  The dynamics of two-dimensional viscous vesicles in shear flow, with
different fluid viscosities $\eta_{\rm in}$ and $\eta_{\rm out}$ inside and
outside, respectively, is studied using mesoscale simulation techniques.
Besides the well-known tank-treading and tumbling motions, an oscillatory
swinging motion is observed in the simulations for large shear rate. The
existence of this swinging motion requires the excitation of higher-order
undulation modes (beyond elliptical deformations) in two dimensions.
Keller-Skalak theory is extended to deformable two-dimensional vesicles, such
that a dynamical phase diagram can be predicted for the reduced shear rate and
the viscosity contrast $\eta_{\rm in}/\eta_{\rm out}$. The simulation results
are found to be in good agreement with the theoretical predictions, when
thermal fluctuations are incorporated in the theory. Moreover, the hydrodynamic
lift force, acting on vesicles under shear close to a wall, is determined from
simulations for various viscosity contrasts. For comparison, the lift force is
calculated numerically in the absence of thermal fluctuations using the
boundary-integral method for equal inside and outside viscosities. Both methods
show that the dependence of the lift force on the distance $y_{\rm {cm}}$ of
the vesicle center of mass from the wall is well described by an effective
power law $y_{\rm {cm}}^{-2}$ for intermediate distances $0.8 R_{\rm p}
\lesssim y_{\rm {cm}} \lesssim 3 R_{\rm p}$ with vesicle radius $R_{\rm p}$.
The boundary-integral calculation indicates that the lift force decays
asymptotically as $1/[y_{\rm {cm}}\ln(y_{\rm {cm}})]$ far from the wall.
