Stabilization of explicit coupling in fluid–structure interaction involving fluid incompressibility

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 L2L2-control on the fluid pressure variations at the interface. For a linear model problem, we prove that the scheme is stable, in the energy norm, irrespectively of the so-called added-mass effect, namely, the fluid–structure density ratio and the geometry of the domain. Numerical experiments, in the linear and non-linear case, show that optimal time accuracy can be obtained by performing one defect-correction iteration.