A local adaptive refinement method with multigrid preconditionning illustrated by multiphase flows simulations.
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.
Affiliations des auteurs :
Franck Boyer 1 ; Celine Lapuerta 2 ; Sebastian Minjeaud 2 ; Bruno Piar 2
@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},
year = {2009},
volume = {27},
doi = {10.1051/proc/2009018},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009018/}
}
TY - JOUR AU - Franck Boyer AU - Celine Lapuerta AU - Sebastian Minjeaud AU - Bruno Piar TI - A local adaptive refinement method with multigrid preconditionning illustrated by multiphase flows simulations. JO - ESAIM. Proceedings PY - 2009 SP - 15 EP - 53 VL - 27 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/2009018/ DO - 10.1051/proc/2009018 LA - en ID - EP_2009_27_a2 ER -
%0 Journal Article %A Franck Boyer %A Celine Lapuerta %A Sebastian Minjeaud %A Bruno Piar %T A local adaptive refinement method with multigrid preconditionning illustrated by multiphase flows simulations. %J ESAIM. Proceedings %D 2009 %P 15-53 %V 27 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/2009018/ %R 10.1051/proc/2009018 %G en %F EP_2009_27_a2
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
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