Abstract: The purpose of this paper is to introduce a new implicit fractional step altorighm of two processes for the calculation of the transport equations of fluid flows i.e., the convection-diffusion process and propagation process.It is found that the second step of the propagation process in the present method resembles the velocity-pressure correction procedure in the SIMPLE-like methods, and the SIMPLEC algorithm is a special case of the proposed method. Two numerical examples of laminar flows show that the rate of convergence can be significantly improved by the change of the optimal coefficient α.

Key words: fractional step method, pressure-correction algorithm, Navier-Stokes equations, implicit-explicit weighting factor