Accuracy and dynamical behavior of several equal-order incompressible schemes

Abstract: Equal-order schemes are increasingly used in the finite element simulation of incompressible flows. Though some methods, such as the GLS method, are quite well established, accuracy and dynamical behavior of these methods has not been thoroughly assessed. More recently, "fourth-order" dissipation schemes that ressemble some finite difference schemes have been introduced. Variants of these schemes have been proposed by Lohner, Habashi, Codina, and other authors.  It is thus important to compare these alternatives in terms of accuracy. Interestingly enough, standard treatment of fourth-order schemes leads to a spurious pressure wave in some cases that will also be discussed, as it may pollute the pressure field for a significant fraction of the simulation time.