AN ANALYSIS OF THE FRACTIONAL STEP METHOD

The fractional step method for solving the incompressible Navier-Stokes equations in primitive variables is analyzed as a block LU decomposition. In this formulation the issues involving boundary conditions for the intermediate velocity variables and the pressure are clearly resolved. In addition, it is shown that poor temporal accuracy (first-order) is not due to boundary conditions, but due to the method itself. A generalized block LU decomposition that overcomes this difficulty is presented, allowing arbitrarily high temporal order of accuracy. The generalized decomposition is shown to be useful for a wide range of problems including steady problems. Technical issues, such as stability and the appropriate pressure update scheme, are also addressed. Numerical simulations of the unsteady, incompressible Navier-Stokes equations in a square domain confirm the theoretical results. © 1993 Academic Press, Inc.