Abstract:Because of the decoupling of the velocity and the pressure computation, the projectionmethod is much more efficient than the fully coupled procedures. This notable advantage hasattracted great attention, and many improved projection methods havebeendeveloped duringthe past 20 years. The projection methods are currently among the most popular methods forsolving viscous incompressible flow based on the primitive variable formulations. According totheir processes of construction, the projection methods are classified into three types in thepresent paper, namely, the Helmholtz-Hodge decomposition projection methods, the operatorsplitting projection methods and the local continuous projection methods. Their development andsolution procedures are introduced in details. From the solution procedures, it is found that thevelocity-pressure decoupling makes it difficult to analyze the accuracy of the projection method,which has often been a subject for debating. Generally speaking, high order convergence in timefor the velocity can be readily obtained, while the computed pressure is typically only first orderaccurate in time. However, by comparing and analyzing the three types of the projection methods,we show that the local continuous projection methods make it possible to develop high orderaccurate projection methods both theoretically and practically, whichmay clarifysome misunderstandings about the accuracy of projection methods.