Stability of the Kinematically Coupled β-Scheme for Fluid-Structure Interaction Problems in Hemodynamics

Abstract

It is well-known that classical Dirichlet-Neumann loosely coupled partitioned schemes for fluid-structure interaction (FSI) problems are unconditionally unstable for certain combinations of physical and geometric parameters that are relevant in hemodynamics. It was shown in [18] on a simple test problem, that these instabilities are associated with the so called “added-mass effect”. By considering the same test problem as in [18], the present work shows that a novel, partitioned, loosely coupled scheme, recently introduced in [11], called the kinematically coupled β-scheme, does not suffer from the added mass effect for any β ∈ [0; 1], and is unconditionally stable for all the parameters in the problem. Numerical results showing unconditional stability are presented for a full, nonlinearly coupled benchmark FSI problem, first considered in [31].