  Dynamics of a single vesicle under shear flow between two parallel plates is
studied using two-dimensional lattice-Boltzmann simulations. We first present
how we adapted the lattice-Boltzmann method to simulate vesicle dynamics, using
an approach known from the immersed boundary method. The fluid flow is computed
on an Eulerian regular fixed mesh while the location of the vesicle membrane is
tracked by a Lagrangian moving mesh. As benchmarking tests, the known vesicle
equilibrium shapes in a fluid at rest are found and the dynamical behavior of a
vesicle under simple shear flow is being reproduced. Further, we focus on
investigating the effect of the confinement on the dynamics, a question that
has received little attention so far. In particular, we study how the vesicle
steady inclination angle in the tank-treading regime depends on the degree of
confinement. The influence of the confinement on the effective viscosity of the
composite fluid is also analyzed. At a given reduced volume (the swelling
degree) of a vesicle we find that both the inclination angle, and the membrane
tank-treading velocity decrease with increasing confinement. At sufficiently
large degree of confinement the tank-treading velocity exhibits a
non-monotonous dependence on the reduced volume and the effective viscosity
shows a nonlinear behavior.
