Numerical modeling of cohesive sediments dynamics in estuaries: Part I—Description of the model and simulations in the Po River Estuary

The present work contributes to the numerical modeling of complex turbulent multiphasic fluid flows occurring in estuarine channels. This research finds its motivation in the increasing need for efficient management of estuaries by taking into account the complex turbulent stratified flows encountered in estuaries and costal zones. A time‐dependent, 3D finite element model of suspended sediment transport taking into account the effects of cohesiveness between sediments is presented. The model estuary is the forced time‐dependent winds, time elevation at open boundaries and river discharge. To cope with the stiffness problems a decoupling method is employed to solve the shallow‐water equations of mass conservation, momentum and suspended sediment transport with the conventional hydrostatic pressure. The decoupling method partitions a time step into three subcycles according to the physical phenomena. In the first sub‐cycle the pure hydrodynamics including the k–ε turbulence model is solved, followed by the advection–diffusion equations for pollutants (salinity, temperature, suspended sediment concentration, (SSC)), and finally the bed evolution is solved. The model uses a mass‐preserving method based on the so‐called Raviart–Thomas finite element on the unstructured mesh in the horizontal plane, while the multi‐layers system is adopted in vertical with the conventional conforming finite element method, with the advantage that the lowermost and uppermost layers of variable height allow a faithful representation of the time‐varying bed and free surface, respectively. The model has been applied to investigate the SSC and seabed evolution in Po River Estuary (PRE) in Italy. The computed results mimic the field data well. Copyright © 2007 John Wiley & Sons, Ltd.     

The role of the configurational force balance in the nonequilibrium epitaxy of films

We discuss the epitaxial growth of an elastic film, allowing for stress and diffusion within the film surface as well as nonequilibrium interactions between the film and the vapor. Our approach, which relies on recent ideas concerning configurational forces, is based on: (i) standard (Newtonian) balance laws for forces and moments together with an independent balance law for configurational forces; (ii) atomic balances, one for each species of mobile atoms; (iii) a mechanical version of the second law that accounts for temporal changes in free energy, energy flows due to atomic transport, and power expended by both standard and configurational forces; (iv) thermodynamically consistent constitutive relations for the film surface and for the interaction between the surface and the vapor environment. The normal component of the configurational force balance at the surface represents a generalization, to a dynamical context involving dissipation, of a condition that would arise in equilibrium by considering variations of the total free energy with respect to the configuration of the film surface. Our final results consist of partial differential equations that govern the evolution of the film surface.     

Conservative Solute Versus Heat Transport in Porous Media During Push-pull Tests

Both heat and solute transport in porous media are described by partial differential equations of similar form. Nevertheless, observing these phenomena in the field on the scale of well tests clearly indicates dissimilar behaviour. This article studies the aforementioned transport processes by interpreting two push-pull tests of different duration. In both tests, chloride is applied as a conservative tracer and lower temperature water is injected in higher temperature pristine water at different flow rates. Simulation and interpretation of the tests are performed by means of ReacTrans, a two-dimensional, axially symmetric, finite-difference, solute and heat transport model. Since conflicting views exist in literature on the relation between solute and thermal dispersivity, analysis of field observations focuses on parameters which describe aquifer characteristics affecting these processes. Parameter estimation is conducted through sensitivity analysis and collinear diagnosis in order to identify derivable parameters. It is concluded that longitudinal solute dispersivity and thermal diffusivity could be inferred accurately from chloride and temperature data sampled from the injection/extraction well respectively. Involving supplementary data sampled from an observation well enables derivation of effective porosity from chloride data and thermal retardation from temperature data. Moreover, it is inferred that longitudinal solute dispersivity is scale dependent. Thermal diffusivity, however, seems not to be. This points to dissimilar development of transition zones during solute and heat transport. It is concluded that conductive transport of heat is much more important than effects of velocity variations through the pore space.     

Modeling of Solute Transport in a 3D Rough-Walled Fracture–Matrix System

Fluid flow and solute transport in a 3D rough-walled fracture–matrix system were simulated by directly solving the Navier–Stokes equations for fracture flow and solving the transport equation for the whole domain of fracture and matrix with considering matrix diffusion. The rough-walled fracture–matrix model was built from laser-scanned surface tomography of a real rock sample, by considering realistic features of surfaces roughness and asperity contacts. The numerical modeling results were compared with both analytical solutions based on simplified fracture surface geometry and numerical results by particle tracking based on the Reynolds equation. The aim is to investigate impacts of surface roughness on solute transport in natural fracture–matrix systems and to quantify the uncertainties in application of simplified models. The results show that fracture surface roughness significantly increases heterogeneity of velocity field in the rough-walled fractures, which consequently cause complex transport behavior, especially the dispersive distributions of solute concentration in the fracture and complex concentration profiles in the matrix. Such complex transport behaviors caused by surface roughness are important sources of uncertainty that needs to be considered for modeling of solute transport processes in fractured rocks. The presented direct numerical simulations of fluid flow and solute transport serve as efficient numerical experiments that provide reliable results for the analysis of effective transmissivity as well as effective dispersion coefficient in rough-walled fracture–matrix systems. Such analysis is helpful in model verifications, uncertainty quantifications and design of laboratorial experiments.     

Solute diffusion in fractured porous media with memory effects due to adsorption

Modelling of solute transport in fractured porous media is a subject of intensive research in many engineering disciplines, such as petroleum engineering, water resources management, civil engineering. Recent field and laboratory experiments show that, in presence of strong adsorption, the behaviour of solute penetrating into the fractured porous medium diverges from classical hypotheses, rendering impossible the adjustment of classical transport models. The aim of this paper is to develop a mathematical continuous model of solute transport, when strong adsorption of solute occurs on the grains of the porous matrix. The macroscopic model is obtained by upscaling the pore and the fracture behaviours, by using the multiple scale expansion method. We obtain a non-standard diffusion behaviour of solute which shows local non-equilibrium between transport in the fractures and in the porous matrix, as well as memory effects. To cite this article: J. Lewandowska et al., C. R. Mecanique 330 (2002) 879–884.     

Morphological evolution of heteroepitaxial islands during Stranski–Krastonov growth

Three-dimensional finite element method is used to simulate the formation, self-assembly and shape transition of heteroepitaxial islands during Stranski–Krastonov growth. In the formulation, strain energy, surface energy, surface anisotropy and elastic anisotropy of a cubic lattice structure are taken into account. In the simulations, the SiGe/Si material system is used as a model system. An empirical surface energy as a function of surface orientation is proposed. The minimum energy surfaces are identified based on existing experimental observations. The simulation results show that the coupling of elastic energy relaxation, surface energy anisotropy and elastic anisotropy strongly influences the surface roughening morphology, self-assembly and shape transition of epitaxial islands, resulting in diverse evolution pathways.     

A Solute Transport in Stratified Media

Two-dimensional and steady solute transport in a stratified porous formation is analysed under assumption that the effect of pore-scale dispersion is negligible. The longitudinal dispersion produced as a result of the vertical variation of hydraulic conductivity is analysed by averaging the variability of a solute flux concentration and conductivity. The evolution of the solute flux concentration is expressed with respect to the correlated variable, that is the travel (arrival) time at a fixed location and the averaging procedure is constructed to satisfy the boundary condition where the inlet concentration is a known function of time. In such a statement, a velocity-averaged solute flux concentration is described by a conventional dispersion model (CDM) with a dispersion coefficient which is a function of the arrival time. It is demonstrated that such CDM satisfies the assumption that hydraulic conductivity of the layers is gamma distributed with the parameter of distribution which is chosen to represent a reasonable value of the field scale solute dispersion. The overall behaviour of the model is illustrated by several examples of two-dimensional mass transport.     

Evolution of fatigue crack corrosion from surface irregularities

A moving boundary model is presented for crack nucleation and growth from surface flaws. It concerns with chemical attack that results in material dissolution. A controlling mechanism for evolution is the rupture of a brittle corrosion-protective film that is built up along the corroding surface. The evolution rate is a function of the degree of protective film damage caused by the surface straining. The problem is formulated for an elastic body containing a single and double pits. Low-frequency cyclic loading is considered. Numerical solution is proposed. The behaviours of a growing crack and of two competing cracks are described. Stages of incubation, blunting and steady-state growth characterise a single crack evolution. The steady-state growth rate is found independent of the initial geometry. Stages of independent growth, interactive growth and arrest of one crack characterise the evolution of two competing cracks. The lengths of the arrested cracks are presented as functions of the ratio between the pit depth for a series of different distances between the pits. It is emphasized that the solutions correspond to a homogeneous material. Further work is required to account for the material microstructure.     

Reactive Solute Transport in a Nonstationary,Fractured Porous Medium: A Dual-Porosity Approach

A numerical method of moment is developed for solute flux through a nonstationary, fractured porous medium. Solute flux is described as a space-time process where time refers to the solute flux breakthrough and space refers to the transverse displacement distribution at a control plane. A first-order mass diffusion model is applied to describe interregional mass diffusion between fracture (advection) and matrix (nonadvection) regions. The chemical is under linear equilibrium sorption in both fracture and matrix regions. Hydraulic conductivity in the fracture region is assumed to be a spatial random variable. In this study, the general framework of Zhang et al.(2000) is adopted for solute flux in a nonstationary flow field. A time retention function related to physical and chemical sorption in the dual-porosity medium is developed and coupled with solute advection along random trajectories. The mean and variance of total solute flux are expressed in terms of the probability density function of the parcel travel time and transverse displacement. The influences of various factors on solute transport are investigated. These factors include the interregional mass diffusion rate between fracture and matrix regions, chemical sorption coefficients in both regions, water contents in both regions, and location of the solute source. In comparison with solute transport in a one-region medium, breakthrough curves of the mean and variance of the total solute flux in a two-region medium have lower peaks and longer tails. As compared with the classical stochastic studies on solute transport in fractured media, the numerical method of moment provides an approach for applying the stochastic method to study solute transport in more complicated fractured media.