Paper 24, Code: S012
MARRAKECH, MOROCCO, JULY 4 - JULY 8, 2005
schemes for a nonlinear hyperbolic conservation law with a flux
involving discontinuous coefficients
Paper 1, Code: A001
Authors: F. Bachmann
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
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
Key words : variational
smoothing, information theory, volumetric medical imaging.
conditions for Petrov-Galekin Finite Volumes
Paper 3, Code: S001
Authors: S. Borel, F. Dubois, C. Le Potier and
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
simulation of convective turbulence
Paper 4, Code: C001
Authors: I. Palymsky
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
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
approximation for an oblique derivative boundary value problem
Paper 6, Code: A003
Authors: A. Bradji and T. Gallouet
In this paper, we consider the
Laplace equation with oblique boundary conditions, on an open bounded
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.
space-time conservative Finite Volume scheme for Hyperbolic
Paper 7, Code: S003
Authors: Q. U. Ain, S. Qamar and G. Warnecke
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.
hyperbolic systems, space-time control volumes, finite volume schemes,
high order accuracy, shock solutions.
Unsteady Natural Convection Flows using Finite Volume Modified Method
Paper 8, Code: C003
El-Amrani and Mohammed Seaid
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,
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
A finite volume
method for the approximation of highly anisotropic diffusion operators
on unstructured meshes
Paper 10, Code S004
Author: C Le Potier
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
Convergence of a Finite Volume Method for a Reaction-Diffusion system
Equations in Electro-Cardiology
Paper 11, Code: A004
Authors: Y. Coudiere and C. Pierre
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
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.
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
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.
words : Finite
element method, SIMPLE algorithm, Die design, Polymer flow, extrusion
Finite Volume Schemes for Nonconservative Hyperbolic Problems
Paper 14, Code: S006
Authors: V. Dolejsi, T. Gallouet
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
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
Key words : nonconservative
hyperbolic equations, nonconservative Roe Finite volume schemes,
well balanced scheme for gas flows in protoplanetary nebulae
Paper 15, Code: S007
Authors: H. Guillard, E. Daniel
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
Locally Moving Mesh Method for Multifluid Flows
Paper 16, Code S008
Authors: A. Chertock, A. Kurganov
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
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.
novel Cartesian cut-cell approach
Paper 18, Code: S009
Authors: I. Wenneker and M. Borsboom
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.
optimal a priori error analysis of the Finite Volume method for linear
Paper 19, Code: A005
Authors: D. Bouche, J.M. Ghidaglia, and F. Pascal
This paper investigates the order of
convergence of the upwind Finite volume method for solving linear
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
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
A Finite volume
scheme for the computation of erosion limiters
Paper 20, Code: A006
Authors: R. Eymard and T. Gallouet
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
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.
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
our numerical method which essentially relies on a Finite Volume
approach and a splitting in 3 steps for the time scheme. Then we
3 new test cases towards the validation of the scheme.
Key words : Multiphase Flow,
Lagrange + Remap, spherical test cases.
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
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
sharing a fixed interface. In each one, a different model is used to
describe the flow. The main difficulty is to give appropriate
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.
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
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
MAC mesh, Stokes equations.
schemes for nonlinear elliptic problems on general 2D meshes
Andreianovy 1, Franck Boyer 2, Florence Hubert 2
Finite volume schemes on general
meshes are studied for nonlinear diffusion problems with non
Dirichlet boundary condition. These schemes allow the discretization
nonlinear fluxes in such a way that the discrete operator
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.
Partitioning for Parallel Computational Fluid Dynamics Applications on
Paper 26, Code: C006
Authors: Y. Mesri, H. Digonnet, H. Guillard
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
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,
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.
estimation for goal-oriented model adaptation in flow simulations
Paper 28, Code: A010
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
model and the inviscid Burgers equations as the approximating or coarse
model. A formulation for the model error is derived using the
dual-weighted residual method. We illustrate the importance of adjoint
boundary conditions for the model-error estimator by two cases with
different initial conditions.
finite volume method for the modeling of CO2 storage
Paper 29, Code: C007
Authors: A. Michel, E. Tillier and L. Trenty
This paper describes a fully coupled
simulator based on the finite volume method for the simulation of CO2
storage. The simulator takes into account convective and diffusive
and chemicals reactions (speciation and mineral precipitation and
dissolution). Currently, the simulator considers only the aqueous phase
in one dimension. The continuous problem and the discrete equations are
presented. Finally, two numerical examples are given.
Key words: reactive transport,
finite volume, CO2 storage
Volume Scheme with Weighted Least Square Reconstruction
Paper 30, Code: S013
article describes development of one variant of ENO scheme with the
so-called weighted least-square reconstruction. The cell-wise
interpolation is achieved by a minimization of the interpolation error
for fixed stencil with data-dependent weights. The stability of the
reconstruction is analyzed theoretically for simple scalar case and
several numerical experiments are done both for multidimensional scalar
case as well as for the case of compressible flows in 2D and
Key words : Finite
volumes, ENO, least-squares, total variation, unstructured mesh
modeling of flow in fractured porous media
Paper 32, Code: C004
Authors: P. Angot, F. Boyer and F. Hubert
This study proposes some zero-
or first-order models to compute the flow outside and inside fractures
supposed to have a small thickness with respect to the macroscopic
lenght scale, and hence reduced to immersed polygonal fault interfaces.
A cell-centered finite volume scheme on general polygonal meshes which
fit the interfaces is derived to solve the set of equations with the
additional algebraic or differential transmission conditions linking
both pressure and normal velocity jumps through the interfaces. The
correction for the angle a corners between the connected
interfaces is addressed. The models are then numerically experimented
for immersed fractures. Some numerical results are reported which show
different kinds of flows in the case of impermeable or permeable
fractures, or also for intermediate cases.
media flow, impermeable fractures, permeable fractures, immersed
polygonal fault interfaces, cell-centered finite volumes.
Modelling with Finite Volumes of the Isolated Current Leads for
Paper 33, Code: C005
Authors: Ioan POPA, Florian
ŞTEFĂNESCU, Dan POPESCU
The article presents the mathematical
model and the results obtained by the numerical simulation of the
thermal state, of isolated electrical leads in the framework
of cryogenic applications. the mathematical Model is based
on 1D and 2D equations of thermal conduction. For the numerical
resolution of the thermal conduction equation one uses the finite
volumes method. The elaborated program enables to get the distribution
of the temperature and the heat flux along the leads. The
results are used for the optimization of these electrical leads.
Key words: finite volumes
method, electrical leads, cryogenic applications.
A finite Volume
scheme for dynamic reliability studies
Paper 34, Code: A012
Cocozza-Thivent, R. Eymard, S. Mercier
The dynamic reliability study of
an industrial device implies the determination of the probability for
this device to be in a given state at a given time. We consider in this
paper a model of dynamic reliability based on the Chapman-Kolmogorov
equations, which can be seen as a system of linear scalar hyperbolic
equations coupled by the right hand side, the solution of which are
probability measures. We propose a finite volume scheme for the
approximation of these measures, and we prove its weak convergence. A
numerical example illustrates this property.
order Finite Volume scheme for phase transition
Paper 35, Code: S015
Semma M. El Ganaoui and A. Cheddadi
A numerical model is achieved
for the analysis of phase change problems including natural convection
effects. In this work, the momentum and energy equations, written in
terms of its primitive variables, are solved using a specific continuum
formulation associated to a finite volume method. A third–order QUICK
scheme is used for the convective terms. The time discretization is
implicit, and a second order Euler scheme is employed. Simulations show
the ability of high order finite volume method to predict phase
change phenomena. Good agreement with the experimental
measurements for materials with high and low energy-momentum coupling is
Key words : Finite
flux limiter, phase change, enthalpy method.
Finite Volume Method for Second Order Elliptic Problems
Paper 36, Code: S016
Delcourte, K. Domelevo, P. Omnes
This paper deals with
applications of the “Discrete-Duality Finite Volume” approach to a
variety of elliptic problems. This is a new finite volume method, based
on the derivation of discrete operators obeying a Discrete-Duality
principle. An appropriate choice of the degrees of freedom allows one
to use arbitrary meshes. We show that the method is naturally related
to finite and mixed finite element methods.
Artificial compression technique applied to shallow water equations
Paper 39, Code: S017
Authors: E.D. Fernandez and V. Martinez
In this work we present an artificial
compression technique to shallow water equations with pollutant. Our
purpose is to avoid the numerical diffusion in contact discontinuities.
This happens when the considered system has linearly degenerated
This technique obtains a new partial differential system where there
not linearly degenerated fields but only genuinely nonlinear fields, in
such a way the solution does not vary. The difficulty of applying
artificial compression to shallow water equations with pollutant is
the primitive variable corresponding to the linearly degenerated field
is zero. For Euler Equations, for example, this is not the case.
we present several tests which apply this technique with Roe and HLL
Key words : artificial
compression, shallow water, pollutant.
Implementation of a Dynamic Overset Unstructured Grid Using Finite
Paper 40, Code: C010
Authors: A. Madrane
The purpose of this study is to
develop an ecient parallel computational algorithm for complex
geometries using overset unstructured grid technique. The strategy
adopted in the parallelization of the overset grids method including
the use of hierarchical data structure and communication, is described.
Numerical results are presented to demonstrate the eciency of the
resulting parallel overset grid method.
Key words :
Overlapping grids, Chimera method, Unstructured , Overset grid, MPI,
fictitious domain method with nonconforming structured meshes
Angot, H. Lomenede and I. Ramiere
Paper 41, Code: S018
This study addresses a new
fictitious domain method for elliptic problems in order to
handle general embedded boundary conditions (E.B.C.) : Fourier,
Neumann and Dirichlet conditions on an immersed interface. The
main interest is to use a simple structured mesh, possibly
uniform, which does not generally fit the interface but defines
approximate one. A cell-centered finite volume scheme with
non-conforming structured mesh is derived to solve the set of
equations with the additional algebraic transmission conditions
linking both flux and solution jumps through the immersed
approximate interface. Hence, a local correction is devised to
take account of the relative surface ratios in each control
for the Fourier or Neumann boundary condition. Then, the
scheme conserves the first-order accuracy with respect to the mesh
step, as observed in the numerical results reported here.
This opens the way to combine the E.B.C. method with the multi-level
solver to increase the precision in the vicinity of the interface
by a local mesh refinement. Such a fictitious domain method is
expected to be very efficient.
Key words :
domain method, embedded boundary conditions, cell-centered finite
volumes, multi-level local mesh refinement.
dissolution and precipitation in a porous media: approximation by a
finite volume scheme
Paper 44, Code: S020
Bouillard, R. Eymard, R. Herbin, P. Montarnal
This paper study a finite
volumes scheme for nonlinear diffusion and dissolution-precipitation
equations with non homogeneous Dirichlet boundary conditions. The
approximate solution is shown to converge to a weak solution which
existence is thus proved. The chemical reaction is kinetics controlled.
It involves two species in liquid phase and one species in solid phase.
Some numerical tests are shown.
On two fractional
step finite volume and finite element schemes for reactive low Mach
Paper 45, Code: S021
Authors: F. Babik, T. Gallouet, J.C. Latche, S.
Suard and D. Vola
We address in this paper a class of
physical problems which can be set under the form of the momentum and
mass balance equations, supplemented by the balance equation of an
independent unknown field z. The fluid density is supposed to be given
as a nonlinear function of this latter unknown. In particular,
governing equations of some reactive low Mach number flows enter this
framework. We present and compare two original fractional steps schemes
devoted to the solution of this system of equations. They combine a
particular finite volume discretization of the balance of z, which
$\LS^\infty$ and $\LS^2$ stability is proven, with a non-conforming
finite element pressure correction method for the solution of the
Navier-Stokes equations. Via numerical experiments, these schemes are
shown to be almost optimally convergent in time and space and to
present remarkable stability properties, in view of the strong
non-linearity of the problems in hand.
Key words : Low Mach
number flows, reactive flows, finite volumes, mixed finite
Finite Volume Methods for hydraulic fracture problems
Paper 46, Code: C011
Author: A. Peirce
Hydraulic fracturing is a process that is
often used in the oil and gas industry to enhance the flow of
hydrocarbons by generating a fracture within a reservoir. The fracture
is propagated by injecting a viscous fluid into a bore-hole under a
sufficiently high pressure to overcome the tensile strength of the rock
and the ambient geological stresses. We describe an Eulerian Finite
Volume scheme based on a fixed rectangular grid to solve the coupled
system of hydraulic fracture nonlinear integro-partial differential
equations. We illustrate the accuracy of the algorithm by comparing the
Finite Volume solution to the exact solution for a radial solution
evolving in a homogeneous elastic medium.
Estimates of blow-up
time for the radial
symmetric semilinear heat equation in the “open-spectrum” case
Paper 48, Code: A015
Authors: N.I. Kavallaris, C.V. Nikolopoulos, D. E.
We estimate the blow-up time for the
reaction diffusion equation u_t = Delta u + L f(u), when f is a
positive, increasing and convex function growing fast enough and
L>L* whereL* is a critical value for the parameter L.
Estimates of the blow-up time are obtained by using comparison methods.
Some numerical results are also presented.
Computation of Laminar Mixed Convection Flow Combined with Mass
Transfer in a Duct
Paper 49, Code: C012
Benhamou, N. Galanis, M. El-Ganaoui
A numerical study is conducted
to investigate a laminar mixed convection flow in a vertical parallel
plates channel. The plates are isothermal and
iso-concentration. The adopted mathematical model includes axial
diffusion of momentum, heat and mass transfer. The numerical
solution of the PDE set modelling the flow field and transfers is based
on the control volumes method. Both upward and downward flows are
considered. Results show that heat and mass transfers are significantly
affected by the direction and the conditions of the flow.
Key words: channel, laminar
flow, heat transfer, mass transfer, mixed convection.
finite volume method for modelling the flood wave propagation:
Application to the Ourika valley
Paper 50, Code: C013
Authors: H. Belhadj, D.
Ouazar, A. Taik
This paper is devoted
to the modeling of the wave propagation resulting from the flood
phenomenon. The flood physical problem is modeled by using the free
surfac flow equations in the shallow water case. The two
dimensional obtained system is generated from the three-dimensional
Navier Stokes equations by integrating the state variables over the
vertical dimension. This system is writen in a conservative form with
hyperbolic homogeneous part. The discretisation is carried out by the
use of the finite volume method on unstructured mesh. For the numerical
experiment, we have studied the realistic case of Ourika valley which
is located in Morocco. The flood occured on August 1995 is simulated
and results gives velocities and free surface elevations at different
stopped times of the simulation.
of Numerical Fluxes for a Locally Exact Finite Volume Scheme Using
Paper 51, Code: S023
Author: J. Fuhrmann
For a recently proposed finite volume
scheme for certain nonlinear convection diffusion problems based on the
solution of local Dirichlet problems, in the special case of power law
nonlinearities, we present a method for the evaluation of the flux
functions which uses the Gauss hypergeometric function.
Key words : Finite Volumes, Nonlinear
Diffusion-Convection Problems, Hypergeometric Function
finite volume solver based on matrix sign for non homogeneous systems
Paper 52, Code: S023
Sahmim, Fayssal Benkhaldoun, Francisco Alcrudo
This article is devoted to the analysis,
and 2D extension of a finite volume scheme proposed recently to handle
a class of non homogeneous systems. The stability analysis of the
considered scheme leads to a new formulation which includes the
Jacobian matrix sign. This formulation is identical to the VFRoe scheme
introduced by Gallouët, in the homogeneous case, and has a natural
extension here to non homogeneous systems. Comparative numerical
experiments for Shallow Water equations with source terms and two
phase problem (Ransom faucet) are presented to validate the scheme.
Key words : Finite volume method, SRNHS scheme,
Shallow water equations, Source terms, Riemann Problems, Tow-phase flow.
and 2D Numerical Solution of Two Phase Flow Problem Using a Dissipative
Paper 54, Code: CO15
Authors: Jan Halama and Fayssal
This work deals with the
numerical simulation of one and two dimensional two phase flows using a
Lax-Wendroff finite volume scheme. An artificial viscosity term is used
to handle the physical and numerical stiffness of the system. One shows
that a good choice of this term can lead to valuable results, even on
very refined meshes.
Third Order Fluctuation Splitting Schemes
Paper 55, Code: S024
This paper addresses the issue of constructing
non-oscillatory, higher than second order, multidimensional,
splitting methods on unstructured triangular meshes. It
reasons why current approaches fail and proposes a potential
these problems. The results presented for a simple steady
advection problem show significant improvements on previous
Key words : fluctuation
splitting, monotonicity, high order.
Volume two steps flux scheme for 1D and 2D non homogeneous systems
Benkhaldoun, Kamel Mohamed and Laure Quivy
Paper 56, Code: S025
In this work we consider a two
steps finite volume scheme, recently developed to solve nonhomogeneous
systems. The first step of the scheme depends on a diffusion control
parameter which we modulate, using the limiters theory. Results on
Shallow water equations and two phase flows are presented.
Finite Volume formulation for
diffusion problems in anisotropic non-homogeneous media
I.M. Nguena, A. Njifenjou
In this paper, we present a new finite volume method
a strong capacity to handle flow problems in anisotropic
non-homogeneous porous media. The conservativity at cell level, the
flux continuity and the
consistency of the approximation of the flux are the main features of
Modelisation of Tumor and Immune System Competition
Paper 58, Code: A016
In this work, we present
mathematical models that describe the interactions and competition
between tumors and the immune system. The evolution of the system may
end up either with the blow-up of the host (with inhibition of the
immune system), or with the suppression of the host due to the action
of the immune system. We particularly develop the model introduced in
[DeAngelis 01], where the capacity of the body to repair cells damaged
is not taken into account. The idea is that for a long time range the
body produces new cells to replace the dead ones in order to try to
reach its normal healthy state. We are particularly interested by the
asymptotic behavior o solutions when time goes to infinity. We
also give some numerical results that show that the model we introduce
is suitable for chronic diseases.
finite volume approximations for stiff fluid mechanics problems
Paper 59, Code: C016
Gilbert Accary, Mohammed El Ganaoui , Isabelle Raspo , Rachid
Two illustrations of Finite
Volume (FV) use for predicting complex 3D flows are developed. The
first concerns the unsteady Rayleigh-Bénard convection in a
fluid close to its gas-liquid critical point. The second concerns the
convection inside a fluid of a low Prandtl number heated from below.
Such situation is particularly encountered during directional
Hydrodynamic numerical simulation of the lake
of Bouregreg using finite volume method
Paper 60, Code: C017
Taik, H. Mouies, D. Ouazar
work deals with the numerical simulation of unsteady circulation model in lake of Bouregreg in order to allow the
delimitation of dead zones where
the eutrophication phenomena may occur.
We use the finite volume method with
unstructured mesh. The cell-centred finite
volume scheme considered here uses a
generalised Roe's approximate Riemann solver with MUSCL technique for the conservative
part and Green-Gauss type interpolation
for the viscous part.
suspended load with moment equations and linear concentration profiles
Paper 61, Code: S027
Khuat Duy B., Dewals B.J., Archambeau P.
1, Erpicum S.,
Detrembleur S., Pirotton M.
simulations, it is always necessary to find an optimum between the
simplicity of the model and a good representation of real phenomena. In
this context, the models using depth-averaged and moment equations are
an interesting compromise between full 3D and simple depth-averaged
models. This paper presents the use of a moment equation for suspended
load transport. A simple but representative model for the sediment
concentration profiles is developed. This original bi-linear
concentration profile is compared to the traditional Rouse-profiles and
shows a good correspondence despite its great simplicity. Advective and
diffusive sediment fluxes are developed analytically and lead to a
concise formulation, which is an asset for practical use. A
differential equation for the sediment concentration moment is also
fully developed, and a special attention is cast to the source term.
The finite volume scheme has been chosen to implement the model,
because it is particularly well suited for highly advective transport
equations, it is conservative and it makes the choice of the upwinding
easier. 1D simulations show the capacity of the model to reproduce
laboratory experiments described in the literature.
Key words: sediment
transport, suspended load, moment equations, depth-averaged, finite
Chaos expansions and FV solution of Stochastic Advection Equation
Paper 62, Code: S028
Zahri, Mohammed Seaıd, Hassan Manouzi, Mofdi El-Amrani
Stochastic uncertainties in advection
flow problems can appear in the advection operator, domain boundary, or
initial condition. In the present work, we propose a robust algorithm
for approximating numerical solution of stochastic advection equations
of Wick type. The method consists on combining the Wiener-Itˆo chaos
expansions for random representation with a finite volume method for
space discretization. The time integration is carried out using a
second order I-stable explicit scheme. As applications, we consider
linear free-advection and the nonlinear inviscid Burgers equations.
Preliminary results, obtained for examples on stochastic problems in
two space dimensions, show that the proposed method is efficient,
stable and highly accurate.
Key words :
Wick-Stochastic Advection Problems,
Wiener-Ito Chaos Expansions, Finite Volume Method, Stochastic
Simulation, White Noise.
extension of the reservoir technique for linear advection equations
Paper 63, Code: S029
Alouges, Gérard Le Coq, and Emmanuel Lorin
this paper we present an extension of the reservoir technique for
multidimensional advection equations with non constant velocities. The
purpose is to make decrease the numerical diffusion correcting the
numerical directions of propagation of the information, using a
so-called corrector vector combined with the reservoirs.
Key words :
finite volume schemes, numerical diffusion.
finite volumes for the numerical simulation of CO2 transport and
assimilation in a leaf
Paper 64, Code: S030
Authors: Emily Gallouet and Raphaele Herbin
This paper deals with the
numerical simulation of CO2 transport in the leaf. We study a
mathematical model of the diffusion and photosynthezing processes, and
present the implementation of an axisymmetric cell centered finite
volume scheme for their numerical simulation. The resulting code
enables the computation of the diffusion coefficient in the leaf porous
medium, from experimental measurements which yield the pointwise value
of internal CO2 concentration. Hence our model and numerical code allow
the analysis of the role of the internal diffusion in the
photosynthesis, porous media, finite volumes.
Finite volume simulation of a supersonic laminar flow: Application to a
flat plate and compression corner model
Paper 65, Code: C018
Authors: Bahia Driss, Salhi Najimy, Boulerhcha Mohammed, and Elmahi Imad
In this paper, the finite volume
method is used for the computation of a supersonic laminar flow. As an
application, we consider the flow over a flat plate and compression
corner with different angles. The inviscid fluxes are approximated
using Steger and Warming Flux Vector Splitting method with the MUSCL
approach to increase the spatial accuracy. The transport properties
(viscosity and conductivity) which are functions of two independent
thermodynamic parameters (T,P), are calculated using a centered scheme.
The performance of the methods used here is shown by some comparisons
with other results.
Numerical analysis, Supersonic flow, Finite volume, Flat plate,
diffuse interface model for the numerical simulation of three-component
Paper 66, Code: A017
Authors: Franck Boyer, Céline Lapuerta
In this paper we propose a new
diffuse interface model for the study of
three-component incompressible viscous flows. The model is based
on the Cahn-Hilliard free energy approach. In
particular, the free energy we consider is built in
such a way that the model is well-posed and consistent with
two-component models. The hydrodynamic of the mixture is taken
into account by coupling the Cahn-Hilliard system
with a Navier-Stokes equation supplemented.
Keywords: Multicomponent flows, Cahn-Hilliard equations