A coupled block implicit solver for the incompressible Navier–Stokes equations on collocated grids

A fully coupled matrix-free method is developed for solving the incompressible steady-state Navier–Stokes equations on a collocated finite volume grid. This is achieved by offsetting the momentum equations relative to the continuity equation they are implicitly coupled to at each cell and updating the solution by sweeping planes in 3D and lines in 2D. The effect of sweeping direction on convergence rate is investigated for the 3D laminar lid driven cavity at Reynolds number 200 and 1000 and 3D laminar backwards facing step at Reynolds number 100 and 200. For these flow cases, a speed-up of up to an order of magnitude compared to SIMPLE schemes of OpenFOAM and ANSYS Fluent and the coupled solver of ANSYS Fluent was observed. • Coupled block implicit solver for Navier–Stokes equations on collocated grids. • Line sweeping optimal for problems with dominant flow direction. • Up to order of magnitude speed up compared to standard commercial steady solvers.