  In this article, three dimensional (3D) lid-driven cubic cavity flows have
been studied numerically for various values of Reynolds number ($Re$). The
numerical solution of the Navier-Stokes equations modeling incompressible
viscous fluid flow in a cubic cavity is obtained via a methodology combining a
first order accurate operator-splitting, $L^2$-projection Stokes solver, a
wave-like equation treatment of the advection and finite element methods. The
numerical results obtained for Re$=$400, 1000, and 3200 show a good agreement
with available numerical and experimental results in literature. Simulation
results predict that the critical Re$_{cr}$ for the transition from steady flow
to oscillatory (a Hopf bifurcation) is somewhere in [1870, 1875] for the mesh
size $h=1/96$. Via studying the flow field distortion of fluid flow at Re
before and after Re$_{cr}$, the occurrence of the first pair of
Taylor-G\"ortler-like vortices is connected to the flow field distortion at the
transition from steady flow to oscillatory flow in 3D lid-driven cubic cavity
flows for Re $< 2000$.
