INTERNATIONAL JOURNAL ON FINITE VOLUMES

The International Journal on Finite Volumes addresses work at the interface between the theortical mathematics, applied mathematics and numerical multiplications. The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics related to the Finite Volumes method. In addition to the traditional issues and problems in mathematical and numerical analysis, the journal also publishes papers describing relevant applications in such fields as fluid dynamics, multiphysics processes, Maxwell equations, physics of solid, engineering and other branches of applied science. The journal strives to be flexible in the type of papers and contributions it publishes and their format. Work coming from the industrial world is also welcome. Review papers and papers on teaching these subjects are also published. Manuscripts submitted for publication are judged on the basis of significance, originality, appropriateness of subject matter, and clarity of presentation. The decision regarding acceptance or rejection of a manuscript is the responsibility of the editors and is based in large part on the recommendations of expert reviewers. The role played by the Journal as an interface between theory and practice means that it will be of great interest to those in both academic and business worlds. The high standard of the Journal will be guaranteed by the presence of an international Editorial Board. This will ensure the efficiency of the refereeing procedure. IJFV publishes two types of articles : Working contributions, which are not subject to review, other than by the Editors; and Refereed Papers, which are subject to the normal process of peer-review. In this process, the papers are first reviewed by the Editor who receives the paper and, if its field is considered to be within the scope of the journal, it is then proposed to some experts of this field for review. Where specialist expertise outside that held by the Editors and Editorial Board members is required, it will be sought from specialists in the field known to the Editors or to Editorial Board members. We are in the process of appointing an international Editorial Board and, in future, members of the Board will act as additional referees. Refereed papers, in other words, will be subject to the full rigour of peer review as it is exercised by scholarly printed journals. The difference between the peer-review process for IJFV and that of printed journals is speed of publication. We expect to publish papers within two to five months of submission. Prospective authors should note that, now digital publications may be submitted for assessment and should be subject to the same quality criteria as papers published by traditional means.

Editorial Board

Editor :

Associate editors :

Guide for Authors:

Manuscripts should be prepared for review following standard procedures for scientific publications.
Please use the style provided here in the file IJFV.cls.
A sample is provided also, to serve as a guide for using IJFV.cls.
Contributions should be submitted electronically to the editor in the following way:

A first document containing your paper in an anonymous form, without the authors name and affiliation.
A second document containing authors name and affiliation.

Please make sure to include a complete address for the corresponding author with telephone, fax numbers and e-mail addresses.

The authors are kindly requested to propose the name of 1 to 5 possible reviewers of their work.

About the reference section:

Volume 1 N°1

A well-balanced numerical scheme for shallow-water equations with topography : resonance phenomena
Description: Authors: Ashwin Chinnayya, Alain-Yves LeRoux, Nicolas Seguin

Abstract : The shallow water model with a source term due to topography gradient is approximated within the frame of Finite Volume numerical methods. The cornerstone of the method is the solution of the inhomogeneous Riemann problem. Thus the numerical scheme can deal simultaneously with discrete steady states, flood, occurrence and covering of dry zones.
We present the parameterization through the discontinuity of topography, emphasizing on the resonance phenomenon. We then build the solution of the inhomogeneous Riemann problem using a continuation method with respect to the jump of topography. Finally, numerical experiments illustrate the agreement of the numerical method with the previous analysis.

Key words : shallow-water equations, source term, well-balanced numerical scheme, resonance.

Date of publication: April 2004

Paper presented by : Professor Jean-Marc Herard
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Added on: 08-Oct-2004 | Downloads: 225

Code Saturne: A Finite Volume Code for Turbulent flows Popular
Description: Authors : Frederic Archambeau, Namane Mehitoua, Marc Sakiz

Abstract :This paper describes the finite volume method implemented in Code Saturne, Electricite de France general-purpose computational fluid dynamic code for laminar and turbulent flows in complex two and three- dimensional geometries. The code is used for industrial applications and research activities in several fields related to energy production (nuclear power thermal-hydraulics, gas and coal combustion, turbomachinery, heating, ventilation and air conditioning…).
The set of equations considered consists of the Navier-Stokes equations for incompressible flows completed with equations for turbulence modelling (eddy-viscosity model and second moment closure) and for additional scalars (temperature, enthalpy, concentration of species, …). The time-marching scheme is based on a prediction of velocity followed by a pressure correction step. Equations for turbulence and scalars are resolved separately afterwards. The discretization in space is based on the fully conservative, unstructured fi nite volume framework, with a fully colocated arrangement for all variables. Speci c eff ort has been put into the computation of gradients at cell centres. Industrial applications illustrate important aspects of physical modelling
such as turbulence (using Reynolds-Averaged Navier-Stokes equations or Large Eddy Simulation), combustion, conjugate heat transfer (coupled with the thermal code SYRTHES ) and fluid-particle coupling with a lagrangian approach. These examples also demonstrate the capability of the code to tackle a large variety of meshes and cell geometries, including hybrid meshes with arbitrary interfaces.

Key words : Navier-Stokes, finite volume, unstructured mesh, colocated arrangement, gradient calculation, turbulent flows, incompressible flows, Reynolds-Averaged Navier-Stokes equations, Large Eddy Simulation, parallel computing, nuclear power, gas and coal combustion, Code Saturne

Date of publication : February 2004

Paper presented by : Professor Jean-Marc Herard
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Added on: 08-Oct-2004 | Downloads: 347

Practical computation of axisymmetrical multifluid flows
Description: Authors: Thomas BARBERON, Philippe HELLUY, Sandra ROUY

Abstract:
We adapt the Saurel-Abgrall front capturing finite volumes method for an industrial simulation of compressible multifluid flows. We then apply the method to the case of air-water flow in the cooling chamber of an axisymmetrical gas generator. We describe successively how to deal with exact and global Riemann solvers, pressure oscillations, unstructured meshes, axisymmetry, boundary conditions and overly restrictive CFL conditions. The resulting algorithm is efficient and robust.

Key words : compressible multifluid, front capturing, nonconservative scheme, axisymmetry.

Date of publication : December 2003

Paper presented by : Professor Thierry Gallouet
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Added on: 08-Oct-2004 | Downloads: 201

Some refined Finite volume methods for elliptic problems with corner singularities
Description: Authors : Karim Djadel, Serge Nicaise and Jalel Tabka

Abstract :
It is well known that the solution of the Laplace equation in a non convex polygonal domain of R 2 has a singular behaviour near non convex corners. Consequently we investigate three refined Finite volume methods (cell-center, conforming Finite volume-element and non conforming Finite volume-element) to approximate the solution of such a problem and restore optimal orders of convergence as for smooth solutions. Numerical tests are presented and confirm the theoretical rates of convergence.

Date of publication: October 2003

paper presented by : Professor Raphaele Herbin
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Added on: 08-Oct-2004 | Downloads: 178

Volume 2 N°1

Simulation of multiphase water flows with changes of phase using the Homogeneous Equilibrium Model Popular
Description: Authors: Florian De Vuyst, Jean-Michel Ghidaglia and Gerard Le Coqq

Full Title: On the numerical simulation of multiphase water flows with changes of phase and strong gradients using the Homogeneous Equilibrium Model

Abstract: We introduce a general method based on a variant of the Flux Characteristic method described by Ghidaglia et al [22] designed to simulate water-vapour two-phase flows. As an example, we use the three equations Homogeneous Equilibrium model (HEM) with hypotheses of local thermodynamic equilibrium. Our purpose here is to analyze the Finite Volume method when strong gradients of density are present and when some derivatives of quantities like speed of sound strongly vary due to phase transitions. As framework for numerical experiments, we consider a complex flow inside an injector-condenser device. The analysis will lead to a variant of the Flux Characteristic method with regularized matrix-valued sign functions. Other applications like water boiling into a hot channel and a fall of pressure in a crack due to friction will be also considered.

Keywords. - Flux Characteristic Methods, two-phase flows, injector-condenser, phase transition, numerical methods, numerical analysis

Date of publication : January 2005

Presented by: Professor Toro

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Added on: 22-Jan-2006 | Downloads: 322

A staggered finite volume scheme II Popular
Description: Authors: R. Eymard and R. Herbin

Full Title: A staggered finite volume scheme on general meshes for the Navier-Stokes equations in two space dimensions

Abstract:
This paper presents a new finite volume scheme for the incompressible steady-state Navier-Stokes equations on a general 2D mesh. The scheme is staggered, i.e. the discrete velocities are not located at the same place as the discrete pressures. We prove the existence and the uniqueness of a discrete solution for a centered scheme under a condition on the data, and the unconditional existence of a discrete solution for an upstream weighting scheme. In both cases (nonlinear centered and upstream weighting schemes), we prove the convergence of a penalized version of the scheme to a weak solution of the problem. Numerical experiments show the efficiency of the schemes on various meshes.

Date of publication: January 2005

Presented by Professor Lazarov

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Added on: 22-Jan-2006 | Downloads: 263

A staggered finite volume scheme I Popular
Description: Authors:
Ph. Blanc, R. Eymard and R. Herbin

Full Title:
A staggered finite volume scheme on general meshes for the
generalized Stokes problem in two space dimensions

Abstract:
This paper presents a new finite volume scheme for the steady Stokes equations on a general 2D mesh. The scheme is staggered, i.e. the discrete velocities are not located at the same place as the discrete pressures. We prove the existence and the uniqueness of a discrete solution.
We then prove convergence of the discrete velocities to the weak solution of the problem. Under additional regularity conditions, we prove the convergence of a penalized version of the scheme to the weak solution of the problem. Numerical experiments on problems with known analytical solutions allow to obtain the rate of convergence for both velocities and pressure.

Date of publication : January 2005

Paper presented by professor Lazarov

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Added on: 22-Jan-2006 | Downloads: 262

Volume 2 N°2

Finite volumes for CO2 transport and assimilation in a leaf
Description: Authors: Emily Gallouet, Raphaele Herbin

Full title: Axisymmetric finite volumes for the numerical simulation of
bulk CO2 transport and assimilation in a leaf

Abstract: This paper deals with the numerical simulation of CO2 transport in the leaf. We study a mathematical model of the diffusion and photosynthesis processes, and present the implementation of an axisymmetric cell centred finite volume scheme for their numerical simulation. The resulting code enables the computation of the lateral diffusion coefficient in the leaf porous medium, from experimental measurements which yield the point wise value of internal CO2 concentration.
Hence our model and numerical code allow the analysis of the role of the internal diffusion in the photosynthesis process. We show here that under moderate light, CO2 does not diffuse across long distances because it is rapidly assimilated by photosynthesising cells.

Key words : CO2 diffusion, photosynthesis, porous medium, finite volumes.

Date of publication : September 2005

Paper presented by Professor Fayssal Benkhaldoun

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Added on: 22-Jan-2006 | Downloads: 180

Numerical model of a compressible multi-fluid fluctuating flow
Description: Authors:

Christophe Berthon and Boniface Nkonga

Abstract:

In the present work, we consider the numerical approximations of multi-fluid compressible fluctuating flows. Assuming that the flow is composed by non mixing compressible fluids, we derived a modellization that can be view as an extension of the standard compressible (k, epsilon) one. This model is fundamentally in non conservation form (the coupling between fluids and turbulence involves non conservative products) and the usual finite volume methods fail. The nonlinear projection scheme is used to preserve, at the discrete level, the main properties of the model. The numerical computations are performed on the Richtmeyer-Meshkov instability to validate the approach and to measure the influence of fluctuations.

Key words: compressible flows, velocity fluctuations, non-conservative equations, nonlinear projection methods.

Date of publication : May 2005

Paper presented by: Professor Jean Marc Herard

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Added on: 22-Jan-2006 | Downloads: 196

Convergence of a streamline method for hyperbolic problems
Description: Author: Bilal Atfeh

Abstract: In this paper we study the convergence of a streamline method for an hyperbolic problem. Our motivation for this method arises from the problem of simulating multi-phase flow in porous media.
In fact, the streamline method has been applied successfully to reservoir simulation. There is however no study of the convergence of this method. We prove the convergence in a simplified case. In particular, we assume that the velocity depends only on the space variable.

Date of publication : February 2005

Paper presented by Professor Jean-Marc Herard

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Added on: 22-Jan-2006 | Downloads: 139

Volume 3 N°1

Computing two dimensional flood wave propagation
Description: Authors: H. Belhadj, A. Taik, D. Ouazar

Long Title: Computing two dimensional flood wave propagation using unstructured finite volume method: Application to the Ourika valley

Abstract: This study is devoted to the flood wave propagation modellingfl corresponding to a realistic situation. The equations that governs the
propagation of a flood wave, in natural rivers, corresponds to the free surface flow equations in the Shallow Water case. The obtained two dimensional system, known as Saint Venant’s system, is derived from the three-dimensional incompressible Navier Stokes equations by depth-averaging of the state variables. This system is written in a conservative form with hyperbolic homogeneous part. The discretization of the convection part is carried out by the use of the finite volume method on unstructured mesh. To increase the accuracy of the scheme, the MUSCL technique is used. The diffusive part is discretized using a Green-Gauss interpolation technique based on a diamond shaped co-volume. For the numerical experiment, we have studied a realistic channel of the Ourika valley which is located in Morocco. The flood occurred on August 1995 is simulated with the objective of evaluating the behavior of the wave propagation in the channel. The results of the proposed numerical model gives velocities and free surface elevations at diffrent stopped times of the simulation.

Key words : Shallow water equations, Finite volume method,
Unstructured mesh, Roe scheme, Green-Gauss interpolation, Manning
equation, Flood, Ourika valley

Paper presented by Prof. F. Benkhaldoun

Publication date: Sept. 2006
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Added on: 26-Jan-2007 | Downloads: 105

Moving Meshes and Higher Order Finite Volume Reconstructions Popular
Description: Title:
Moving Meshes and Higher Order Finite Volume Reconstructions

Author:
Fredrik Svensson

Abstract:
In this paper, we present and evaluate a moving mesh Finite Volume method for hyperbolic conservation laws. The method consists of two parts; a mesh moving scheme based on the algorithm of Tang and Tang, and a third order accurate bi-hyperbolic reconstruction which is an extension of Marquina’s PHM. The resulting algorithm calculates the solution of the conservation laws directly in physical space, without any transformation of the computational grid or the hyperbolic equations. Numerical experiments in one and two space dimensions indicate high numerical accuracy of the method.

Key words :
Moving mesh method, hyperbolic conservation law, Finite volume method, high-order reconstruction.

Publication date: February, 7, 2006

Paper presented by: Prof. Benkhaldoun
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Added on: 07-Feb-2006 | Downloads: 333

Convergence and Sensitivity Analysis of Repair Algorithms in 1D
Description: Title:
Convergence and Sensitivity Analysis of Repair Algorithms in 1D

Authors:
Bruno Despres, Raphael Loubere

Abstract:
We prove the convergence of some repair algorithms for linear advection in dimension one. The convergence depends on the size of the box where the distribution of the mass excess is performed. Various numerical examples illustrate the theoretical results. Applications to gas dynamics in dimension one is also discussed.

Paper presented by Prof. R. Abgrall

Publication date: January, 19, 2006

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FV schemes for a non linear Hyperbolic CL with a flux function involving discontinuous coefficients
Description: Title:
Finite volume schemes for a non linear hyperbolic conservation law with a flux function involving discontinuous coefficients

Author:
Florence Bachmann

Abstract:
A model for two phase flow in porous media with distinct permeabilities leads to a non linear hyperbolic conservation law with a discontinuous flux function. In this paper for such a problem, the notion of entropy solution is presented and existence and convergence of a finite volume scheme are proved. No hypothesis of convexity or genuine non linearity on the flux function is assumed, which is a new point in comparison with preceding works. As the trace of the solution along the line of discontinuity of the flux function can not be considered, this problem is more complex. To illustrate these results, some numerical tests are presented.

Paper presented by Prof. F. Benkhaldoun

Publication date: January, 19, 2006

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A Simple Finite-Volume Method for Compressible Isothermal Two-Phase Flows Simulation Popular
Description: Title:
A Simple Finite-Volume Method for Compressible Isothermal Two-Phase Flows Simulation

Authors:
F. Caro, F. Coquel, D. Jamet, S. Kokh

Abstract:
We present a simple method for simulating isothermal compressible two-phase flows with mass transfer. The convective part of the model is compatible with the Least Action Principle and the system is endowed with an entropy inequality which accounts for phase change terms and phasic pressure unbalance. A study of the system as a relaxed model of two equilibrium models is performed. This study allows the design of two-step relaxation-convection Finite-Volume discretization scheme which complies with the entropy balance of the model which drives the mass transfer phase-change process. Numerical results involving dynamical phase-change are presented.

Paper presented by Prof. J.M. Herad

Publication date: January, 18, 2006
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Added on: 18-Jan-2006 | Downloads: 270

Volume 3 N°2

Error estimate for Finite volume approximate solutions of oblique derivative boundary value problem
Description: Title:
Error estimate for Finite volume approximate solutions of some oblique derivative boundary value problems

Authors:
A. Bradji, T. Gallouet

Abstract:
This paper is an improvment of [BG 05], concerning the Laplace equation with an oblique boundary condition. When the boundary condition involves a regular coefficient, we present a weak formulation of the problem and we prove some existence and uniqueness results of the weak solution. We develop a Finite volume scheme and we prove the convergence of the Finite volume solution to the weak solution, when the mesh size goes to zero. We also present some partial results for the interesting case of a discontinuous coefficient in the boundary condition. In particular, we give a Finite volume scheme, taking in consideration the discontinuities of this coefficient Finally, we obtain some error estimates (in a convenient norm) of order ph (where h is the mesh size), when the solution u is regular enough.

Key words :
oblique derivative, smooth coefficient piecewise constant
coefficient unstructured mesh, Finite volume, error estimate.

Paper presented by:
Prof. F. Benkhaldoun
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Added on: 17-Oct-2006 | Downloads: 125

A rough scheme to couple free and porous media
Description: Title:
A rough scheme to couple free and porous media

Author:
Jean-Marc Herard

Abstract:
This paper is devoted to the computation of flows between free and porous media separated by a thin interface . The basic strategy relies on some ideas developed earlier by J.M. Greenberg and A.Y. Leroux on their work on well balanced schemes. This approach requires introducing a set of partial differential equations at the interface, in order to account for the sudden change of medium. The main features of the interface PDE are investigated. We afterwards propose to compute approximations of solutions with help of an approximate Godunov scheme. A linear interface Riemann solver is introduced, which aims at enforcing the continuity of the two (steady wave-) Riemann invariants. Numerical computations involving shock waves or rarefaction waves are examined and the agreement with the entropy inequality is tracked. Effects of the mesh refinement and the impact of the smoothing of the thin interface are also adressed in the paper.

Key words :
Porous media / Interfacial coupling / Godunov scheme

Paper presented by:
Prof. F. Benkhaldoun
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Added on: 16-Oct-2006 | Downloads: 107

Volume 4 N°1

The coupling of homogeneous models for two-phase flows
Description: Title:
The coupling of homogeneous models for two-phase flows

Authors:
Annalisa Ambroso, Christophe Chalons, Frederic Coquel, Edwige Godlewski,
Frederic Lagoutiere, Pierre-Arnaud Raviart, Nicolas Seguin

Abstract:
We consider the numerical coupling at a fixed spatial interface of two homogeneous models used for describing non isothermal compressible two phase flows. More precisely, we concentrate on the numerical coupling of the homogeneous equilibrium model and the homogeneous relaxation model in the context of finite volume methods. Three methods of coupling are presented. They are based on one of the following requirements: continuity of the conservative variable through the coupling interface, continuity of the primitive variable and global conservation of mass, momentum and energy. At the end, several numerical experiments are presented in order to illustrate the ability of each method to provide results in agreement with their principle of construction.

Papers presented by: Prof. T. Gallouet and Prof. J.M. Herard
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Added on: 27-Feb-2007 | Downloads: 93

Volume 5 N°1

Convergence analysis of an MPFA method
Description: Title:
Convergence analysis of an MPFA method for flow problems in anisotropic heterogeneous porous media

Authors:
A. Njifenjou, A. J. Kinfack

Abstract:
Our purpose in this paper is to present the theoretical analysis of a Multi-Point Flux Approximation method (MPFA method). We start with the derivation of the discrete problem, and then we give a result of existence and uniqueness of a solution for that problem. As in finite element theory, Lagrange interpolation is used to define three classes of continuous and locally polynomial approximate solutions. For analyzing the convergence of these different classes of solutions, the notions of weak and weak-star MPFA approximate solutions are introduced. Their theoretical properties, namely stability and error estimates (in discrete energy norms, L2 norm and L(infinity) norm), are investigated. These properties play a key role in the analysis (in terms of error estimates for diverse norms) of different classes of continuous and locally polynomial approximate solutions mentioned above.

Key words:

diffusion problems, nonhomogeneous anisotropic media, multi-point flux approximation method, weak and weak-star approximate solutions, discrete energy norm, stability, error estimates.

Paper presented by:
Prof. R. Herbin
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Added on: 09-May-2008 | Downloads: 32

Description of numerical shock profiles of non-linear Burgers’ equation
Description: Title:

Description of numerical shock profiles of non-linear Burgers’ equation by asymptotic solution of its differential approximations

Authors: A.V. Porubov, D. Bouche, G.Bonnaud

Abstract:

An analysis of dispersive/dissipative features of the difference schemes used for simulations of the non-linear Burgers’ equation is developed based on the travelling wave asymptotic solutions of its differential approximation. It is shown that these particular solutions describe well deviations in the shock profile even outside the formal applicability of the asymptotic expansions, namely for shocks of moderate amplitudes. Analytical predictions may be used to improve calculations by suitable choice of the parameters of some familiar schemes, i.e., the Lax-Wendroff, Mac-Cormack etc. Moreover, an improvement of the scheme may be developed by adding artificial terms according to the asymptotic solution.

Key words :

Scheme dispersion and dissipation, non-linear shock wave, asymptotic and numerical solutions.

Presented by: Prof. F. Benkhaldoun
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Added on: 08-Feb-2008 | Downloads: 35

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