  We consider numerical algorithms for the simulation of the rheology of
two-dimensional vesicles suspended in a viscous Stokesian fluid. The vesicle
evolution dynamics is governed by hydrodynamic and elastic forces. The elastic
forces are due to local inextensibility of the vesicle membrane and resistance
to bending. Numerically resolving vesicle flows poses several challenges. For
example, we need to resolve moving interfaces, address stiffness due to
bending, enforce the inextensibility constraint, and efficiently compute the
(non-negligible) long-range hydrodynamic interactions.
  Our method is based on the work of {\em Rahimian, Veerapaneni, and Biros,
"Dynamic simulation of locally inextensible vesicles suspended in an arbitrary
two-dimensional domain, a boundary integral method", Journal of Computational
Physics, 229 (18), 2010}. It is a boundary integral formulation of the Stokes
equations coupled to the interface mass continuity and force balance. We extend
the algorithms presented in that paper to increase the robustness of the method
and enable simulations with concentrated suspensions.
  In particular, we propose a scheme in which both intra-vesicle and
inter-vesicle interactions are treated semi-implicitly. In addition we use
special integration for near-singular integrals and we introduce a spectrally
accurate collision detection scheme. We test the proposed methodologies on both
unconfined and confined flows for vesicles whose internal fluid may have a
viscosity contrast with the bulk medium. Our experiments demonstrate the
importance of treating both intra-vesicle and inter-vesicle interactions
accurately.
