Steady state numerical simulation of the particle collection efficiency of a new urban sustainable gravity settler using design of experiments by FVM

The aim of this work is to analyze the efficiency of a new sustainable urban gravity settler to avoid the solid particle transport, to improve the water waste quality and to prevent pollution problems due to rain water harvesting in areas with no drainage pavement. In order to get this objective, it is necessary to solve particle transport equations along with the turbulent fluid flow equations since there are two phases: solid phase (sand particles) and fluid phase (water). In the first place, the turbulent flow is modelled by solving the Reynolds-averaged Navier-Stokes (RANS) equations for incompressible viscous flows through the finite volume method (FVM) and then, once the flow velocity field has been determined, representative particles are tracked using the Lagrangian approach. Within the particle transport models, a particle transport model termed as Lagrangian particle tracking model is used, where particulates are tracked through the flow in a Lagrangian way. The full particulate phase is modelled by just a sample of about 2,000 individual particles. The tracking is carried out by forming a set of ordinary differential equations in time for each particle, consisting of equations for position and velocity. These equations are then integrated using a simple integration method to calculate the behaviour of the particles as they traverse the flow domain. The entire FVM model is built and the design of experiments (DOE) method was used to limit the number of simulations required, saving on the computational time significantly needed to arrive at the optimum configuration of the settler. Finally, conclusions of this work are exposed.     

A numerical model of density currents in estuaries of Siberian rivers

A numerical model for studying the dynamic mixing of sea and river waters in estuary areas is proposed. The model is based on two-dimensional longitudinal vertical stratified fluid mechanics equations and an equation of salt transport. The model is used to simulate local density currents in the estuaries of branched deltas of Siberian rivers. The results of numerical experiments are given. The flow dynamic structure and the salinity profile are compared with observational data.     

Linear and nonlinear instabilities of a granular bed: Determination of the scales of ripples and dunes in rivers

Granular media are frequently found in nature and in industry and their transport by a fluid flow is of great importance to human activities. One case of particular interest is the transport of sand in open-channel and river flows. In many instances, the shear stresses exerted by the fluid flow are bounded to certain limits and some grains are entrained as bed-load: a mobile layer which stays in contact with the fixed part of the granular bed. Under these conditions, an initially flat granular bed may be unstable, generating ripples and dunes such as those observed on the bed of rivers. In free-surface water flows, dunes are bedforms that scale with the flow depth, while ripples do not scale with it. This article presents a model for the formation of ripples and dunes based on the proposition that ripples are primary linear instabilities and that dunes are secondary instabilities formed from the competition between the coalescence of ripples and free surface effects. Although simple, the model is able to explain the growth of ripples, their saturation (not explained in previous models) and the evolution from ripples to dunes, presenting a complete picture for the formation of dunes.     

Modelling and numerical aspects in 2d river flow simulation

Flow simulation in rivers is used for the prediction of waterlevel and runoff quantities. The presently used simulation by the German Federal Institute of Hydrology is based on a network approach with coupled 1d models in which the river flow is described by the St. Venant‐equations. Work is underway to extend this by 2d submodel elements using the shallow water equations to allow simulations in greater detail. The wetting and drying of parts of the river bed at varying waterlevels force us to formulate the flow simulation as free boundary problem. The constraints of embedding the 2d model into the existing network approach suggest to use a fixed grid approach. This leads to the problem of solving the shallow water equations on the whole grid. However, the shallow water equations degenerate for dry beds and therefore do not allow a straight forward discretisation.     

Numerical simulation of the performance of a snow fence with airfoil snow plates by FVM

The aim of this work is to analyze the efficiency of a snow fence with airfoil snow plates to avoid the snowdrift formation, to improve visibility and to prevent blowing snow disasters on highways and railways. In order to attain this objective, it is necessary to solve particle transport equations along with the turbulent fluid flow equations since there are two phases: solid phase (snow particles) and fluid phase (air). In the first place, the turbulent flow is modelled by solving the Reynolds-averaged Navier-Stokes (RANS) equations for incompressible viscous flows through the finite volume method (FVM) and then, once the flow velocity field has been determined, representative particles are tracked using the Lagrangian approach. Within the particle transport models, we have used a particle transport model termed as Lagrangian particle tracking model, where particulates are tracked through the flow in a Lagrangian way. The full particulate phase is modelled by just a sample of about 15,000 individual particles. The tracking is carried out by forming a set of ordinary differential equations in time for each particle, consisting of equations for position and velocity. These equations are then integrated using a simple integration method to calculate the behaviour of the particles as they traverse the flow domain. Finally, the conclusions of this work are exposed.     

Analysis of a two-dimensional grade-two fluid model with a tangential boundary condition

This article studies the solutions in H¹ of a two-dimensional grade-two fluid model with a non-homogeneous Dirichlet tangential boundary condition, on a Lipschitz-continuous domain. Existence is proven by splitting the problem into a generalized Stokes problem and a transport equation, without restricting the size of the data and the constant parameters of the fluid. A substantial part of the article is devoted to a sharp analysis of this transport equation, under weak regularity assumptions. By means of this analysis, it is established that each solution of the grade-two fluid model satisfies energy equalities and converges strongly to a solution of the Navier–Stokes equations when the normal stress modulus α tends to zero. When the domain is a polygon, it is shown that the regularity of the solution is related to that of a Stokes problem. Uniqueness is established in a convex polygon, with adequate restrictions on the size of the data and parameters.     

Simulation of the spread of a viscous fluid using a bidimensional shallow water model

In this paper we propose a numerical method to solve the Cauchy problem based on the viscous shallow water equations in an horizontally moving domain. More precisely, we are interested in a flooding and drying model, used to modelize the overflow of a river or the intrusion of a tsunami on ground. We use a nonconservative form of the two-dimensional shallow water equations, in eight velocity formulation and we build a numerical approximation, based on the Arbitrary lagrangian eulerian formulation, in order to compute the solution in the moving domain.     

Negro and Danube are mirror rivers

We study the European river Danube and the South American river Negro daily water levels. We present a fit for the Negro daily water level period and standard deviation. Unexpectedly, we discover that the river Negro and Danube are mirror rivers in the sense that the daily water levels fluctuations histograms are close to the universal non-parametric BHP and reversed BHP, respectively. Hence, the probability of a certain positive fluctuation range in the river Negro is, approximately, equal to the probability of the corresponding symmetric negative fluctuation range in the river Danube.     

The water bag model and gyrokinetic applications

Predicting turbulent transport in nearly collisionless fusion plasmas requires to solve kinetic (or more precisely gyrokinetic) equations. In spite of considerable progress, several pending issues remain; although more accurate, the kinetic calculation of turbulent transport is much more demanding in computer resources than fluid simulations. An alternative approach is based on a water bag representation of the distribution function which is not an approximation but rather a special class of initial conditions allowing to reduce the full kinetic Vlasov equation into a set of hydrodynamic equations while keeping its kinetic character. This model has been applied to gyrokinetic modelling with very encouraging results. The instability threshold for ITG instability is found to be very close to the results obtained from continuous Maxwellian distribution, even for only 10 bags.     

The Interaction Between Noise and Transport Mechanisms in PDEs

The understanding of transport mechanisms in PDEs is at the core of some of the main open problems in fluid dynamics. The introduction of random perturbations in these equations may have an influence on the properties of transport. We report here some recent progresses on the interaction between noise and transport. The Lagrangian viewpoint is used to investigate the problem. In some example we observe that noise improves the properties of the Lagrangian motion and restores uniqueness or prevents blow-up of the associated PDE; in other examples this does not happen.     

Model Equations for Gravity-Capillary Waves in Deep Water

The Euler equations for water waves in any depth have been shown to have solitary wave solutions when the effect of surface tension is included. This paper proposes three quadratic model equations for these types of waves in infinite depth with a two-dimensional fluid domain. One model is derived directly from the Euler equations. Two further simpler models are proposed, both having the full gravity-capillary dispersion relation, but preserving exactly either a quadratic energy or a momentum. Solitary wavepacket waves are calculated for each model. Each model supports the elevation and depression waves known to exist in the Euler equations. The stability of these waves is discussed, as is the dynamics resulting from instabilities and solitary wave collisions.     

Partitioned penalty methods for the transport equation in the evolutionary Stokes–Darcy‐transport problem

There has been a surge of work on models for coupling surface‐water with groundwater flows which is at its core the Stokes–Darcy problem, as well as methods for uncoupling the problem into subdomain, subphysics solves. The resulting (Stokes–Darcy) fluid velocity is important because the flow transports contaminants. The numerical analysis and algorithm development for the evolutionary transport problem has, however, focused on a quasi‐static Stokes–Darcy model and a single domain (fully coupled) formulation of the transport equation. This report presents a numerical analysis of a partitioned method for contaminant transport for the fully evolutionary system. The algorithm studied is unconditionally stable with one subdomain solve per step. Numerical experiments are given using the proposed algorithm that investigates the effects of the penalty parameters on the convergence of the approximations.     

A perturbation solution for bacterial growth and bioremediation in a porous medium with bio-clogging

We investigate a flow problem of relevance in bioremediation and develop a mathematical model for transport of contamination by groundwater and the spreading, confinement, and remediation of chemical waste. The model is based on the fluid mass and momentum balance equations and simultaneous transport and consumption of the pollutant (hydrocarbon) and nutrient (oxygen). Particular emphasis is placed on the study of processes involving the full coupling of reaction, transport and mechanical effects. Dimensional analysis and asymptotic reduction are used to simplify the governing equations, which are then solved numerically.     

Numerical Solution of a Fluid Filtration Problem in a Fractured Medium by Using the Domain Decomposition Method

Under consideration are the numerical methods for simulation of a fluid flow in fractured porous media. The fractures are taken into account explicitly by using a discrete fracture model. The formulated single-phase filtering problem is approximated by an implicit finite element method on unstructured grids that resolve fractures at the grid level. The systems of linear algebraic equations (SLAE) are solved by the iterative methods of domain decomposition in the Krylov subspaces using the KRYLOVlibrary of parallel algorithms. The results of solving some model problem are presented. A study is conducted of the efficiency of the computational implementation for various values of contrast coefficients which significantly affect the condition number and the number of iterations required for convergence of the method.     

Bornes sur la densité pour un problème de Navier–Stokes compressible à frontière variable avec conditions aux limites de Dirichlet

We extend a compactness result shown by P.-L. Lions in 1998 to an isentropic compressible Navier–Stokes problem ($\gamma ?1$) defined on a time dependent domain with Dirichlet boundary conditions. This result can be useful for the study of some fluid–structure interaction problems, for the analysis of some pollution water problems (shallow water equations with free boundary: $\gamma =1$) or for the modelling of a river level. To cite this article: F. Flori, B. Giudicelli, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Random Dynamics of the Boussinesq System with Dynamical Boundary Conditions

Abstract

A coupled system of the two-dimensional Navier–Stokes equations and the salinity transport equation with spatially correlated white noise on the boundary as well as in fluid is investigated. The noise affects the system through a dynamical boundary condition. This system may be considered as a model for gravity currents in oceanic fluids. The noise is due to uncertainty in salinity flux on fluid boundary. After transforming this system into a random dynamical system, we first obtain asymptotic estimates on system evolution, and then show that the long time dynamics is captured by a random attractor.     

Effect of channel connection on flow and salinity distribution of Danshuei River estuary

Numerical models are often used to evaluate the potential impact of human alteration of natural water bodies and to help the design the alternation to mitigate its impacts. A vertical (laterally integrated) two-dimensional hydrodynamic model was expanded to include the capability of simulating river loops as well as tributaries. The model was performed and applied to the Danshuei River estuarine system in northern Taiwan which consists of three major tributaries: the Tahan Stream, Hsintien Stream, Keelung River, and one river loop under the Chung-Hsin Bridge. The expanded model was reverified with observational field data of 2000. The verified model was then used to hindcast the river hydrodynamic conditions with a loop connection between the Danshuei River and Keelung River, which existed prior to 1965. It was found that the configuration of river loop connection has significant impacts on the residual transport along the connecting channel and the salinities in the connected river branches. The results show that the model may provide an ideal tool for management decision.     

Implicit formulation for advection–diffusion simulation based on particle distribution moments

This paper introduces an implicit method for advection–diffusion equations called Implicit DisPar, based on particle displacement moments applied to uniform grids. The present method tries to solve constraints associated with explicit methods also based on particle displacement methods, in which diffusivity-dominated situations can only be handled by considerably increasing the associated computational costs. In fact, a higher particle destination nodes number allows the use of higher diffusion coefficients for the transport simulation without instabilities. The average was evaluated by an analogy between the Fokker–Planck and the transport equations. The variance is considered to be Fickian. The particle displacement distribution is used to predict deterministic mass transfers between domain nodes. Mass conservation was guaranteed by the distribution concept. In the truncation error analysis, it was shown that the linear Implicit DisPar formulation does not have numerical error up to v − 1 order, if the first v particle moments are forced by the Gaussian moments. It was shown by theoretical tests for linear conditions that the model accuracy level is proportional to the number of particle destination nodes.     

The effects of bed form roughness on total suspended load via the Lattice Boltzmann Method

Bed forms in natural rivers and man-made channels provide the dominant contribution to overall flow resistance and hence significantly affect sediment transport rate. Many laboratory experiments and field observations have been conducted on bed forms, and it was found that theoretical flat-bed assumptions do not give the correct estimation for the total suspended load (TSL). In this study, we present a systematic numerical investigation of turbulent open-channel flows over bed forms using the Lattice Boltzmann Method (LBM). A static Smagorinsky model is incorporated into LBM to account for turbulence, and the dynamic interface between fluid and air is captured by a free-surface model. The time-averaged flow velocity, turbulence intensity and Reynolds shear stress in LBM simulations show an excellent agreement with the available experimental data. In addition, the coherent flow structures induced by the bed forms qualitatively agree with previous numerical results from Large Eddy Simulations based the Navier–Stokes equations. We then proceed to investigate the effects of bed form roughness, quantified by the total friction factor f_T, on sediment transport. It is found that the prediction of the TSL based on the theoretical flat-bed assumptions may lead to an overestimation of up to 30%, depending on the bed form roughness. In addition, the normalized TSL is linearly proportional to f_T and nearly inversely proportional to the ratio of downward settling velocity and upward turbulence induced diffusion. Our work proposes a general law linking these quantities to estimate the TSL, which has the potential for a more efficient and accurate engineering design of man-made channels and improved river management.