The Accuracy of the Fractional Step Method

Abstract

We analyze the accuracy of the fractional step method of Kim and Moin [J. Comput. Phys., 59 (1985), pp. 308--323] for the incompressible Navier--Stokes equations. We show that the boundary conditions cannot be exactly satisfied in the projection step and that this limits the accuracy of the method. We also show that the pressure in any projection method can be at best first-order accurate. Our analysis is simpler and more direct than the previous analyses of this method. We also show that there is no numerical boundary layer for velocity or pressure, but there is one for the auxiliary pressure variable.