A direction-splitting Navier–Stokes solver on co-located grids

We introduce a new finite-difference solver for the incompressible Navier-Stokes equations that exploits the direction-splitting method proposed by Guermond and Minev in 2010, but is formulated on a co-located grid. The main ingredients of the new solver are: i) the direction-splitting approach adopted for both the momentum and the pressure equations; and ii) the co-located grid approach. The solver is parallelised by the Schur-complement method, and achieves very high performance levels on thousands of processors. Several test cases are proposed to assess the accuracy and efficiency of the method.