Geodesic
A local adaptive refinement method with multigrid preconditionning illustrated by multiphase flows simulations.
Franck Boyer1 ; Celine Lapuerta2 ; Sebastian Minjeaud2 ; Bruno Piar2
1 Laboratoire d'Analyse, Topologie et Probabilités (LATP), Faculté des Sciences et Techniques de Saint-Jérôme - Case Cour A, Université Paul Cézanne, Avenue Escadrille Normandie-Niemen, 13397 MARSEILLE Cedex 20, France.
2 Institut de Radioprotection et de Sûreté Nucléaire (IRSN), DPAM/SEMIC/LIMSI, BP-3, 13115 Saint-Paul-lez-Durance, France.
ESAIM. Proceedings, Tome 27 (2009), pp. 15-53.

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The aim of this paper is to describe some numerical aspects linked to incompressible three-phase flow simulations, thanks to Cahn-Hilliard type model. The numerical capture of transfer phenomenon in the neighborhood of the interface require a mesh thickness which become crippling in the case where it is applied to the whole computational domain. This suggests the use of a local refinement method which allows to dynamically focus on problematic areas. The notion of refinement pattern, introduced for Lagrange finite elements, allows to build a conceptual hierarchy of nested conformal approximation spaces which is then used to implement the so-called CHARMS local refinement methods. Properties of these methods are proved ensuring in particular the conformity of approximation spaces at every time of simulations. Furthermore, the multilevel structure obtained by this method, is used to construct multigrid preconditioners. Finally, after a validation on a model problem, the performance of the whole method is illustrated on an example of a liquid lens spreading between two stratified fluids.
DOI : 10.1051/proc/2009018

Franck Boyer 1 ; Celine Lapuerta 2 ; Sebastian Minjeaud 2 ; Bruno Piar 2

1 Laboratoire d'Analyse, Topologie et Probabilités (LATP), Faculté des Sciences et Techniques de Saint-Jérôme - Case Cour A, Université Paul Cézanne, Avenue Escadrille Normandie-Niemen, 13397 MARSEILLE Cedex 20, France.
2 Institut de Radioprotection et de Sûreté Nucléaire (IRSN), DPAM/SEMIC/LIMSI, BP-3, 13115 Saint-Paul-lez-Durance, France. 
@article{EP_2009_27_a2,
     author = {Franck Boyer and Celine Lapuerta and Sebastian Minjeaud and Bruno Piar},
     title = {A local adaptive refinement method with multigrid preconditionning illustrated by multiphase flows simulations.},
     journal = {ESAIM. Proceedings},
     pages = {15--53},
     publisher = {mathdoc},
     volume = {27},
     year = {2009},
     doi = {10.1051/proc/2009018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009018/}
}
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Franck Boyer; Celine Lapuerta; Sebastian Minjeaud; Bruno Piar. A local adaptive refinement method with multigrid preconditionning illustrated by multiphase flows simulations.. ESAIM. Proceedings, Tome 27 (2009), pp. 15-53. doi : 10.1051/proc/2009018. http://geodesic.mathdoc.fr/articles/10.1051/proc/2009018/

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