IJFV International Journal On Finite Volumes
http://www.ijfv.org/
The International Journal on Finite Volumes addresses work at the interface between the theortical mathematics, applied mathematics and numerical computation. 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 peerreview. 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 peerreview 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.enSPIP  www.spip.netRobust MUSCL Schemes for TenMoment Gaussian Closure Equations with Source Terms
https://ijfv.math.cnrs.fr/spip.php?article59
https://ijfv.math.cnrs.fr/spip.php?article5920171017T06:30:37Ztext/htmlenAsha Kumari Meena, Kumar Harish
<p>Abstract: In this article, we present positivity preserving secondorder numerical schemes to approximate TenMoment Gaussian closure equations with source terms. The challenge here is to preserve the positivity of the density and the symmetric pressure tensor. We propose MUSCL type numerical schemes to overcome these difficulties. The principal components of the proposed schemes are a Strang splitting of the source terms, positivity preserving first order scheme and suitable linear (...)</p>

<a href="https://ijfv.math.cnrs.fr/spip.php?rubrique25" rel="directory">21. Volume 13 (2017)</a>
<div class='rss_texte'><p>Abstract:</p> <p>In this article, we present positivity preserving secondorder numerical schemes to approximate TenMoment Gaussian closure equations with source terms. The challenge here is to preserve the positivity of the density and the symmetric pressure tensor. We propose MUSCL type numerical schemes to overcome these difficulties. The principal components of the proposed schemes are a Strang splitting of the source terms, positivity preserving first order scheme and suitable linear reconstruction process which ensures the positivity of the reconstructed variables. To achieve positivity of reconstructed variables, we impose the additional restrictions on the slopes of the linear reconstructions. Additionally, the source is discretized using both explicit and implicit methods. In the case of explicit source discretization, we derive the appropriate condition on the time step for discretization to be positivity preserving. Implicit discretization of the source terms is shown to be unconditionally positivity preserving. Numerical examples are presented to demonstrate the superior robustness and stability of the proposed numerical schemes.</p> <p>Key words : TenMoment equations, Finite Volume Methods, MUSCL Scheme, Positivity preserving schemes.</p> <p>Paper presented by: Thierry Gallouët</p></div>
A simple and accurate coupled HLLtype approximate Riemann solver for the twofluid twopressure model of compressible flows
https://ijfv.math.cnrs.fr/spip.php?article56
https://ijfv.math.cnrs.fr/spip.php?article5620161222T10:20:55Ztext/htmlenChalons Christophe
<p>Abstract: This paper is concerned with the design of a very simple and efficient Godunovtype method for the socalled twofluid twopressure compress ible model for twophase flows. It is a contribution to the proceedings of a workshop organized by the EDF R&D French utility company and devoted to the verification of numerical schemes for twophase flows. The present study focuses on the convective part of the twofluid twopressure model and is a short form of a longer paper [1] (...)</p>

<a href="https://ijfv.math.cnrs.fr/spip.php?rubrique23" rel="directory">19. EDF Special Workshop (2015)</a>
<div class='rss_texte'><p>Abstract:</p> <p>This paper is concerned with the design of a very simple and efficient Godunovtype method for the socalled twofluid twopressure compress ible model for twophase flows. It is a contribution to the proceedings of a workshop organized by the EDF R&D French utility company and devoted to the verification of numerical schemes for twophase flows. The present study focuses on the convective part of the twofluid twopressure model and is a short form of a longer paper [1] where the numerical strategy also takes into account additional terms associated with sources, pressure relaxation and drag forces. Numerical simulations and comparisons with other strategies are proposed in the last section.</p> <p>Keywords :</p> <p>Paper presented by: JeanMarc Hérard</p></div>
A comparative study of numerical schemes for the BaerNunziato model
https://ijfv.math.cnrs.fr/spip.php?article57
https://ijfv.math.cnrs.fr/spip.php?article5720161213T06:49:44Ztext/htmlenDallet Sophie
<p>Abstract: The present paper is devoted to a comparison of numerical methods for the convective part of a twophase flow model. Four explicit schemes are tested using Riemann problems or regular solutions. The main criteria for comparing the methods are: the accuracy for a fixed size of mesh, the convergence, the robustness and the CPU time cost necessary to reach a fixed error. The conclusions of this study are the following. The clas sical Rusanov scheme is not competitive, as expected. (...)</p>

<a href="https://ijfv.math.cnrs.fr/spip.php?rubrique23" rel="directory">19. EDF Special Workshop (2015)</a>
<div class='rss_texte'><p>Abstract:</p> <p>The present paper is devoted to a comparison of numerical methods for the convective part of a twophase flow model. Four explicit schemes are tested using Riemann problems or regular solutions. The main criteria for comparing the methods are: the accuracy for a fixed size of mesh, the convergence, the robustness and the CPU time cost necessary to reach a fixed error. The conclusions of this study are the following. The clas sical Rusanov scheme is not competitive, as expected. The relaxation scheme seems to be more efficient than the VFROEncv method, espe cially regarding robustness. The staggered scheme, recently investigated for this model, is sometimes less accurate for a fixed size of mesh than the VFROEncv and relaxation schemes but is the most acurate for a fixed run time.</p> <p>Keywords : BaerNunziato model, benchmark study, explicit schemes.</p> <p>Paper presented by: JeanMarc Hérard</p></div>
Verification of a twophase flow code based on an homogeneous model
https://ijfv.math.cnrs.fr/spip.php?article58
https://ijfv.math.cnrs.fr/spip.php?article5820161110T17:29:00Ztext/htmlenHELLUY Philippe, Hurisse Olivier, Le Coupanec Erwan
<p>Abstract We present some verification test cases applied to a code developed at EDF R&D for the simulation of twophase flows with mass transfer. The aim of this code is to allow the simulation of a wide range of industrial situations by considering all the thermodynamic disequilibria between the phases  pressure, temperature and chemical potential and by assuming the kinematic equilibrium  a single velocity for both phases. The under lying homogeneous model [1, 13] is based on the (...)</p>

<a href="https://ijfv.math.cnrs.fr/spip.php?rubrique23" rel="directory">19. EDF Special Workshop (2015)</a>
<div class='rss_texte'><p>Abstract</p> <p>We present some verification test cases applied to a code developed at EDF R&D for the simulation of twophase flows with mass transfer. The aim of this code is to allow the simulation of a wide range of industrial situations by considering all the thermodynamic disequilibria between the phases  pressure, temperature and chemical potential and by assuming the kinematic equilibrium  a single velocity for both phases. The under lying homogeneous model [1, 13] is based on the Euler system of equations supplemented by a complex pressure law describing the behaviour of the mixture of the two phases. Different firstorder schemes are compared on the basis of two analytical solutions: a classical Riemann problem and a steadystate heated pipe test.</p> <p>Key words : Homogeneous model, twophase flows, verification.</p> <p>Paper presented by: JeanMarc Hérard</p></div>
An integral approach to compute compressible fluid flows in domains containing obstacles
https://ijfv.math.cnrs.fr/spip.php?article55
https://ijfv.math.cnrs.fr/spip.php?article5520151211T08:12:04Ztext/htmlenHérard JeanMarc, Martin Xavier
<p>Abstract : We detail in this paper an integral approach in order to cope with the computation of flows of a compressible fluid in a physical domain containing many small obstacles. The basic methodology and the main ingredients used in schemes are provided, together with some exact solutions that are used to benchmark the integral approach. The latter is compared to the reference solution that accounts for all obstacles through standard wallboundary conditions. Numerical results are also (...)</p>

<a href="https://ijfv.math.cnrs.fr/spip.php?rubrique22" rel="directory">18. Volume 12 (2015)</a>
<div class='rss_texte'><p>Abstract :</p> <p>We detail in this paper an integral approach in order to cope with the computation of flows of a compressible fluid in a physical domain containing many small obstacles. The basic methodology and the main ingredients used in schemes are provided, together with some exact solutions that are used to benchmark the integral approach. The latter is compared to the reference solution that accounts for all obstacles through standard wallboundary conditions. Numerical results are also shown to be more accurate than the standard wellbalanced approach. This work is actually the sequel of paper [1] that investigates the computation of compressible flows in variable crosssection ducts.</p> <p>Keywords : Paper presented by: Jiri Furst</p></div>
Convergence of a finite volume scheme for a corrosion model
https://ijfv.math.cnrs.fr/spip.php?article54
https://ijfv.math.cnrs.fr/spip.php?article5420150609T08:55:34Ztext/htmlenChainais Claire, Colin PierreLouis, LacroixViolet Ingrid
<p>Abstract In this paper, we study the numerical approximation of a system of partial differential equations describing the corrosion of an iron based alloy in a nuclear waste repository. In particular, we are interested in the convergence of a numerical scheme consisting in an implicit Euler scheme in time and a ScharfetterGummel finite volume scheme in space. Keywords : finite volume scheme, corrosion model, convergence analysis, driftdiffusion system Paper presented by: Pascal (...)</p>

<a href="https://ijfv.math.cnrs.fr/spip.php?rubrique22" rel="directory">18. Volume 12 (2015)</a>
<div class='rss_texte'><p>Abstract</p> <p>In this paper, we study the numerical approximation of a system of partial differential equations describing the corrosion of an iron based alloy in a nuclear waste repository. In particular, we are interested in the convergence of a numerical scheme consisting in an implicit Euler scheme in time and a ScharfetterGummel finite volume scheme in space.</p> <p>Keywords : finite volume scheme, corrosion model, convergence analysis, driftdiffusion system</p> <p>Paper presented by: Pascal Omnes</p></div>
Formulations of two phase liquid gas compositional Darcy flows with phase transitions
https://ijfv.math.cnrs.fr/spip.php?article53
https://ijfv.math.cnrs.fr/spip.php?article5320140901T07:14:13Ztext/htmlenMasson Roland, Trenty Laurent, Zhang Yumeng
<p>Abstract In this article, three formulations of two phase compositional Darcy flows taking into account phase transitions are compared. The first formulation is the so called natural variable formulation commonly used in reservoir simulation, the second has been introduced in [14] and uses the phase pressures, saturations and component fugacities as main unknowns, and the third is an extension to general compositional two phase flows of the pressure pressure formulation introduced in [2] (...)</p>

<a href="https://ijfv.math.cnrs.fr/spip.php?rubrique21" rel="directory">17. Volume 11 (2014)</a>
<div class='rss_texte'><p>Abstract</p> <p>In this article, three formulations of two phase compositional Darcy flows taking into account phase transitions are compared. The first formulation is the so called natural variable formulation commonly used in reservoir simulation, the second has been introduced in [14] and uses the phase pressures, saturations and component fugacities as main unknowns, and the third is an extension to general compositional two phase flows of the pressure pressure formulation introduced in [2] in the case of two compo nents. The three formulations are shown to lead to equivalent definitions of the phase transitions for our gas liquid thermodynamical model. Then, they are compared numerically in terms of solution and convergence of the Newton type non linear solver on several 1D and 3D test cases including gas appearance and liquid disappearance. The 3D discretization is based on the Vertex Approximate Gradient (VAG) scheme [10] and takes into account discontinuous capillary pressures.</p> <p>Key words : Darcy flow, twophase flow, phase transitions, composi tional models, finite volume scheme, discontinuous capillary pressures</p> <p>Paper presented by: Professor Thierry Gallouet</p></div>
Application of an homogeneous model to simulate the heating of twophase flows
https://ijfv.math.cnrs.fr/spip.php?article52
https://ijfv.math.cnrs.fr/spip.php?article5220140521T15:39:16Ztext/htmlenHurisse Olivier
<p>Abstract This paper is dedicated to the simulation of twophase flows on the basis of an homogeneous model that allows to account for the disequilibrium of the pressure, temperature and chemical potential (mass transfer). The numerical simulations are performed using a fractional step method treat ing separately the convective part of the model and the source terms. On the basis of analytical solutions for the convective part of the model, nu merical investigations are performed to (...)</p>

<a href="https://ijfv.math.cnrs.fr/spip.php?rubrique21" rel="directory">17. Volume 11 (2014)</a>
<div class='rss_texte'><p>Abstract
This paper is dedicated to the simulation of twophase flows on the basis of an homogeneous model that allows to account for the disequilibrium of the pressure, temperature and chemical potential (mass transfer). The numerical simulations are performed using a fractional step method treat ing separately the convective part of the model and the source terms. On the basis of analytical solutions for the convective part of the model, nu merical investigations are performed to compare different finite volume schemes. Eventually, a test case of the heating of a mixture of steam and water is presented.</p> <p>Key words : Homogeneous model, twophase flows, mass transfer.</p> <p>Paper presented by: Professor Thierry Gallouet</p></div>
An entropy preserving MOOD scheme for the Euler equations
https://ijfv.math.cnrs.fr/spip.php?article51
https://ijfv.math.cnrs.fr/spip.php?article5120140128T10:18:10Ztext/htmlenBerthon Christophe, Desveaux Vivien
<p>Abstract The present work concerns the derivation of entropy stability properties to be satisfied by highorder accurate finite volume methods. Such a sta bility turns out to be crucial when approximating the weak solutions of hyperbolic systems of conservation laws. In fact, several recent works pro pose some kind of discrete entropy inequalities associated to highorder schemes. However, these entropy preserving schemes do not seem relevant to impose that the converged solution (in the (...)</p>

<a href="https://ijfv.math.cnrs.fr/spip.php?rubrique21" rel="directory">17. Volume 11 (2014)</a>
<div class='rss_texte'><p>Abstract
The present work concerns the derivation of entropy stability properties to be satisfied by highorder accurate finite volume methods. Such a sta bility turns out to be crucial when approximating the weak solutions of hyperbolic systems of conservation laws. In fact, several recent works pro pose some kind of discrete entropy inequalities associated to highorder schemes. However, these entropy preserving schemes do not seem relevant to impose that the converged solution (in the sense of the LaxWendroff Theorem) satisfies the required entropy inequalities. We illustrate such a failure by exhibiting numerical schemes that, from one hand, satisfy en tropy stability and, from the other hand, do not prevent numerical blow up. Here, we recall the expected highorder discrete entropy inequalities to be certain that the approximate solution converges to an entropy solution. Equipped with these sufficient numerical entropy stability, we propose to extend the recently introduced highorder MOOD scheme to satisfy the required highorder entropy inequalities. In fact, the MOOD approach is based on an a posteriori estimation and it seems impossible to impose a posteriori the whole set of discrete entropy inequalities. We solve this dif ficulty by considering a finite volume scheme, which involves (at least one) discrete entropy inequalities with a numerical transport property. From one selected numerical transport discrete entropy inequality, we establish that all the needed discrete entropy inequalities are satisfied. Arguing this specific numerical transport entropy, we derive the expected a posteriori entropy condition to get an entropy preserving highorder MOOD scheme. Numerical experiments illustrate the relevance of the suggested numerical procedure.</p> <p>Keywords : Euler equations, numerical approximation, finite volume methods, highorder approximation, discrete entropy inequalities.</p> <p>Paper presented by: Professor Thierry Gallouet</p></div>
OpenCL simulations of twofluid compressible flows with a random choice method
https://ijfv.math.cnrs.fr/spip.php?article50
https://ijfv.math.cnrs.fr/spip.php?article5020130710T16:24:04Ztext/htmlenHELLUY Philippe, Jung Jonathan
<p>Abstract In this paper, we propose a new very simple numerical method for solving liquidgas compressible flows. Such flows are difficult to simulate because classic conservative finite volume schemes generate pressure oscillations at the liquidgas interface. We extend to several dimensions the random choice scheme that we have constructed in [2]. The extension is performed through Strang dimensional splitting. The resulting scheme exhibits in teresting conservation and stability (...)</p>

<a href="https://ijfv.math.cnrs.fr/spip.php?rubrique20" rel="directory">15. Volume 10 special</a>
<div class='rss_texte'><p>Abstract
In this paper, we propose a new very simple numerical method for solving liquidgas compressible flows. Such flows are difficult to simulate because classic conservative finite volume schemes generate pressure oscillations at the liquidgas interface. We extend to several dimensions the random choice scheme that we have constructed in [2]. The extension is performed through Strang dimensional splitting. The resulting scheme exhibits in teresting conservation and stability properties. For achieving high perfor mance, the scheme is tested on recent multicore processors and GPUs, using the OpenCL environment.</p> <p>Key words : OpenCL, GPU, twofluid compressible flow, Lagrange projection, Glimm, Strang splitting</p> <p>Paper presented by JM Hérard and T. Gallouët on July, 10, 2013</p></div>