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We present a new energy-stable open boundary condition, and an associatednumerical algorithm, for simulating incompressible flows with outflow/openboundaries. This open boundary condition ensures the energy stability of thesystem, 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 tothe usual convective boundary condition. One prominent feature of this boundarycondition is that it provides a control over the velocity on the outflow/openboundary. This is not available with the other energy-stable open boundaryconditions from previous works. Our numerical algorithm treats the proposedopen boundary condition based on a rotational velocity-correction typestrategy. It gives rise to a Robin-type condition for the discrete pressure anda Robin-type condition for the discrete velocity on the outflow/open boundary,respectively at the pressure and the velocity sub-steps. We present extensivenumerical experiments on a canonical wake flow and a jet flow in open domain totest the effectiveness and performance of the method developed herein.Simulation results are compared with the experimental data as well as withother previous simulations to demonstrate the accuracy of the current method.Long-time simulations are performed for a range of Reynolds numbers, at whichstrong vortices and backflows occur at the outflow/open boundaries. The resultsshow that our method is effective in overcoming the backflow instability, andthat it allows for the vortices to discharge from the domain in a fairlynatural fashion even at high Reynolds numbers.

A Convective-like Energy-Stable Open Boundary Condition for Simulations of Incompressible Flows