Open boundary conditions for the velocity-correction scheme of the Navier–Stokes equations

► We implement open boundary conditions for the velocity correction schemes. ► We illustrate a second-order accuracy in time on a manufactured test case. ► We study the Reynolds number effect on the flow structure in a bifurcated tube. ► We verify the solution obtained for the unsteady flow around a square cylinder. In this paper we propose to study open boundary conditions for incompressible Navier–Stokes equations, in the framework of velocity-correction methods. The standard way to enforce this type of boundary condition is described, followed by an adaptation of the one we proposed in [36] that provides higher pressure and velocity convergence rates in space and time for pressure-correction schemes. These two methods are illustrated with a numerical test with both finite volume and spectral Legendre methods. We conclude with three physical simulations: first with the flow over a backward-facing step, secondly, we study, in a geometry where a bifurcation takes place, the influence of Reynolds number on the laminar flow structure, and lastly, we verify the solution obtained for the unsteady flow around a square cylinder.