Two-phase SPH modelling of advective diffusion processes

This paper deals with a two-dimensional numerical model based on the smoothed particle hydrodynamics (SPH) technique for the evaluation of the concentration field of pollutants in water. A SPH model is formulated to solve the fickian diffusion equation applied to pollutants with the same density as the water. A lagrangian SPH formalism of the advective diffusion equation is also developed for pollutant-water, taking into account the effects of molecular diffusion and natural advection induced by differences between the fluid densities. These equations are coupled with the fluid mechanics equations. Attention is paid to the numerical aspects involved in the solution procedure and to the optimization of the model parameters. Environmental engineering problems concerning diffusion and natural advection phenomena occur in the presence of a pollutant in still water. Numerical tests referring to a strip and a bubble of contaminant in a water tank with different initial concentration laws have been carried out. The results obtained by the proposed SPH models are compared with other available SPH formulations, showing an overall better agreement with standard analytical solutions in terms of spatial evolution of the concentration values. Capabilities and limits of the proposed SPH models to simulate advective diffusion phenomena for a wide range of density ratios are discussed.     

Spreading of oil on water in the surface-tension regime

The third stage of oil spreading on water, in which surface-tension force promotes spreading against the resisting viscous effect, is investigated using a similarity solution in combination with an integral boundary-layer technique to solve the unidirectional oil-spreading dynamics problem in the last stage of spreading. The thin layer is assumed to be supplied by oil from a bulk boundary. Using a constitutive equation for oil-film surface tension versus oil-film thickness, analytical solutions near the bulk boundary and near the edge are developed. Using the asymptotic solutions to initiate integration, the differential equations for the oil thickness, oil velocity, and boundary-layer profiles are integrated starting from the leading edge and bulk boundary, which after matching provide a complete solution. The results for the spreading-law prefactors are found to differ by about 10 % from published theoretical results using the same constitutive equation. Using an empirical constitutive equation for oil-film surface tension versus distance from the bulk boundary leads to a spreading-law prefactor that is in excellent agreement with the published experimental result and published theoretical work providing and using the same empirical constitutive equation.     

Plume rise and spread in buoyant releases from elevated sources in the lower atmosphere

This study focuses on the influence of emission conditions—velocity and temperature—on the dynamics of a buoyant gas release in the atmosphere. The investigations are performed by means of wind tunnel experiments and numerical simulations. The aim is to evaluate the reliability of a Lagrangian code to simulate the dispersion of a plume produced by pollutant emissions influenced by thermal and inertial phenomena. This numerical code implements the coupling between a Lagrangian stochastic model and an integral plume rise model being able to estimate the centroid trajectory. We verified the accuracy of the plume rise model and we investigated the ability of two Lagrangian models to evaluate the plume spread by means of comparisons between experiments and numerical solutions. A quantitative study of the performances of the models through some suitable statistical indices is presented and critically discussed. This analysis shows that an additional spread has to be introduced in the Lagrangian trajectory equation in order to account the dynamical and thermal effects induced by the source conditions.     

Analytical solutions of three-dimensional contaminant transport in uniform flow field in porous media: A library

The purpose of this study is to present a library of analytical solutions for the three-dimensional contaminant transport in uniform flow field in porous media with the first-order decay, linear sorption, and zero-order production. The library is constructed using Green’s function method (GFM) in combination with available solutions. The library covers a wide range of solutions for various conditions. The aquifer can be vertically finite, semi-infinitive or infinitive, and laterally semi-infinitive or infinitive. The geometry of the sources can be of point, line, plane or volumetric body; and the source release can be continuous, instantaneous, or by following a given function over time. Dimensionless forms of the solutions are also proposed. A computer code FlowCAS is developed to calculate the solutions. Calculated results demonstrate the correctness of the presented solutions. The library is widely applicable to solve contaminant transport problems of one- or multiple- dimensions in uniform flow fields.     

A numerical model of periodically forced circulation near the shore of a lake

Numerical calculations for a model of the near-shore circulation in a lake subject to two diurnal forcing mechanisms are presented. The first mechanism is a heating/cooling term in the heat equation representing the daytime heating and nighttime cooling of the diurnal cycle. The second is a periodic surface stress modelling a sea-breeze/gully wind system typical of some coastal regions. The two forcing mechanisms can either act together or against each other depending on their relative phase. The numerical solutions are compared with previously published analytical solutions and used to explore the extra dynamics associated with non-linear effects (specifically advection). The latter dynamics include the formation of gravity currents and unstable density profiles leading to secondary circulation.     

Analytical evaluation of mesoscale fluxes and pressure field

Terrain in natural areas is never homogeneous: there may be a variety of vegetation types and patches of vegetated and unvegetated areas which can modify the mesoscale atmospheric flow. Moreover, horizontal thermal inhomogeneities in the planetary boundary layer are a well known source of mesoscale circulation systems such as land and sea breezes, mountain-valley winds, and urban heat island circulations. Since those phenomena are not resolved in regional scale numerical models, therefore an analytic procedure able to evaluate the relative importance of mesoscale and turbulent heat fluxes associated with surface thermal heterogeneities is of crucial importance in the optic of developing a parameterization of mesoscale effects generated by these heterogeneities for use in larger scale models. In the present paper we analyze how small a horizontal variation in surface heating can be and still produce a significant mesoscale circulation, how the heat and momentum fluxes associated to mesoscale flows can penetrate deeply into the mid-troposphere, and how they modify tropospheric relevant climate parameters, such as the atmospheric static stability. In addition, we evaluate the terms of the pressure gradient force, nonlinear and linear, non-hydrostatic and hydrostatic, as function of time and space scales of the mesoscale flow. The present paper is mainly a review of analytical results, the numerical comparison and verification using RAMS is in progress.     

Analytical solution of the system sensitivity equation associated with a linear model

In this paper an analytical derivation of the sensitivity of a linear model to a given parameter is presented. This derivation avoids the numerical solution of the system sensitivity equation associated with the model

$\text{dx/dt=Ax, x(0)=x}{}_0$

and thus reduces the amount of computer time and memory needed to make a comprehensive analysis. Moreover, because of its analytical nature no numerical errors of approximation are made.     

Testing Accuracy of Finite Element and Random Walk Schemes in Prediction of Pollutant Dispersion in Coastal Waters

Distribution of pollutants in coastal waters is usually represented by depth averaged twodimensional convection-dispersion equation. Under very specific conditions this equation can be solved analytically. Although such a solution is restricted to simplified situations it provides a very useful case for testing the performance of various numerical solution techniques currently available for the simulation of convective-dispersion of pollutants in natural water systems. In this paper the analytical solution of the convective dispersion equation is used as a benchmark against which the accuracy of other techniques are assessed. These assessments are based on quantitative comparisons between the results of the solution of two-dimensional convection-dispersion equation by the deterministic finite element and stochastic random walk methods. Both Eulerian and Lagrangian frameworks are employed to obtain the finite element solution of the convection-dispersion problem. It has been shown that the Lagrange–Galerkin finite element scheme yields the most accurate results for the case under study. However, computational costs of the Lagrange–Galerkin method can be relatively high and under certain conditions it may be reasonable to use a less accurate but cost effective random walk scheme to make water quality management decisions.     

Analytical solution of two-dimensional advection–dispersion equation with spatio-temporal coefficients for point sources in an infinite medium using Green’s function method

In the present study analytical solutions of a two-dimensional advection–dispersion equation (ADE) with spatially and temporally dependent longitudinal and lateral components of the dispersion coefficient and velocity are obtained using Green’s Function Method (GFM). These solutions describe solute transport in infinite horizontal groundwater flow, assimilating the spatio-temporal dependence of transport properties, dependence of dispersion coefficient on velocity, and the particulate heterogeneity of the aquifer. The solution is obtained in the general form of temporal dependence and the source term, from which solutions for instantaneous and continuous point sources are derived. The spatial dependence of groundwater velocity is considered non-homogeneous linear, whereas the dispersion coefficient is considered proportional to the square of spatial dependence of velocity. An asymptotically increasing temporal function is considered to illustrate the proposed solutions. The solutions are validated with the existing solutions derived from the proposed solutions in three special cases. The effect of spatially/temporally dependent heterogeneity on the solute transport is also demonstrated. To use the GFM, the ADE with spatio-temporally dependent coefficients is reduced to a dispersion equation with constant coefficients in terms of new position variables introduced through properly developed coordinate transformation equations. Also, a new time variable is introduced through a known transformation.     

Can pollution tax rebates protect low-wage earners?

Pollution taxes are believed to burden low-income households that spend a greater than average share of income on pollution-intensive goods. Some proposals offset that effect by returning revenue to low-income workers via reduced labor tax. We build analytical general equilibrium models with both high-skilled and low-skilled labor, and we solve for the change in real net wage of each group. Decomposition shows the separate effects of the tax rebate, higher product prices, and the changes in relative wage rates. We also include numerical examples. Even though the pollution tax injures both types of labor, in most cases we find that returning all of the revenue to low-skilled workers is still not enough to offset higher product prices. Changes in relative wage rates may further hurt low-skilled labor. Protecting low-income workers is possible in this model only if they are defined as those below a relatively low wage threshold, but we discuss many possible elaborations of this model that could affect those results.     

Modelling nature-like fishway flow around unsubmerged obstacles using a 2D shallow water model

In the scope to create efficient nature like fish ramps using large-scale roughness elements, the present study is an audit of modelling such complex 3D free surface flows using an industrial 2D code solving shallow water equations. Validation procedure is based upon the comparison between numerous experimental measurements and numerical runs around large-scale roughness patterns disposed on the flume bottom in order to determine what 2D reliable numerical results can be expected. In this paper, we focused on cases of unsubmerged obstacles. The results demonstrate that 2D shallow water modelling using an industrial code such as TELEMAC-2D can be a convenient way for the hydraulic engineer to help design a nature-like fishway. This article emphasizes the limitations due to 2D depth integration of velocities and turbulence modelling and gives the domain of validity of the method.     

气相抽提去除红壤中挥发性有机污染物的去污机理探讨

通过探讨土壤气相抽提去除红壤中挥发性有机污染物的去污机理,建立了一维稳态条件下污染物在土壤多孔介质中传质的总微分方程,分别求出了平衡模型和动力学模型的解析解和数值解,并用实验结果对平衡模型和动力学模型进行了模拟和验证.实验结果和模型模拟结果表明理论模型与实验结果吻合良好,平衡模型和动力学模型在描述污染物在土柱通风过程中的传质时,分别适用于不同的阶段.在通风初期平衡模型能够很好地描述实验结果,而随着时间的推移,平衡模型的预测曲线逐渐偏离数据点,到了通风中后期,只有动力学模型才能够较好地描述和预测实验结果.     

Environmental conflicts in mineral development

In the 1980s conflicts over the extraction and use of natural resources will increase. While some of these controversies are unavoidable, many are manufactured when people choose inappropriate methods for responding to problems. This paper explores five ways industry creates its own problems and how it can avoid doing so. They are: failure to provide adequate information to the public; relying on stereotypes in making decisions; ignoring a problem, hoping that it will disappear; assuming that technical solutions are sufficient to solve a problem; depending on archaic techniques for conducting business with the public. Specific tools for managing environmental conflict are suggested.     

Survival analysis of stochastic single-species population models in polluted environments

This paper reports on the behaviors of single species models with and without pollution. We consider three basic models, one is deterministic, and others are stochastic. We first obtained the acute thresholds between local extinction and (stochastic) weakly persistent in the mean for population respectively. Then we study the attainability of population size 0 for the stochastic cases and show that a randomized non-autonomous logistic equation will be stochastic permanent under some conditions. Finally, we introduce some numerical simulink graphics to illustrate our main results.     

Environmental chemistry in the twenty-first century

Human society actually faces many environmental challenges such as environmental pollution, climate changes and loss of biodiversity. These issues induce major risks for ecosystems and are a serious threat for further life on Earth. Anthropogenic pressure may continue to exacerbate the present-day problems. Prevention and mitigation of environmental issues demands sound science and dedicated political support. For that, environmental chemistry is a central and multidisciplinary science that will provide new concepts and applied methods to solve actual environmental issues. Here, we outline the scope of environmental chemistry. The Anthropocene era and major chemical disasters are discussed. We present also the challenges of atmospheric chemistry, analytical chemistry, statistics and chemometrics, and education in environmental chemistry.     

A σ-coordinate transport model coupled with rotational boussinesq-type equations

This paper describes a σ-coordinate scalar transport model coupled with a Boussinesq-type hydrodynamic model. The Boussinesq model has the ability to calculate both three-dimensional velocity distributions and the water surface motion. To capture ‘dispersion’ processes in open channel flow, horizontal vorticity effects induced by a bottom shear stress are included in the Boussinesq model. Thus, a reasonable representation of vertical flow structure can be captured in shallow and wavy flow fields. To solve the coupled Boussinesq and scalar transport system, a finite-volume method, based on a Godunov-type scheme with the HLL Riemann solver, is employed. Basic advection and advection–diffusion numerical tests in a non-rectangular domain were carried out and the computed results show good agreement with analytic solutions. With quantitative comparisons of dispersion experiments in an open channel, it is verified that the proposed coupled model is appropriate for both near and far field scalar transport predictions. From numerical simulations in the surf zone, physically reasonable results showing expected vertical variation are obtained.     

One-dimensional numerical modelling of dam-break waves over movable beds: application to experimental and field cases

This paper reports a numerical study on dam-break waves over movable beds. A one-dimensional (1-D) model is built upon the Saint-Venant equations for shallow water waves, the Exner equation of sediment mass conservation and a spatial lag equation for non-equilibrium sediment transport. The set of governing equations is solved using an explicit finite difference scheme. The model is tested in various idealized experimental cases, with fairly good agreement between the numerical predictions and measurements. Discrepancies are observed at the earlier stage of the dam-break wave and around the dam location due to no vertical velocity component being taken into account. Sensitivity tests confirm that the friction coefficient is an important parameter for the evaluation of sediment transport processes operating during a dam-break wave. The influence of the non-equilibrium adaptation length (or the lag distance) is negligible on the wavefront celerity and weak on the free surface and bed profiles, which indicates that one may ignore the spatial lag effect in dam-break wave studies. Finally, the simulation of the Lake Ha!Ha! dyke-break flood event shows that the model can provide relevant results if a convenient formula for computing the sediment transport capacity and an appropriate median grain diameter of riverbed material are selected.     

Models predicting the fate of pollutants in rivers

The spill of 2,4,‐D in the Rhine river was used to show the evolution from simple to sophisticated models. The first simulation was done with an analytical solution of the dispersion‐advection equation without elimination. Elimination was introduced in a second simulation. The third simulation was carried out with a numerical model. This included elimination and variable dispersion. The lack of data limited the use of very detailed models.     

Particulate pollution case studies which illustrate uses of individual particle analysis by scanning electron microscopy

Individual particle analysis by scanning electron microscopy is a high resolution analytical technique which can provide the detail necessary to solve many particulate pollution problems. In an electron microscope a beam of electrons is focused on a specimen resulting in a number of signals which are used to collect chemical and morphological information from individual features either manually or automatically. Case studies are presented which illustrate the applications of the technique to three paniculate pollution problems of differing complexity.