A fractional-step method for the incompressible Navier-Stokes equations related to a predictor-multicorrector algorithm

An implicit fractional-step method for the numerical solution of the time-d ependent incompressible Navier-Stokes equations in primitive variables is s tudied in this paper. The method, which is first-order accurate in the time step, is shown to converge to an exact solution of the equations. By adequ ately splitting the viscous term, it allows the enforcement of full Dirichl et boundary conditions on the velocity in all substeps of the scheme, unlik e standard projection methods. The consideration of this method was actuall y motivated by the study of a well-known predictor-multicorrector algorithm , when this is applied to the incompressible Navier-Stokes equations. A new derivation of the algorithm in a general setting is provided, showing in w hat sense it can also be understood as a fractional-step method; this justi fies, in particular, why the original boundary conditions of the problem ca n be enforced in this algorithm. Two different finite element interpolation s are considered for the space discretization, and numerical results obtain ed with them for standard benchmark cases are presented. (C) 1998 John Wile y & Sons, Ltd.