A sub-cell discretization method for the convective terms in the incompressible Navier-Stokes equations

In this contribution we present a sub-cell discretization method for the computation of the interface velocities involved in the convective terms of the incompressible Navier-Stokes equations. We compute the interface velocity by solving a local two-point boundary value problem (BVP) iteratively. To account for the two-dimensionality of the interface velocity we introduce a constant cross-flux term in our computation. The discretization scheme is used to simulate the flow in a lid-driven square cavity.