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Issue ESAIM: PROC
Volume 29, 2009
Multiresolution and Adaptive Methods for Convection-Dominated Problems
Page(s) 73 - 88
DOI 10.1051/proc/2009056
Published online 10 December 2009

ESAIM: Proc., 2009, Vol. 29, pp. 73-88
DOI: 10.1051/proc/2009056

Local time stepping with adaptive time step control for a two-phase fluid system

Frédéric Coquel1, 2, Quang Long Nguyen3, Marie Postel1, 2 and 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


Published online: 10 December 2009

Abstract
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.


Résumé
Cet article aborde la question de l'utilisation efficace des maillages adaptatifs en vue de simuler correctement le transport des fronts sur des temps longs avec un coût CPU raisonnable. Ces singularités proviennent des systèmes de lois de conservation modélisant les écoulements diphasiques à travers les conduites pétrolières. Nous proposons non seulement un cadre multirésolution afin d'ajuster le pas d'espace à la régularité locale de la solution, mais aussi une stratégie de pas de temps local afin d'alléger les contraintes dues à la condition CFL de stabilité. Nous examinerons plus particulièrement le choix optimal des micro pas de temps à l'intérieur d'un macro pas de temps. Nous présentons les simulations numériques pour illustrer l'efficacité des méthodes préconisées.



© EDP Sciences, ESAIM 2009


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