Approximate projection methods: Part I. Inviscid analysis

The use of approximate projection methods for modeling low Mach number flow s avoids many of the numerical complications associated with exact projecti on methods, but introduces additional design choices in developing a robust algorithm. In this paper we first explore these design choices in the sett ing of inviscid incompressible ow using several computational examples. We then develop a framework for analyzing the behavior of the different design variations and use that analysis to explain the features observed in the c omputations. As part of this work we introduce a new variation of the appro ximate projection algorithm that combines the advantages of several of the previous versions.