On the stability of a loosely-coupled scheme based on a Robin interface condition for fluid-structure interaction
For researchers in fluid-structure interaction, this work provides theoretical stability bounds for a loosely coupled scheme, though it is incremental as it extends existing analysis to a specific Robin condition.
This paper analyzes the stability of an explicit Robin-Neumann scheme for fluid-structure interaction, deriving sufficient conditions for instability and stability that relate the time step, interface parameter, and added mass effect. Numerical experiments confirm the theory and identify optimal interface parameters for accuracy.
We consider a loosely coupled algorithm for fluid-structure interaction based on a Robin interface condition for the fluid problem (explicit Robin-Neumann scheme). We study the dependence of the stability of this method on the interface parameter in the Robin condition. In particular, for a model problem we find sufficient conditions for instability and stability of the method. In the latter case, we found a stability condition relating the time discretization parameter, the interface parameter, and the added mass effect. Numerical experiments confirm the theoretical findings and highlight optimal choices of the interface parameter that guarantee an accurate solution with respect to an implicit one.