  In this article, three-dimensional (3D) lid-driven flows in semicircular
cavities are studied. The numerical solution of the Navier-Stokes equations
modeling incompressible viscous fluid flow in cavities is obtained via a
methodology combining a first-order accurate operator-splitting scheme, a
fictitious domain formulation, and finite element space approximations. The
critical Reynolds numbers (Re_{cr}) for having oscillatory flow (a Hopf
bifurcation) are obtained. The associated oscillating motion in a semicircular
cavity with length equal to width has been studied in detail. Based on the
averaged velocity field in one period of oscillating motion, the flow
difference (called oscillation mode) between the velocity field and averaged
one at several time instances in such period shows almost the same flow pattern
for the Reynolds numbers close to Re_{cr}. This oscillation mode in a
semicircular cavity shows a close similarity to the one obtained in a shallow
cavity, but with some difference in a shallow cavity which is triggered by the
presence of two vertical side walls and downstream wall.
