Nonconforming Grids for the Simulation of Fluid-Structure Interaction

Fluid structure interaction phenomena occur in a large number of applications and the literature on the subject is quite important, both from the practical and implementation point of view. Nevertheless, most of the applications are focused on a particular range of situations in which the domain that is occupied by the fluid is essentially assumed to be independent on time. Recently, a lot of effort has been made on the numerical simulations of fluid structure interactions in the case where this assumption is no more true and, in particular, in situations where the shape of the domain occupied by the fluid is among the unknowns of the problem. We refer for instance to the works [9, 10, 11] and also to some web pages where medical and engineering applications are displayed. We refer also to [6] for an analysis of the mathematical problem. This new range of applications is made possible thanks to the increase in computing power available and the recent advances in CSD and CFD. Indeed, the current implementations for the simulation of the coupled phenomena are mostly based on the effective coupling of codes devoted to fluid simulations for the ones, and structure simulations for the others. Such a coupling procedure allows for flexibility in the choice of the separate constitutive laws and modelisations of the fluid and structure separately and allows also for the rapid development of the simulation of the interaction phenomenon. This flexibility is however at the price of the definition of correct decoupling algorithms of the different codes that lead to a resolution of the coupled situation. In this direction, some attention has to be given for the time decoupling and we refer to [11, 10, 8] for numerical analysis of this part. Another problem has to be faced which consists in the coupling of the spatial discretizations. This difficulty, already present in the former works (where the shape of the fluid part is fixed), is certainly enhanced now that the time dependency has increased by one order of magnitude the size of the computations. Indeed, it is mostly impossible to afford the same mesh size on the fluid and on the structure computational domains, especially in three dimensional situations.