scholarly journals Un modèle Darcy-Forchheimer pour un écoulement dans un milieu poreux fracturé

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Najla Frih ◽  
Jean E. Roberts ◽  
Ali Saada
Keyword(s):  
Porous Medium ◽  
Numerical Model ◽  
Incompressible Fluid ◽  
Single Phase ◽  
Darcy's Law ◽  
Nous Proposons ◽  
Rock Matrix ◽  
International Audience ◽  
Milieu Poreux ◽  
Forchheimer’S Law

International audience We propose a numerical model for the flow of a single phase,incompressible fluid in a porous medium with fractures. In this model, the flow obeys Forchheimer's law in the fracture and Darcy's law in the rock matrix. Nous proposons un modèle numérique d'un écoulement monophasique d'un fluide incompressible dans un milieu poreux fracturé. Les lois d'écoulement sont celle de Forchheimer dans la fracture et de Darcy dans la matrice rocheuse.

scholarly journals Décomposition de domaine pour un milieu poreux fracturé : un modèle en 3D avec fractures

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Laila Amir ◽  
Michel Kern ◽  
Jean E. Roberts ◽  
Vincent MARTIN
Keyword(s):  
Porous Medium ◽  
Domain Decomposition ◽  
Single Phase ◽  
Decomposition Methods ◽  
Interface Problem ◽  
Domain Decomposition Methods ◽  
Standard Interface ◽  
International Audience ◽  
Milieu Poreux ◽  
Phase Fluid

International audience In this paper, we are interested in modeling the flow of a single phase fluid in a porous medium with fractures, using domain decomposition methods. In the proposed approach, the fracture is regarded as an active interface, the transmission conditions and the exchanges between the rock and the fracture taking into account the flow in the fracture. The problem to be solved is then a non standard interface problem which takes into account the flow in the fractures.

scholarly journals Contribution to image restoration using a neural network model

2002 ◽  
Vol Volume 1, 2002 ◽  
Author(s):  
Karim Achour ◽  
Nadia Zenati ◽  
Oualid Djekoune
Keyword(s):  
Neural Network ◽  
Image Restoration ◽  
Network Model ◽  
Neural Network Model ◽  
Hopfield Neural Network ◽  
Optimization Method ◽  
Nous Proposons ◽  
International Audience ◽  
High Level

International audience The reduction of the blur and the noise is an important task in image processing. Indeed, these two types of degradation are some undesirable components during some high level treatments. In this paper, we propose an optimization method based on neural network model for the regularized image restoration. We used in this application a modified Hopfield neural network. We propose two algorithms using the modified Hopfield neural network with two updating modes : the algorithm with a sequential updates and the algorithm with the n-simultaneous updates. The quality of the obtained result attests the efficiency of the proposed method when applied on several images degraded with blur and noise. La réduction du bruit et du flou est une tâche très importante en traitement d'images. En effet, ces deux types de dégradations sont des composantes indésirables lors des traitements de haut niveau. Dans cet article, nous proposons une méthode d'optimisation basée sur les réseaux de neurones pour résoudre le problème de restauration d'images floues-bruitées. Le réseau de neurones utilisé est le réseau de « Hopfield ». Nous proposons deux algorithmes utilisant deux modes de mise à jour: Un algorithme avec un mode de mise à jour séquentiel et un algorithme avec un mode de mise à jour n-simultanée. L'efficacité de la méthode mise en œuvre a été testée sur divers types d'images dégradées.

scholarly journals Numerical modelling of agglomeration process in a granular bed containing melting particles

2021 ◽  
Vol 2057 (1) ◽  
pp. 012063
Author(s):  
I G Donskoy
Keyword(s):  
Thermal Decomposition ◽  
Porous Medium ◽  
Numerical Model ◽  
Numerical Modelling ◽  
Side Wall ◽  
Low Grade ◽  
Granular Bed ◽  
Agglomeration Process ◽  
Simulation Results ◽  
Implicit Numerical Method

Abstract The paper considers a numerical model of a flow in a porous medium containing particles of a melting component (polymer). For this, an implicit numerical method of splitting in directions is used. Calculations are carried out for two heating methods (through the side wall, or by the input gas). The simulation results qualitatively reproduce some of the experimentally observed features of the thermal decomposition of polymer-containing mixtures. The results obtained are of interest in the study of low-grade fuels processing, often accompanied by agglomeration, as well as in the development of methods by which agglomeration can be prevented.

Incorporation of Interfacial Areas in Models of Two-Phase Flow

1999 ◽  
Author(s):  
William G. Gray ◽  
Michael A. Celia
Keyword(s):  
Porous Media ◽  
Hydraulic Conductivity ◽  
Single Phase ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Hydraulic Gradient ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Α Phase ◽  
Flow Through

The mathematical study of flow in porous media is typically based on the 1856 empirical result of Henri Darcy. This result, known as Darcy’s law, states that the velocity of a single-phase flow through a porous medium is proportional to the hydraulic gradient. The publication of Darcy’s work has been referred to as “the birth of groundwater hydrology as a quantitative science” (Freeze and Cherry, 1979). Although Darcy’s original equation was found to be valid for slow, steady, one-dimensional, single-phase flow through a homogeneous and isotropic sand, it has been applied in the succeeding 140 years to complex transient flows that involve multiple phases in heterogeneous media. To attain this generality, a modification has been made to the original formula, such that the constant of proportionality between flow and hydraulic gradient is allowed to be a spatially varying function of the system properties. The extended version of Darcy’s law is expressed in the following form: qα=-Kα . Jα (2.1) where qα is the volumetric flow rate per unit area vector of the α-phase fluid, Kα is the hydraulic conductivity tensor of the α-phase and is a function of the viscosity and saturation of the α-phase and of the solid matrix, and Jα is the vector hydraulic gradient that drives the flow. The quantities Jα and Kα account for pressure and gravitational effects as well as the interactions that occur between adjacent phases. Although this generalization is occasionally criticized for its shortcomings, equation (2.1) is considered today to be a fundamental principle in analysis of porous media flows (e.g., McWhorter and Sunada, 1977). If, indeed, Darcy’s experimental result is the birth of quantitative hydrology, a need still remains to build quantitative analysis of porous media flow on a strong theoretical foundation. The problem of unsaturated flow of water has been attacked using experimental and theoretical tools since the early part of this century. Sposito (1986) attributes the beginnings of the study of soil water flow as a subdiscipline of physics to the fundamental work of Buckingham (1907), which uses a saturation-dependent hydraulic conductivity and a capillary potential for the hydraulic gradient.

scholarly journals Development of An Integrated Numerical Model for Simulating Wave Interaction with Permeable Submerged Breakwaters Using Extended Navier–Stokes Equations

2020 ◽  
Vol 8 (2) ◽  
pp. 87 ◽  
Author(s):  
Paran Pourteimouri ◽  
Kourosh Hejazi
Keyword(s):  
Porous Medium ◽  
Wave Propagation ◽  
Numerical Model ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stokes Wave ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
The Impact

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.

scholarly journals Geometric variational approach to the dynamics of porous medium, filled with incompressible fluid

2020 ◽  
Vol 231 (9) ◽  
pp. 3897-3924
Author(s):  
Tagir Farkhutdinov ◽  
François Gay-Balmaz ◽  
Vakhtang Putkaradze
Keyword(s):  
Porous Medium ◽  
Incompressible Fluid ◽  
Variational Approach
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