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 causin2005added 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 causin2005added, the present work shows that a novel, partitioned, loosely coupled scheme, recently introduced in MarSun, 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 formaggia2001coupling.
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