The Projection-Method

NaSt3DGP employs a Chorin-type projection method for the decoupling of momentum and continuity equations. The general procedure for projection methods is a predictor-corrector approach. In a first step a preliminary velocity field is computed utilising the momentum equations. This velocity does not satisfy the continuity equation. In a second step a poisson-type equation for the pressure is solved which is derived using the continuity equation. In the last step the preliminary velocity field is projected onto a divergence-free velocity field using the computed pressure.

Neglecting the spatial discretization (for the time being) this
procedure reads

1. Given , solve

2. Solve

Application of the divergence operator to () leads to the Poisson equation for the pressure