Explicit Robin–Neumann schemes for the coupling of incompressible fluids with thin-walled structures

• Partitioned methods invoking the fluid and solid solvers only once per time-step.
• The implicit treatment of the sole fluid/solid-inertia coupling guarantees stability.
• A priori error estimates guarantee optimal (first-order) accuracy.
• New insights on the partitioned solution of implicit coupling.
• A comprehensive list of numerical tests supports the theory.

We introduce a class of explicit coupling schemes for the numerical solution of fluid–structure interaction problems involving a viscous incompressible fluid and a general thin-walled structure (e.g., including damping and non-linear behavior). The fundamental ingredient in these methods is a (parameter free) explicit Robin interface condition for the fluid, which enables the fluid–solid splitting through appropriate extrapolations of the solid velocity and fluid stress on the interface. The resulting solution procedures are genuinely partitioned. Stability and error estimates are provided for all the variants (depending on the extrapolations), using energy arguments within a representative linear setting. In particular, we show that one of them simultaneously yields added-mass free unconditional stability and optimal (first-order) time accuracy. A comprehensive numerical study, involving different examples from the literature, supports the theory.