  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 \cite{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
\cite{causin2005added}, the present work shows that a novel, partitioned,
loosely coupled scheme, recently introduced in \cite{MarSun}, called the
kinematically coupled $\beta$-scheme, does not suffer from the added mass
effect for any $\beta \in [0,1]$, 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 \cite{formaggia2001coupling}.
