We present a set of new energy-stable open boundary conditions for tackling the backflow instability in simulations of outflow/open boundary problems for incompressible flows. These boundary conditions are developed through two steps: (i) devise a general form of boundary conditions that ensure the energy stability by re-formulating the boundary contribution into a quadratic form in terms of a symmetric matrix and computing an associated eigen problem; and (ii) require that, upon imposing the boundary conditions from the previous step, the scale of boundary dissipation should match a physical scale. These open boundary conditions can be re-cast into the form of a traction-type condition, and therefore they can be implemented numerically using the splitting-type algorithm from a previous work. The current boundary conditions can effectively overcome the backflow instability typically encountered at moderate and high Reynolds numbers. These boundary conditions in general give rise to a n 查看全文>>