Geodesic
Local time stepping with adaptive time step control for a two-phase fluid system
Frédéric Coquel1, 2 ; Quang Long Nguyen3 ; Marie Postel1, 2 ; Quang Huy Tran3
1 UPMC Univ Paris 06, UMR 7598 LJLL, Paris, F-75005 France
2 CNRS, UMR 7598 LJLL, Paris, F-75005 France
3 IFP, Département Mathématiques Appliquées, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France
ESAIM. Proceedings, Tome 29 (2009), pp. 73-88.

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This paper is concerned with how to make effective use of adaptive grids to correctly simulate the transportation of fronts over a long range of time under reasonable CPU time. These step gradients arise from systems of conservation laws modelling two-phase flows in pipelines. We propose not only a multi-resolution setup in order to adapt the space grid to the local smoothness of the solution, but also a local time stepping strategy in order to alleviate the constraints due to the CFL stability condition. A special focus is given to the optimal choice of micro time steps within a macro time step. Numerical simulations are presented to illustrate the efficiency of the methods put forward.
DOI : 10.1051/proc/2009056

Frédéric Coquel 1, 2 ; Quang Long Nguyen 3 ; Marie Postel 1, 2 ; Quang Huy Tran 3

1 UPMC Univ Paris 06, UMR 7598 LJLL, Paris, F-75005 France
2 CNRS, UMR 7598 LJLL, Paris, F-75005 France
3 IFP, Département Mathématiques Appliquées, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France 
@article{EP_2009_29_a6,
     author = {Fr\'ed\'eric Coquel and Quang Long Nguyen and Marie Postel and Quang Huy Tran},
     title = {Local time stepping with adaptive time step control for a two-phase fluid system},
     journal = {ESAIM. Proceedings},
     pages = {73--88},
     publisher = {mathdoc},
     volume = {29},
     year = {2009},
     doi = {10.1051/proc/2009056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009056/}
}
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Frédéric Coquel; Quang Long Nguyen; Marie Postel; Quang Huy Tran. Local time stepping with adaptive time step control for a two-phase fluid system. ESAIM. Proceedings, Tome 29 (2009), pp. 73-88. doi : 10.1051/proc/2009056. http://geodesic.mathdoc.fr/articles/10.1051/proc/2009056/

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