  A three-dimensional deformable capsule convected through a square duct with a
corner is studied via numerical simulations. We develop an accelerated boundary
integral implementation adapted to general geometries and boundary conditions.
A global spectral method is adopted to resolve the dynamics of the capsule
membrane developing elastic tension according to the neo-Hookean constitutive
law and bending moments in an inertialess flow. The simulations show that the
trajectory of the capsule closely follows the underlying streamlines
independently of the capillary number. The membrane deformability, on the other
hand, significantly influences the relative area variations, the advection
velocity and the principal tensions observed during the capsule motion. The
evolution of the capsule velocity displays a loss of the time-reversal symmetry
of Stokes flow due to the elasticity of the membrane. The velocity decreases
while the capsule is approaching the corner as the background flow does,
reaches a minimum at the corner and displays an overshoot past the corner due
to the streamwise elongation induced by the flow acceleration in the downstream
branch. This velocity overshoot increases with confinement while the maxima of
the major principal tension increase linearly with the inverse of the duct
width. Finally, the deformation and tension of the capsule are shown to
decrease in a curved corner.
