Algebraic Splitting for Incompressible Navier–Stokes Equations

Fully discretized incompressible Navier–Stokes equations are solved by splitting the algebraic system with an approximate factorization. This splitting affects the temporal convergence order of velocity and pressure. The splitting error is proportional to the pressure variable, and a simple analysis shows that the original convergence order of the time-integration scheme can be retained by solving for incremental pressure. The combination of splitting and incremental pressure is shown to be equivalent to an error-correcting method using the full pressure. In numerical experiments employing a third-order time-integration scheme and various orders for the pressure increment, the splitting error is shown to control the convergence order, and the full order of the scheme is recaptured for both velocity and pressure. The difference between perturbing the momentum or the continuity equation is also explored.