Higher order projection schemes for solving the incompressible Navier-Stokes equations

Chorin's projection method is a well-established numerical scheme to efficiently find solutions of the incompressible Navier-Stokes equations at low computational costs. A rigorous convergence analysis of the method can be performed by reformulation as a semi-explicit pressure-stabilization method, see [6], [4], and has been proposed on the ENUMATH-95 conference by the author. This presentation focuses on the higher order projection scheme of Van Kan (in [8]) and its analysis. In particular, problems arising in incompatibly posed flow problems are addressed that reduce the quality of the approximate solution in a significant way, and a new numerical strategy is proposed to circumvent these problems.