REVIEW ON THE PROJECTION METHODS IN THE NUMERICAL SOLUTION OF THE INCOMPRESSIBLE FLOW

Because of the decoupling of the velocity and the pressure computation,the projection method is much more efficient than the fully coupled procedures.This notable advantage has attracted great attention, and many improved projection methods have been developed during the past 20 years.The projection methods are currently among the most popular methods for solving viscous incompressible flow based on the primitive variable formulations.According to their processes of construction,the projection methods are classified into three types in the present paper,namely,the Helmholtz-Hodge decomposition projection methods,the operator splitting projection methods and the local continuous projection methods.Their development and solution procedures axe introduced in details.From the solution procedures,it is found that the velocity-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 time for the velocity can be readily obtained,while the computed pressure is typically only first order accurate 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 order accurate projection methods both theoretically and practically,which may clarify some misunderstandings about the accuracy of projection methods.