A numerical oscillation problem of particle methods for CG animations of incompressible fluid dynamics

The discrete time Navier-Stokes equation (22) by the semi-implicit lime evolution scheme gives an approximate solution to the incompressible Navier-Stokes equation (4). But the pressure P* and the posidon U* in die equation (22) do not satisfy die incompressibility (2), Thus die computed pressure P* oscillates numerically. The discrete lime Navier-Slokes equation (22) must be modified in order to converge to die Navier-Stokes equation (4).