ACCEPTED PAPERS

FVCA4, MARRAKECH, MOROCCO, JULY 4 - JULY 8, 2005

http://averoes.math.univ-paris13.fr/fvca4

Paper 24, Code: S012FVCA4, MARRAKECH, MOROCCO, JULY 4 - JULY 8, 2005

http://averoes.math.univ-paris13.fr/fvca4

Finite volume
schemes for a nonlinear hyperbolic conservation law with a flux
function
involving discontinuous coefficients

Paper 1, Code: A001

Authors: F. Bachmann

Abstract:

Key words: discontinuous flux, entropy solution, finite volume scheme.

Paper 1, Code: A001

Authors: F. Bachmann

Abstract:

A model for two phase flow in
porous media with distinct permeabilities leads to a non linear
hyperbolic conservation law with discontinuous flux function. One
presents in this paper for such a problem, the notion of entropy
solution, proves existence, uniqueness and convergence of finite
volume scheme. One remarks that no hypothesis of convexity or
genuine non linearity on the flux function is assumed, which is a
new point in comparaison with preceding works. This brings a new
difficulty because one can not consider the trace of the solution
along the line of discontinuity of the flux function.

Key words: discontinuous flux, entropy solution, finite volume scheme.

Variational Smoothing of
Volumetric Medical Images

Paper 2, Code: A002

Authors: A. Ben Hamza

Abstract:

Key words : variational smoothing, information theory, volumetric medical imaging.

Boundary conditions for Petrov-Galekin Finite Volumes

Paper 3, Code: S001

Authors: S. Borel, F. Dubois, C. Le Potier and M.M. Tekitek

Abstract:

We consider the Petrov-Galerkin finite volumes method based on dual Raviart-Thomas basis functions and the least square method. We propose a numerical scheme for various boundary conditions. First numerical tests indicates good convergence properties. [FVCA4, april

2005]

Direct numerical simulation of convective turbulence

Paper 4, Code: C001

Authors: I. Palymsky

Abstract:

Paper 2, Code: A002

Authors: A. Ben Hamza

Abstract:

We propose an
information-theoretic variational model for volumetric medical image
smoothing. It is a result of minimizing a functional subject to some
noise constraints, and takes a hybrid form of a negative-entropy
variational integral for small gradient magnitudes and a total
variational integral for large gradient magnitudes. The core idea
behind this approach is to use geometric insight in helping construct
regularizing functionals and avoiding a subjective choice of a prior in
maximum a posteriori estimation. Illustrating experimental results
demonstrate a much improved performance of the approach in the presence
of noise.

Key words : variational smoothing, information theory, volumetric medical imaging.

Boundary conditions for Petrov-Galekin Finite Volumes

Paper 3, Code: S001

Authors: S. Borel, F. Dubois, C. Le Potier and M.M. Tekitek

Abstract:

We consider the Petrov-Galerkin finite volumes method based on dual Raviart-Thomas basis functions and the least square method. We propose a numerical scheme for various boundary conditions. First numerical tests indicates good convergence properties. [FVCA4, april

2005]

Direct numerical simulation of convective turbulence

Paper 4, Code: C001

Authors: I. Palymsky

Abstract:

Turbulent
convective flow of water in horizontal layer with free horizontal
boundaries, arising at heating from below, is
numerically simulated by spectral method using the Boussinesq model
without any semiempirical relationships (DNS) in 2-D case. It is
shown that numerical results have good agreement with experimental data
and results of numerical simulations with rigid boundary
conditions at enough high supercriticality and that this simulation
reflects the transition to hard turbulence. We study also the role of
boundary conditions (free-rigid).

A complete flux scheme for
one dimensional combustion simulation

Paper 5, Code: C002

Authors: J.H.M ten Thije Boonkkamp

Abstract:

Finite Volume approximation for an oblique derivative boundary value problem

Paper 6, Code: A003

Authors: A. Bradji and T. Gallouet

Key words : Oblique derivative, non structured mesh, diffusion equation.

A space-time conservative Finite Volume scheme for Hyperbolic conservation laws

Paper 7, Code: S003

Authors: Q. U. Ain, S. Qamar and G. Warnecke

Keywords: Conservation
laws,
hyperbolic systems, space-time control volumes, finite volume schemes,
high order accuracy, shock solutions.

Solution of Unsteady Natural Convection Flows using Finite Volume Modified Method of Characteristics

Paper 8, Code: C003

Authors: Mofdi El-Amrani and Mohammed Seaid

Abstract:

Key words : Incompressible Navier-Stokes Equations; Boussinesq Approximation; Modified Method of Characteristics; Finite Volume Method; Natural Convection flow Simulation.

A finite volume
method for the approximation of highly anisotropic diffusion operators
on unstructured meshes

Paper 10, Code S004

Author: C Le Potier

Stability and Convergence of a Finite Volume Method for a Reaction-Diffusion system of Equations in Electro-Cardiology

Paper 11, Code: A004

Authors: Y. Coudiere and C. Pierre

Abstract:

Experimental and numerical investigation on heat transfer for polyethylene flowing through extrusion die

Paper 13, Code C005

Authors: M. KARKRI A. NACHAOUI Y. JARNY P. MOUSSEAU

Key words : Finite element method, SIMPLE algorithm, Die design, Polymer flow, extrusion die

On Finite Volume Schemes for Nonconservative Hyperbolic Problems

Paper 14, Code: S006

Authors: V. Dolejsi, T. Gallouet

Abstract:

Key words : nonconservative hyperbolic equations, nonconservative Roe Finite volume schemes, numerical flux.

A well balanced scheme for gas flows in protoplanetary nebulae

Paper 15, Code: S007

Authors: H. Guillard, E. Daniel

Abstract:

Key words : Origin solar system, planetary formation, hydrodynamics, finite volume methods, well-balanced schemes

Conservative Locally Moving Mesh Method for Multifluid Flows

Paper 16, Code S008

Authors: A. Chertock, A. Kurganov

Abstract:

Convergence of the water-air flow model to Richards model

Paper 17, Code: A008

Authors: R. Eymard, M. Ghilani and M. Marhraoui

Abstract:

The aim of this work is to prove the convergence of the system which models the air-water flow in the soils to the Richards model when the air mobility tends to infinity. The convergence is obtained in two steps. In the first one we prove the convergence of the discrete solution obtained by the implicit finite volumes scheme to the weak solution of the continues problem independently of the air mobility . This step is obtained thanks to the priori estimates of the water saturation and the gradient of the water and capillary pressures. In the second step we prove the convergence of the weak solutions as the mobility tends to infinity.

A novel Cartesian cut-cell approach

Paper 18, Code: S009

Authors: I. Wenneker and M. Borsboom

Abstract:

Key words : cut cells, Cartesian grids, inviscid flows.

An optimal a priori error analysis of the Finite Volume method for linear convection problems

Paper 19, Code: A005

Authors: D. Bouche, J.M. Ghidaglia, and F. Pascal

Abstract:

Key words: Finite Volume Method ; Consistency and Accuracy ; Geometric Corrector ; Unstructured Meshes.

A Finite volume scheme for the computation of erosion limiters

Paper 20, Code: A006

Authors: R. Eymard and T. Gallouet

Abstract :

Key words : Hyperbolic inequations, Finite volume methods, erosion and sedimentation models.

A MULTIDIMENSIONAL MULTIPHASE FLOW FINITE VOLUME SOLVER USING A LAGRANGIAN PHASE AND A PROJECTION TECHNIQUE

Paper 21, Code S010

Authors: B. Desjardins, J. Francescatto, J.M. Ghidaglia

Abstract :

Key words : Multiphase Flow, Lagrange + Remap, spherical test cases.

Homogeneous two-phase flow models: coupling by finite volume methods

Paper 22, Code: S011

Authors: A. Ambroso, C. Chalons, F. Coquel, E. Godlewski, F. Lagoutiere, P.A. Raviart, N. Seguin

Abstract:

Key words : Model coupling, hyperbolic systems, two-phase flow, phase transition.

Convergence of a finite volume scheme on a MAC mesh for the Stokes problem with right-hand side in H−1

Paper 23, Code: A007

Authors: P. Blanc

Abstract:

We consider a finite volume scheme on MAC meshes for the Sto equations with right-hand side in H−1 and we prove the convergence the scheme.

Key words: Finite volume scheme, MAC mesh, Stokes equations.

Finite-volume schemes for nonlinear elliptic problems on general 2D meshes

Paper 5, Code: C002

Authors: J.H.M ten Thije Boonkkamp

Abstract:

A discretisation scheme for the
conservation equations describing a one-dimensional laminar flame is
presented. The scheme is a finite volume discretisation combined with a
generalized exponential scheme, the so-called complete flux scheme, for
the computation of the numerical fluxes. The numerical flux
contains two terms, viz. one corresponding to the homogeneous and one
corresponding to the particular solution of the differential equation.
Its derivation is based on the advection-diffusion-reaction
equation. As an example, numerical results for a methane/air
flame
are presented.

Finite Volume approximation for an oblique derivative boundary value problem

Paper 6, Code: A003

Authors: A. Bradji and T. Gallouet

Abstract :

In this paper, we consider the
Laplace equation with oblique boundary conditions, on an open bounded
polygonal
connected domain. We introduce an admissible
mesh and we develop a finite volume scheme. We prove
that the finite volume solutions arising from this scheme
converge to the weak solution of the problem, when the mesh
size tends to zero.

Key words : Oblique derivative, non structured mesh, diffusion equation.

A space-time conservative Finite Volume scheme for Hyperbolic conservation laws

Paper 7, Code: S003

Authors: Q. U. Ain, S. Qamar and G. Warnecke

Abstrac:

We present a second order scheme
for the numerical solution of hyperbolic systems which treats space and
time in a unified manner. The flow variables and their slopes are the
basic unknowns in the scheme. The scheme utilizes the advantages
of the space-time conservation element and solution element
(CE/SE) method (Chang 1995) as well as central schemes (Nessyahu and
Tadmor 1990). However, unlike the CE/SE method the present scheme
is Jacobian-free and hence like the central schemes can also be applied
to any hyperbolic system. In Chang's method they used a
finite difference approach for the slope calculation in case of
nonlinear hyperbolic equations. We propose to propagate the slopes by a
scheme even in the case of nonlinear systems. By introducing a suitable
limiter for the slopes of flow variables, we can apply the same
scheme to linear and non-linear problems with discontinuities.
The scheme is simple, efficient and has a good resolution especially at
contact discontinuities. We derive the scheme for the one and two space
dimensions. In two-space dimensions we use triangular meshes. The
second order accuracy of the scheme has been verified by numerical
experiments. Several numerical test computations presented in this
article validate the accuracy and robustness of the present scheme.

Solution of Unsteady Natural Convection Flows using Finite Volume Modified Method of Characteristics

Paper 8, Code: C003

Authors: Mofdi El-Amrani and Mohammed Seaid

Abstract:

This paper proposes a finite
volume modified method of characteristics for the numerical solution of
natural convection flows. The unsteady, viscous incompressible, and
thermal flows are modelled by a set of coupled Navier-Stokes/Boussinesq
equations involving conservation of mass, momentum, and energy
equations. To develop an accurate and efficient solver for the model,
we
implement a modified method of characteristics in the finite volume
framework. The presented method is unconditionally stable, independent
of the Rayleigh number, and can be easily implemented on unstructured
meshes. Numerical results are shown for the two benchmark problems: the
model problem of natural convection in a square cavity and also for
heated flow over a cylinder.

Key words : Incompressible Navier-Stokes Equations; Boussinesq Approximation; Modified Method of Characteristics; Finite Volume Method; Natural Convection flow Simulation.

Paper 10, Code S004

Author: C Le Potier

Abstract:

We introduce a finite volume method for highly anisotropic diffusion operators on unstructured meshes. The main idea is to calculate the gradient on each cell vertex using the cell-centered unknown and other unknowns calculated on the cell faces. These degrees of freedom are eliminated imposing flux continuity conditions. The resulting global matrix is symmetric and positive definite. We show the robustness and the accuracy of the method in comparison with analytical solutions and results obtained with other numerical schemes.

We introduce a finite volume method for highly anisotropic diffusion operators on unstructured meshes. The main idea is to calculate the gradient on each cell vertex using the cell-centered unknown and other unknowns calculated on the cell faces. These degrees of freedom are eliminated imposing flux continuity conditions. The resulting global matrix is symmetric and positive definite. We show the robustness and the accuracy of the method in comparison with analytical solutions and results obtained with other numerical schemes.

Stability and Convergence of a Finite Volume Method for a Reaction-Diffusion system of Equations in Electro-Cardiology

Paper 11, Code: A004

Authors: Y. Coudiere and C. Pierre

Abstract:

In the field of
Electro-cardiology, the mono-domain equations model the electrical
phenomena occurring in the he muscle, considered as an anisotropic
conducting medium. Is is a coupled system of one
semi-linear parabolic PDE of reaction-diffusion type and one or
severa ODEs. Numerical difficulties are due to the different time
and space scales in the equations. Actually, the solution exhibit very
sharp fronts propagating at high speeds. Simulations needs
unstructured,
fine and/or locally refined meshes.

Hence, we propose a Finite Volume methods, and address here the difficult problem of numerical stability for two simple time-stepping methods. Convergence results are also proved.

Hence, we propose a Finite Volume methods, and address here the difficult problem of numerical stability for two simple time-stepping methods. Convergence results are also proved.

Experimental and numerical investigation on heat transfer for polyethylene flowing through extrusion die

Paper 13, Code C005

Authors: M. KARKRI A. NACHAOUI Y. JARNY P. MOUSSEAU

Abstract:Experimental and numerical study is
carried out on the conjugate thermal transport in polyethylene (PE)
flowing through extrusion die. This paper deals with the experimental
design and with SIMPLE (Semi-Implicit Method for Pressure-Linked
Equations Patankar and Spalding 1972) method for solving the
continuity,
momentum and energy equations. The simulation is performed to determine
the influence of conduction through the die wall and the pressure drops
on the transport in the polymer and on the temperature profiles in the
interface channel-wall. The computational model has been validated with
the experimental results, and good agreement has been observed.

Key words : Finite element method, SIMPLE algorithm, Die design, Polymer flow, extrusion die

On Finite Volume Schemes for Nonconservative Hyperbolic Problems

Paper 14, Code: S006

Authors: V. Dolejsi, T. Gallouet

Abstract:

We deal with a numerical solution of a
nonconservative system of hyperbolic equations arising from a °ow
simulation of a solid-liquid-gas mixture. This system has at least one
eigenvalue which changes its sign in the interior of the computational
domain and it can cause a fail of some numerical schemes. We discuss a
use of several Roe-type ¯nite volume methods, which are based on a
solution of linearized Riemann problems. We show that the mentioned
property of the system can completely spoil a solution of the
linearized
Riemann problem and consequently a collapse of a computational process.
We propose a numerical scheme which does not su®er from the
mentioned drawbacks and which e±ciently simulates flows of
solid-liquid-gas slurries.

Key words : nonconservative hyperbolic equations, nonconservative Roe Finite volume schemes, numerical flux.

A well balanced scheme for gas flows in protoplanetary nebulae

Paper 15, Code: S007

Authors: H. Guillard, E. Daniel

Abstract:

This
work deals with the study of the long time evolution of the gas and
dust protoplanetary nebula where planets are supposed to form. In a
preliminary step, we show here how to construct a well-balanced FV
scheme preserving the equilibrium state of a gas flow rotating in the
gravitational field of a central star.

Key words : Origin solar system, planetary formation, hydrodynamics, finite volume methods, well-balanced schemes

Conservative Locally Moving Mesh Method for Multifluid Flows

Paper 16, Code S008

Authors: A. Chertock, A. Kurganov

Abstract:

We present
a conservative locally moving mesh finite-volume-particle method for
computing compressible multifluids flows. The idea behind the new
method is to use different schemes for the flow and the interface
tracking: the Euler equations are numerically integrated using a
finite-volume scheme, while a particle method is used to track the
moving interface and obtain a subcell information needed to create an
adaptive locally moving mesh such that the material interface always
coincides with the moving cell boundary. The method does not generate
significant oscillations across the material interface and provides an
enhanced resolution of the contact discontinuities.

Convergence of the water-air flow model to Richards model

Paper 17, Code: A008

Authors: R. Eymard, M. Ghilani and M. Marhraoui

Abstract:

The aim of this work is to prove the convergence of the system which models the air-water flow in the soils to the Richards model when the air mobility tends to infinity. The convergence is obtained in two steps. In the first one we prove the convergence of the discrete solution obtained by the implicit finite volumes scheme to the weak solution of the continues problem independently of the air mobility . This step is obtained thanks to the priori estimates of the water saturation and the gradient of the water and capillary pressures. In the second step we prove the convergence of the weak solutions as the mobility tends to infinity.

A novel Cartesian cut-cell approach

Paper 18, Code: S009

Authors: I. Wenneker and M. Borsboom

Abstract:

An alternative to the Cartesian cut-cell
method is introduced. Its formulation is fundamentally different from
the formulations usually encountered in literature, since it avoids
discretization of the boundary conditions on cut cells. In the approach
presented here, the boundary condition is extrapolated by means of a
Taylor series expansion to a nearby gridline of the Cartesian grid. A
simple Cartesian grid method uses then this extrapolated boundary
condition. This leads to a simple yet accurate discretization of the
boundary conditions. The resulting geometric issues are very limited in
number and straightforward. Moreover, the method can be applied to more
complicated boundary conditions than closed boundary conditions.

Key words : cut cells, Cartesian grids, inviscid flows.

An optimal a priori error analysis of the Finite Volume method for linear convection problems

Paper 19, Code: A005

Authors: D. Bouche, J.M. Ghidaglia, and F. Pascal

Abstract:

This paper investigates the order of
convergence of the upwind Finite volume method for solving linear
steady
convection problem on a bounded domain and with natural boundary
conditions. In order to overcome the non consistency in the fiite
differences sense of the scheme, we introduce a sequence of what we
call
geometric correctors and which is associated with every finite volume
mesh and every constant convection vector. Under a local
quasi-uniformity condition for the triangulation and if the continuous
solution is regular enough, we first establish a link between the
convergence of the Finitevolume scheme and these geometric correctors.
Hence the study of this corrector in the case of uniformly rened
triangular meshes in two dimensions leads to the proof of the optimal
order of convergence for the Finite volume scheme. We then focus the
second part of the paper on the Peterson case where for a non uniformly
refined mesh and a convection direction parallel to one side of the
domain, a loss of accuracy was proved.

Key words: Finite Volume Method ; Consistency and Accuracy ; Geometric Corrector ; Unstructured Meshes.

A Finite volume scheme for the computation of erosion limiters

Paper 20, Code: A006

Authors: R. Eymard and T. Gallouet

Abstract :

Sedimentation and erosion processes, in
sedimentary basins, can be modeled by a scalar hyperbolic equation,
under an erosion limiting condition. We present in this paper a Finite
volume scheme for the approximation of this problem and the proof of
its
convergence. This proof is based on the uniqueness of a weaker solution
to this problem, involving Lagrange multipliers, which is shown to be
the limit of the numerical scheme.

Key words : Hyperbolic inequations, Finite volume methods, erosion and sedimentation models.

A MULTIDIMENSIONAL MULTIPHASE FLOW FINITE VOLUME SOLVER USING A LAGRANGIAN PHASE AND A PROJECTION TECHNIQUE

Paper 21, Code S010

Authors: B. Desjardins, J. Francescatto, J.M. Ghidaglia

Abstract :

On our way to design a numerical platform
able to reproduce complex turbulent mixing flows, we report here
on some numerical benchmarks of the code. We shall first rapidly
present
our numerical method which essentially relies on a Finite Volume
approach and a splitting in 3 steps for the time scheme. Then we
present
3 new test cases towards the validation of the scheme.

Key words : Multiphase Flow, Lagrange + Remap, spherical test cases.

Homogeneous two-phase flow models: coupling by finite volume methods

Paper 22, Code: S011

Authors: A. Ambroso, C. Chalons, F. Coquel, E. Godlewski, F. Lagoutiere, P.A. Raviart, N. Seguin

Abstract:

The simulation of complex configurations
often requires to use specific models in the different parts of the
domain of computation in order to account for specific behaviors of the
flow. The models must be coupled to obtain a complete and coherent
description of the system as a whole. We study here two separate
domains
sharing a fixed interface. In each one, a different model is used to
describe the flow. The main difficulty is to give appropriate
conditions
at the interface in a way to obtain a coherent description of the
unsteady flow according to physical considerations. In this work, we
present the coupling of two different hyperbolic systems. As an example, the coupling of the
homogeneous equilibrium model and the homogeneous relaxation model is
studied and illustrated by numerical results.

Key words : Model coupling, hyperbolic systems, two-phase flow, phase transition.

Convergence of a finite volume scheme on a MAC mesh for the Stokes problem with right-hand side in H−1

Paper 23, Code: A007

Authors: P. Blanc

Abstract:

We consider a finite volume scheme on MAC meshes for the Sto equations with right-hand side in H−1 and we prove the convergence the scheme.

Key words: Finite volume scheme, MAC mesh, Stokes equations.

Finite-volume schemes for nonlinear elliptic problems on general 2D meshes

Authors: Boris Andreianovy 1, Franck Boyer 2, Florence Hubert 2

Abstract:

Finite volume schemes on general
meshes are studied for nonlinear diffusion problems with non
homogeneous
Dirichlet boundary condition. These schemes allow the discretization
nonlinear fluxes in such a way that the discrete operator
inherits
the key properties of the continuous one. The schemes being nonlinear,
we show that the approximate solution exists and is unique. The
convergence rate is analyzed for W_2^p solutions.

Key words : Finite-volume methods, Error estimates, Leray-Lions operators.

Mesh Partitioning for Parallel Computational Fluid Dynamics Applications on a Grid

Paper 26, Code: C006

Authors: Y. Mesri, H. Digonnet, H. Guillard

Abstract:

The problem of partitioning unstructured
meshes on a homogeneous architecture is largely studied. However,
existing partitioning schemes fail when the target architecture
introduces heterogeneity in resource characteristics. With the advent
of
heterogeneous architecture as the Grid, it becomes imperative to study
the partitioning problem taking into account the heterogeneous
platforms. In this work, we present a new mesh partitioning scheme,
that
takes into account the heterogeneity of CPU and networks. Our load
balancing mesh partition strategy improves the performance of parallel
applications running in a heterogeneous environment. The use of these
techniques are applied to some model problems in CFD. Experimental
results conrm that these techniques can improve the performance of
applications on a computational Grid.

Key words: Grid computing, mesh partitioning, Distributed computing, Load balancing, performance study.

Model-error estimation for goal-oriented model adaptation in flow simulations

Paper 28, Code: A010

Authors: J.M. Cnossen

Abstract:

We derive a model-error
estimator for output-oriented model adaptation in flow simulations.
Model adaptation is expected to save CPU time in aerospace engineering
problems requiring large number of CFD computations. In this paper we
derive the model error estimator for a well-known model problem for the
Euler vs. Navier-Stokes equations: the unsteady 1-D Burgers problem. In
this problem the viscous Burgers equation acts as the sophisticated
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