Splitting Techniques with Staggered Grids for the Navier–Stokes Equations in the 2D Case

A pseudo-spectral approximation for the Navier–Stokes equations in the 2D case is presented using a new splitting technique based on the Uzawa algorithm. The system is decoupled into Helmholtz equations for the velocity and an equation with the pseudo-Laplacian for the pressure. Staggered grids with Gauss– and Gauss–Lobatto nodes are employed. Preconditioning with finite differences is considered. By extrapolation, a stable second-order method in time for the velocity and at least a first-order method for the pressure can be achieved.