Un schema Volumes-Finis pour Ia simulation d'un modele bi-ftuide d' ecoulements diphasiques compressibles gaz-solide
Keywords:
two-phase flows, two-fluid model, finite volumes, fractional step method, approximate Riemann solver, non conservative hyperbolic systems, maximum principleAbstract
A Finite- Volume scheme which enables to compute compressible gas-solid twophase flows using the two-fluid approach is presented herein The time-dependent scheme is implemented on unstructured meshes. The fractional step method is such that the maximum principle for the volumetric fraction is fulfilled. Some two-dimensional test cases including shocks and rarefaction waves within both phases are described.
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[BAL 95] BALZER G., BOELLE A., SIMONIN 0., «Eulerian gas-solid flow modelling
of dense fluidized bed~, Proceedings of the International Symposium
of the Eng. Foundation Fluidization VIII, Tours, 14-19 mai, 1995.
[BAR 91] BARAILLE R., Developpement de schemas numeriques adaptes a l'hydrodynamique,
These de doctorat de l'universite de Bordeaux I, 13 decembre
(BAR 92] BARAILLE R., BOURDIN G., DUBOIS F., LEROUX A.Y., «Une
version a pas fractionnaires du schema de Godunov pour l 'hydrodynamique
», C. R. A cad. Sci. Paris, 1992, t 314, Serie I, p. 147-152.
[BOE 95] BOELLE A., BALZER G., SIMONIN 0., «Second-order prediction of
the particle-phase stress tensor of inelastic spheres in simple shear dense
suspensions», Proceedings of ASME, ASME FED Vol. 228, p. 9-18, 1995.
[BRU 96] BRUN G., HERARD J.M., LEAL DE SOUSA L., UHLMANN M.,
«Numerical modelling of turbulent compressible flows using second order
models», Proceedings of the first International Symposium on Finite
Volumes for Complex Applications, Rouen, France, july 15-18, 1996, pp
-346.
[BUF 93a] BUFFARD T., Analyse de quelques methodes de volumes finis non structures
pour la resolution des equations d'Euler, These de doctorat de
l'universite Paris VI, France, 1993.
[BUF 93b] BUFFARD T., HERARD J.M., «Un schema conservatif a pas fractionnaires
pour resoudre les equations d'Euler en maillage non structure»,
C. R. Acad. Sci. Paris, 1993, t 316, Serie II, p. 575-582.
[BUF 96] BUFFARD T., GALLOUET T., HERARD J.M., Schema VFROE en
variables caracteristiques - Principe de base et application aux gaz reels,
Rapport EDF HE41/96/41/A.
[CHA 92] CHAMPIER S., GALLOUET T., «Convergence d'un schema decentre
amont sur un maillage triangulaire pour un probleme hyperbolique lineaire
», Af AN, 1992, Vol 26(7), p. 835-853.
[CHA 93] CHAMPIER S., GALLOUET T., HERBIN R., «Convergence of an upstream
finite volume scheme on a triangular mesh for a nonlinear hyperbolic
equation», Numer. Math., 1993, Vol66, p. 139-157.
(COM 95a] COMBE L., Solveur de Godunov pour les equations d'Euler isentropique,
Rapport EDF HE41/95/008/ A.
(COM 95b] COMBE L., HERARD J.M., Modelisation numerique des ecoulements
diphasiques gaz-solide (Modeles bi-fiuides)- Rapport d'avancement 1,
Rapport EDF HE41/95/043/ A.
(COM 96a] COMBE L., FABRE J., HERARD J.M., SIMONIN 0., «On the numerical
preservation of the maximum principle for gas-solid flows», Proceedings
of A.S.M.E. Fluids Engineering, Summer Meeting, San Diego,
California, July 7-11, 1996. ASME FED vol.236, p. 181-188.
[COM 96b] COMBE L., HERARD J.M., Principe du maximum pour un modele
diphasique gaz-solide a trois equations, Rapport EDF HE41/96/045/ A.
[COM 97] COMBE L., These de doctorat de l'lnstitut National Polytechnique de
Toulouse, France, en preparation.
[COQ 96] COQUEL F., EL AMINE K., GODLEWSKI E., PERTHAME B.,
RASCLE P., Numerical method using upwind schemes for the resolution
of two-phase flows, Publications du laboratoire d'analyse numerique,
Universite Paris VI, juillet 1996, R 96014.
[DAL 95] DAL MASO G., LE FLOCH P., MURAT F., «Definition and weak stability
of nonconservative products,., J. Math. Pures Appl., Vol 74, p.
-548, 1995.
[ECO 96]
[EYM 97]
(GAL 92]
[GAL 96a]
[GAL 96b]
[GAY 97]
[GID 93]
[GOD 92]
ECOLE CEA-EDF-INRIA, Problemes non lineaires appliques, Methodes
numeriques pour les ecoulements diphasiques, INRIA Rocquencourt, 18-
novembre 1996.
EYMARD R., GALLOUET T., HERBIN R., Finite volume methods, En
preparation pour Handbook of Numerical Analysis, Editions P.G. Ciarlet
et J.L. Lions, North Holland.
GALLOUET T., An introduction to finite volume methods, Ecoie CEAEDF-
INRIA, 1992.
GALLOUET T., «Rough schemes for complex hyperbolic systems,., Proceedings
of the first International Symposium on Finite Volumes for
Complex Applications, Rouen, France, july 15-18, 1996, Ed. Hermes, pp
-14.
GALLOUET T., MASELLA J.M., «Un schema de Godunov approche,.,
C. R. Acad. Sci. Paris, 1996, t. 323, Serie I, p. 77-84.
GAVRILYUK S.L., FABRE J., «Lagrangian coordinates for a drift-flux
model of a gas-liquid mixture,., a paraitre dans Int. J. of Multiphase
Flow.
GIDASPOW D., Multiphase flow and fluidization, Academic Press, 1993.
GODLEWSKI E., RAVIART P.A., Hyperbolic systems of conservation
laws, coli. SMA! n°3/4, 1992, Ellipses.
[GODU 59] GODUNOV S.K., «A difference method for numerical calculation of discontinuous
equations of hydrodynamics,., Math. Sb., 47(89}, p. 271-300,
[GOL 96] GOLDSTEIN A., SHAPIRO M., GUTFINGER C., «Mechanics of collisional
motion of granular materials. Part 3. Self-similar shock wave
propagation,., J. Fluid Mech., 1996, Vol316, p. 29-51.
[HER 94] HERARD J.M., COMBE L., Un systeme diphasique bi-fluide pour
Ia modelisation des ecoulements gaz-solide, Coli. notes internes DER
NB00077.
[HER 95] HERARD J.M., Solveur de Riemann approche pour un systeme hyperbolique
non conservatif issu de Ia turbulence compressible, Rapport EDF
HE41/95/009/ A.
[HERB 95] HERBIN R., «An error estimate for a finite volume scheme for a
diffusion-convection problem on a triangular mesh,., Numer. Meth. Part.
Diff. Equations, Vol. 11, 1995.
[ISH 75] ISHII M., Thermo-fluid dynamic theory of two-phase flow, Collection de
Ia Direction des Etudes et Recherches d'Electricite de France, Eyrolles,
[KUM 93] KUMBARO A., Modelisation, analyse mathematique et numerique des
modeles bifluides d'ecoulement diphasique, These de doctorat de l'universite
Paris XI, France, 1993.
[LAX 57] LAX P.D., «Hyperbolic systems of conservation laws Ih, Commun. Pure
Appl. Math., 1957, Vol X, p. 537-566.
[LAX 72] LAX P.D., «Hyperbolic systems of conservation laws and the mathematical
theory of the schock wawes*, C. B. M.S. Regional Conference Series
in Applied Mathematics 11, SIAM, Philadelphia, 1972.
[LEF 88] LE FLOCH P., «Entropy weak solutions to nonlinear hyperbolic systems
under nonconservative form», Commun. Partial Diff. Equations, 1988,
Vol 13(6), p. 669-727.
[LEF 92] LE FLOCH P., LIU T.P., Existence theory for nonlinear hyperbolic systems
in non-conservative form, Publication Ecole Polytechnique-Centre
de Mathematiques Appliquees, jan. 1992, n° 254.
[MAS 96] MASELLA J.M., FAILLE 1., GALLOUET T., •A rough Godunov
scheme*, Soumis a publication.
[MAS 97] MASELLA J.M., Quelques methodes numeriques pour les ecoulements
diphasiques bi-fluides en conduites petrolieres, These de doctorat de
l'universite Paris VI, France, 1997.
[RAY 95] RAVIART P.A., SAINSAULIEU L., «A non conservative hyperbolic system
modeling spray dynamics. Part 1 : Solution of the Riemann problem*,
Math. Models Methods Appl. Sciences, 1995.
[ROE 81] ROE P.L., «Approximate Riemann solvers, parameter vectors, and difference
schemes*, J. Comput. Phys., 1981, Vol 43, p. 357-372.
[SAl 91] SAINSAULIEU L., «Ondes progressives solutions de systemes convectifsdiffusifs
et systemes hyperboliques non conservatifs*, C. R. Acad. Sci.
Paris, 1991, t. 312, Serie I, p. 491-494.
[SAl 92] SAINSAULIEU L., «Finite volume approximation of two phase-fluid
flows based on an approximate Roe-type Riemann solveP, J. Comput.
Phys., 1995, Vol 121, p. 1-28.
[SAl 95] SAINSAULIEU L., Contribution a Ia modelisation mathematique et numerique
des ecoulements diphasiques constitues d'un nuage de particules
dans un ecoulement de gaz, These d'habilitation, 20/01/95, Paris VI,
France.
(SAU 94] SAUREL R., FORESTIER A., VEYRET D., LORAUD J.C., «A finite
volume scheme for two-phase compressible flows*, Int. J. Numer. Methods
Fluids, 1994, Vol 18, p. 803-819.
(SMO 83] SMOLLER J., Schock waves and reaction-diffusion equations, SpringerVerlag,
[TOU 96] TOUMI 1., KUMBARO A., «An approximate linearized Riemann solver
for a two-fluid modeh, J. Comput. Phys., 1996, Vol 124, p. 286-300.
