Analysis of an explicit and matrix free fractional step method for incompressible flows

In this paper we present the analysis of an explicit and matrix free fractional step method for incompressible flows. The presented method can be employed in either conservation or non-conservation form. The stabilization, convergence and conservation aspects of the presented method are discussed. A procedure for eliminating the first order error in time introduced by the split is proposed. Some benchmark steady and unsteady state examples are presented to demonstrate the proposed new aspects of the matrix free scheme.