Exact Fractional Step Methods for Solving the Incompressible Navier-Stokes Equations

Fractional step (or projection) methods are a widely used technique for uncoupling the pressure solution in the incompressible Navier-Stokes equations while still satisfying the incompressibility constraint. Traditional fractional step methods have a time splitting error that can become quite significant if any of the terms in the momentum equation are treated implicitly. Higher order splittings with less error are possible but can be expensive and cumbersome. In this paper an approach is demonstrated that still eliminates the pressure efficiently yet results in no splitting error. It is shown that this approach is relatively general and can also be applied to different numerical methods and other types of constraints (such as immersed boundary constraints). In addition, it is shown that iterative inversion methods require fewer iterations (and therefore reduced cost) when the exact projection method is used compared to more traditional approaches.