface sediment transport pattern. The strong dependence of water flushing time on the initial tidal phase can also be explained by the significant intra-tidal variation of the Lagrangian residual velocity. To investigate the hydrodynamic mechanism governing the nonlinearity of the M 2 tidal system, a set of nonlinearity indexes were defined and analysed. In the surface layer, horizontal advection is the main contributor to the strong nonlinearity near the bay mouth, while in the bottom layer, the strong nonlinearity near the bay mouth may result from the vertical viscosity and horizontal advection. 相似文献
16.
Water Resources - The relationship between turbulent diffusion with Eulerian and Lagrangian scales of turbulence in natural flows is considered. An estimate of the depth-averaged Lagrangian time... 相似文献
17.
Mostafa Bakhoday Paskyabi 《Ocean Dynamics》2016,66(11):1429-1448
The dispersion and transport of single inertial particles through an oscillatory turbulent aquatic environment are examined numerically by a Lagrangian particle tracking model using a series of idealised test cases. The turbulent mixing is incorporated into the Lagrangian model by the means of a stochastic scheme in which the inhomogeneous turbulent quantities are governed by a one-dimensional k- ε turbulence closure scheme. This vertical mixing model is further modified to include the effects of surface gravity waves including Coriolis-Stokes forcing, wave breaking, and Langmuir circulations. To simplify the complex interactions between the deterministic and the stochastic phases of flow, we assume a time-invariant turbulent flow field and exclude the hydrodynamic biases due to the effects of ambient mean current. The numerical results show that the inertial particles acquire perturbed oscillations traced out as time-varying sinking/rising orbits in the vicinity of the sea surface under linear and cnoidal waves and acquire a non-looping single arc superimposed with the high-frequency fluctuations beneath the nonlinear solitary waves. Furthermore, we briefly summarise some recipes through the course of this paper on the implementation of the stochastic particle tracking models to realistically describe the drift and suspension of inertial particles throughout the water column. 相似文献
18.
The residence time of a tracer in a control domain is usually computed by releasing tracer parcels and registering the time when each of these tracer parcels cross the boundary of the control domain. In this Lagrangian procedure, the particles are discarded or omitted as soon as they leave the control domain. In a Eulerian approach, the same approach can be implemented by integrating forward in time the advection–diffusion equation for a tracer. So far, the conditions to be applied at the boundary of the control domain were uncertain. We show here that it is necessary to prescribe that the tracer concentration vanishes at the boundary of the control domain to ensure the compatibility between the Lagrangian and Eulerian approaches. When we use the Constituent oriented Age and Residence time Theory (CART), this amounts to solving the differential equation for the residence time with boundary conditions forcing the residence time to vanish at the open boundaries of the control domain. Such boundary conditions are likely to induce the development of boundary layers (at outflow boundaries for the tracer concentration and at inflow boundaries for the residence time). The thickness of these boundary layers is of the order of the ratio of the diffusivity to the velocity. They can however be partly smoothed by tidal and other oscillating flows. 相似文献
19.
A Lagrangian marker particle in Eulerian finite difference cell solution to the three-dimensional incompressible mass transport equation was developed for predicting particulate transport in coastal and estuarine waters. Special features of the solution procedure include a finite difference grid network which translates horizontally and vertically with the mean particle motion and expands with the dispersive growth of the marker particle cloud. The cartesian vertical coordinate of the three-dimensional mass transport equation has been transformed, using instantaneous water column depth to allow adaptation to flow situations with a temporally and spatially varying bottom topography and free surface. Results from this model for turbulent diffusion and advection of a uniform plug flow of sediment in an unbounded uniform flow field with various sediment settling velocities were in excellent agreement with the corresponding analytic solutions. Using current information from a two-dimensional vertically averaged hydrodynamic's model, the model was utilized to predict the long term diffusion and advection of dilute neutrally and negatively buoyant suspended sediment clouds resulting from a hypothetical instantaneous release of dredge spoil waste at Brown's Ledge in Rhode Island Sound. 相似文献
20.
Andrew Lane 《Ocean Dynamics》2005,55(5-6):541-548
The development and application of a Lagrangian particle-tracking model to simulate sediment transport in the Mersey Estuary
(UK) is described. Each of the particles (up to a million in total) is advected horizontally by the 3-D tidal currents. Related
vertical movements are: (1) downwards by settlement at a prescribed velocity w
s and (2) both upwards and downwards by a distance related to the vertical eddy diffusivity. In a novel departure from traditional
practice, where initial distributions of surficial sediments are specified, all particles are introduced at the seaward boundary
of the model. Provenance studies indicate surficial sediments are overwhelmingly of marine origin. For the predominant fine
sediments, ‘cyclical convergence’ in suspended sediment concentrations is approximated after about two spring-neap tidal cycles.
Comparisons are shown between the suspended sediment concentrations and net deposition rates computed by this model against
observed values and earlier computations utilising both 1-D and 3-D Eulerian models. While all of these results are in broad
agreement, the flexibility of the Lagrangian approach for simulating flocculation, consolidation and mixed sediments illustrates
its future potential. 相似文献