A new class of truly consistent splitting schemes for incompressible flows

A new class of splitting schemes for incompressible flows is introduced. The new schemes are based on a weak form of the pressure Poisson equation and, at each time step, only require to solve a set of Helmholtz-type equations for the velocity and a Poisson equation (in the weak form) for the pressure, just as pressure-correction and velocity-correction schemes. However, unlike pressure-correction and velocity-correction schemes, the new splitting schemes are free of splitting errors and deliver full accuracy on the vorticity and the pressure.