Normal Mode Analysis of Second-order Projection Methods for Incompressible Flows

A rigorous normal mode error analysis is carried out for two second-order projection type methods. It is shown that although the two schemes provide second-order accuracy for the velocity in L-norm, their accuracies for the velocity in H1-norm and for the pressure in L2-norm are different, and only the consistent splitting scheme introduced in [6] provides full second-order accuracy for all variable in their natural norms. The advantages and disadvantages of the normal mode analysis vs. the energy method are also elaborated.