  We present a new energy-stable open boundary condition, and an associated
numerical algorithm, for simulating incompressible flows with outflow/open
boundaries. This open boundary condition ensures the energy stability of the
system, even when strong vortices or backflows occur at the outflow boundary.
Under certain situations it can be reduced to a form that can be analogized to
the usual convective boundary condition. One prominent feature of this boundary
condition is that it provides a control over the velocity on the outflow/open
boundary. This is not available with the other energy-stable open boundary
conditions from previous works. Our numerical algorithm treats the proposed
open boundary condition based on a rotational velocity-correction type
strategy. It gives rise to a Robin-type condition for the discrete pressure and
a Robin-type condition for the discrete velocity on the outflow/open boundary,
respectively at the pressure and the velocity sub-steps. We present extensive
numerical experiments on a canonical wake flow and a jet flow in open domain to
test the effectiveness and performance of the method developed herein.
Simulation results are compared with the experimental data as well as with
other previous simulations to demonstrate the accuracy of the current method.
Long-time simulations are performed for a range of Reynolds numbers, at which
strong vortices and backflows occur at the outflow/open boundaries. The results
show that our method is effective in overcoming the backflow instability, and
that it allows for the vortices to discharge from the domain in a fairly
natural fashion even at high Reynolds numbers.
