Presure boundary conditions in the collocated finite-volume method for the steady Navier–Stokes equations

The pressure boundary conditions for the steady-state solution of the incompressible Navier–Stokes equations with the collocated finite-volume method are discussed. This work is based on inf-sup stable coupled flux approximation. The flux is derived based on the linearity assumption of the velocity and pressure unknowns that yields one-sided flux expressions. Enforcing continuity of these expressions on internal interface we reconstruct the interface velocity and pressure and obtain single continuous flux. As a result, the conservation for the momentum and the divergence is discretely exact. However, on boundary interfaces additional pressure boundary condition is required to reconstruct the interface pressure.