Coupled FAS Multigrid for the Incompressible Navier-Stokes Equations on Collocated Grids

This work is an extension of a fully coupled matrix-free method for the incompressible steady-state Navier–Stokes equations previously developed by the authors where it has now been implemented within an FAS multigrid scheme. Testing for the 3D laminar lid driven cavity and the 3D laminar backwards facing step show up to two orders of magnitude speed up compared to the OpenFOAM SIMPLE scheme and the ANSYS Fluent coupled solver which uses a linear correction multigrid scheme. Linear scaling with problem size (textbook efficiency) is also observed. The effect of different multigrid cycles, and sweeping directions on the convergence rate of the solver is also investigated. The relative performance compared to the single grid method (without FAS multigrid) has also been considered. • Matrix free, fully coupled FAS multigrid method on nonuniform collocated grids. • Up to two orders of magnitude speed up compared to standard steady solver methods. • Linear scaling with problem size (textbook efficiency). • Investigated different multigrid cycles and sweeping directions on convergence.