You are probably very familiar with it, but this has been the basis of most numerical solvers for the Navier-Stokes equations since the late 1960s: https://en.

You are probably very familiar with it, but this has been the basis of most numerical solvers for the Navier-Stokes equations since the late 1960s: https://en.wikipedia.org/wiki/Projection_method_(fluid_dynamics) https://en.wikipedia.org/wiki/Projection_method_(fluid_dynam... A disadvantage is that you get a splitting error term that tends to dominate, so you gain nothing from using higher-order methods in time.