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

Resume. 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 cout CPU raisonnable. Ces singularites proviennent des systemes de lois de conservation modelisant lesdiphasiques ` travers les conduites petrolieres. Nous proposons non seulement un cadre multiresolution afin d'ajuster le pas d'espacela regularite locale de la solution, mais aussi une strategie de pas de temps local afin d'alleger les contraintes duesla condition CFL de stabilite. Nous examinerons plus particulierement le choix optimal des micro pas de tempsl'interieur d'un macro pas de temps. Nous presentons les simulations numeriques pour illustrer l'efficacite des methodes preconisees. 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.

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