International audienceWe address the numerical simulation of fluid-structure systems involving an incompressible viscous fluid. This issue is particularly difficult to face when the fluid added-mass acting on the structure is strong, as it happens in hemodynamics for example. Indeed, several works have shown that, in such situations, implicit coupling seems to be necessary in order to avoid numerical instabilities. Although significant improvements have been achieved during the last years, solving implicit coupling often exhibits a prohibitive computational cost. In this work, we introduce a semi-implicit coupling scheme which remains stable for a reasonable range of the discretization parameters. The first idea consists in treating implicitly the added-mass effect, whereas the other contributions (geometrical non-linearities, viscous and convective effects) are treated explicitly. The second idea, relies on the fact that this kind of explicit-implicit splitting can be naturally performed using a Chorin-Temam projection scheme in the fluid. We prove (conditional) stability of the scheme for a fully discrete formulation. Several numerical experiments point out the efficiency of the present scheme compared to several implicit approaches

This paper aims at introducing a partitioned Newton based method for solving nonlinear coupled systems arising in the numerical approximation of fluid-structure interaction problems. We provide a method which characteristic lies in the use of exact cross jacobians evaluation involving the shape derivative of the fluid state with respect to solid motion perturbations. Numerical tests based on an implementation inside a 3D fluid-structure interaction code show how the exactness of the cross jacobians computation guarantee the overall convergence of the Newton's loop.

In this work we propose a stabilized explicit coupling scheme for fluid-structure interaction problems involving a viscous incompressible fluid. The coupled discrete formulation is based on Nitsche's method with a time penalty term giving L 2 -control on the fluid pressure variations at the interface. The scheme is stable, in the energy norm, irrespectively of the fluid-structure density ratio. Numerical experiments, in two and three dimensions, show that optimal time accuracy can be obtained by performing a few defect-correction iterations.Key-words: Fluid-structure interaction, Nitsche's method, fluid incompressibility, time discretization, explicit coupling, loosely coupled schemes, defectcorrection method

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