Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
ISSN: 0377-0427

hal-00530820
https://hal.archives-ouvertes.fr/hal-00530820
DOI : 10.1016/j.cam.2008.08.014

Éditeur(s) : HAL CCSD Global Science Press
Résumé : International audience
In this paper, the authors present two different time-discretization schemes combined with a finite-volume space discretization for the incompressible Navier-Stokes equations. They show that the collocated space discretization, usually used with a projection method, can also be extended to other time discretizations over previous projection methods, like the splitting methods. The main advantage of this splitting method is that the pressure approximation is truly of second order. In the first and second parts of this article, two different time-discretization schemes are considered with a collocated space discretization and it is explained how the unknown can be correctly coupled. Numerical simulations are presented in the last part. Tests of spatial and time accuracies are made. The numerical results when the Navier-Stokes problem is solved are shown, in the model problem of the driven cavity.
ISSN: 1815-2406

hal-00730191
https://hal.archives-ouvertes.fr/hal-00730191

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Algorithms issued from the NonLinear Galerkin method have been used in many situations and with different discretizations for the resolution of evolutionary nonlinear equations. The main idea of these methods is to use a splitting of the solution in order to model the equation. According to the splitting of the solution, a splitting of the equation is obtained. The modeling principle is to freeze terms which have a small time variation. In this work we use wavelet discretizations of the 2-D Burgers equations and compare the results with the hierarchical finite elements method. The numerical tests indicate that wavelets give better results than finite elements
ISSN: 0885-7474

hal-00383423
https://hal.archives-ouvertes.fr/hal-00383423
DOI : 10.1007/s10915-004-4806-4

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
This article is intended as a preliminary report on the implementation of a finite volume multilevel scheme for the discretization of the incompressible Navier-Stokes equations. As is well known, the use of staggered grids (e.g., MAC grids [M. Perić, R. Kessler and G. Scheuerer, Comput. & Fluids 16 (1988), no. 4, 389-403; Zbl 0672.76018]) is a serious impediment for the implementation of multilevel schemes in the context of finite differences. This difficulty is circumvented here by the use of a colocated finite volume discretization [S. Faure, J Laminie and R. Temam, "Colocated finite volume schemes for fluid flows'', submitted; M. Perić, R. Kessler and G. Scheuerer, op. cit.], for which the algebra of multilevel methods is much simpler than in the context of MAC type finite differences. The general ideas and the numerical simulations are presented in this article in the simplified context of a two-dimensional Burgers equation; the two- and three-dimensional Navier-Stokes equations, which introduce new difficulties related to the incompressibility condition and the time discretization, will be considered elsewhere [see S. Faure, J Laminie and R. Temam, op. cit.; "Finite volume discretization and multilevel methods for the Navier-Stokes equations'', in preparation].
ISSN: 0885-7474

hal-00730193
https://hal.archives-ouvertes.fr/hal-00730193

Éditeur(s) : HAL CCSD Institute for Scientific Computing and Information
Résumé : International audience
In this paper, we solve a problem describing the mechanical deformations of a porous medium in the presence of a monophasic linear flow or a two phase nonlinear flow with the purpose of modelizing subsidence of hydrocarbon reservoirs. An essential characteristics of this problem is that the mechanical deformation and the flow have different time scales. In petroleum industry, one uses different very efficient simulators for the flow problem and the mechanical deformations, which enables to handle complex models. Therefore it is necessary to be able to combine as efficiently as possible the exploitation of these simulators. We propose two alternative splitting approaches. The first one is the staggered algorithm used by engineers, which amounts to a Gauss-Seidel method in the one phase linear case. The second approach is based upon the preconditioned conjugate gradient method. We use a numerical multi-scale method in both of these algorithms. We compare these two approaches and we show that the preconditioned conjugate gradient algorithm is faster and more robust than the staggered algorithm. Applying the preconditioned conjugate gradient algorithm therefore seems to compensate for the fact that the inf-sup condition for the mixed discretization method is not satisfied when combining the simulators for the mechanical deformations and for the flow computations.
ISSN: 1705-5105

Droits : http://creativecommons.org/licenses/by/
hal-01449039
https://hal.archives-ouvertes.fr/hal-01449039
https://hal.archives-ouvertes.fr/hal-01449039/document
https://hal.archives-ouvertes.fr/hal-01449039/file/DHLE.pdf

Éditeur(s) : HAL CCSD
Résumé : Avec la centrale de Bouillante, la Guadeloupe possède le seul site français de géothermie haute énergie conventionnelle. Le principe de fonctionnement est simple : des forages de production artésiens permettent la remontée naturelle d'une saumure à haute température. En surface la baisse de pression entraîne la vaporisation du fluide produit. Vapeur et eau sont ensuite séparées. La vapeur qui emmagasine une partie du contenu énergétique du fluide est turbinée .pour la production d'électricité. L'eau chaude n'est pas exploitée. Une partie est rejetée à la mer après refroidissement, l'autre est réinjectée dans le réservoir. Le réservoir est un milieu perméable (roches fracturées) rempli d'une saumure dont les conditions de température et pression sont très variables. La présence de fumerolles en surface atteste que certaines zones sont diphasiques sur le pourtour du champ, aux conditions atmosphériques. Lorsque l'on considère la source de chaleur du système hydrothermal, on doit prendre en compte des gammes de température et pressions pouvant aller jusqu'à 1000°C et une centaine de MPa avec un fluide potentiellement supercritique. Le problème est défini par les équations de conservation de la masse et de l'énergie, par la loi de Darcy et par les lois d'état obtenues à partir d'une implémentation libre des tables d'état IAPWS-IF97 (Freesteam). On rajoutera ultérieurement une loi de conservation du sel et les tables thermodynamiques associées pour modéliser le comportement de la saumure exploitée à Bouillante. On a choisi comme variables principales la pression et l'enthalpie pour des raisons de stabilité par rapport aux lois d'états. Les équations étant essentiellement hyperboliques on a retenu des schémas volumes finis pour la discrétisation. À ce jour nous testons différentes méthodes dans le but de comprendre le comportement des équations dans le cadre de la mise en place du champ géothermal à l'échelle géologique (" état naturel " du champ).
19ème Conférence Géologique de la Caraïbe
Le Gosier, Guadeloupe, France

hal-00609480
https://hal-brgm.archives-ouvertes.fr/hal-00609480

Éditeur(s) : HAL CCSD Institute for Scientific Computing and Information
Résumé : International audience
The production of oil in soft highly compacted reservoirs produces a significant reduction in the pore space which in turn causes the surface to subside. The authors couple two simulators to model the mechanical deformations in the presence of a Darcy flow, both one- and two-phase. The simulators solve for flow in a porous medium using a finite volume method, and solve for the mechanical deformation of the porous media using a finite element method. The flow equations and the deformation equations are coupled using Biot's law. The authors use two different methods for the coupling: the first uses a staggered algorithm; the second is based on a preconditioned conjugate method. The authors use a multiscale method in both approaches. The authors show that the inf-sup condition is not satisfied, because of the mixed discretization which is done by using two separate simulators. The authors give convergence comparisons for the two methods for several examples. Two of the examples are for the linear problem (one-phase) where they know the exact solution and one is for the nonlinear problem (two-phase). In all cases, the preconditioned conjugate algorithm is faster and more robust, in particular when the inf-sup condition is not satisfied. In the nonlinear problem the authors state that the results agree with physical predictions but do not give actual empirical data. Finally, they show the effects of grid orientation on the nonlinear problem.
ISSN: 1705-5105

hal-00730673
https://hal.archives-ouvertes.fr/hal-00730673

Éditeur(s) : HAL CCSD
Résumé : Nous proposons dans cet article de mettre en avant quelques idées pour la simulation numérique de plusieurs classes d'équations d'ondes dispersives (KdV, Benjamin-Ono) ou non (Kuramoto-Sivashinski) par des méthodes multiniveaux. Nous partons des idées initialement développés pour les équations dissipatives et en proposons une extension. Il en ressort que la présence d'une régularisation en temps est nécessaire pour pouvoir traiter de manière stable, et avec des schémas appropriés, les différentes échelles de la solution, préalablement générées à l'aide de méthodes hierarchiques (inconnues incrémentales, ondelettes, Fourier)
https://hal.inria.fr/inria-00271154

inria-00271154
https://hal.inria.fr/inria-00271154
https://hal.inria.fr/inria-00271154/document
https://hal.inria.fr/inria-00271154/file/cclz.pdf

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
ISSN: 0885-7474

hal-00601484
https://hal.archives-ouvertes.fr/hal-00601484
DOI : 10.1007/s10915-011-9480-8

Éditeur(s) : HAL CCSD Wiley
Résumé : International audience
We describe the simulation of an exterior problem using a magnetic field deriving from magnetostatics, with a numerical method mixing the approaches of C. I. Goldstein and L.-A. Ying. This method is based on the use of a graded mesh obtained by gluing homothetic layers in the exterior domain. On this mesh, we use an edge elements discretization and a recently proposed mixed formulation. In this paper, we provide both a theoretical and numerical study of the method. We establish an error estimate, describe the implementation, propose some preconditioning techniques and show the numerical results. We also compare these results with those obtained from an equivalent boundary elements approach. In this way, we retain that our method leads to a practical numerical implementation, a saving of storage, and turns out to be an alternative to the classical boundary elements method.
ISSN: 0749-159X

hal-00730196
https://hal.archives-ouvertes.fr/hal-00730196
DOI : 10.1002/num.10064