hi, I have experience in working with SIMPLE algorithms. Very recently I came to know about projection methods that only one iteration is required per time step. After reading literatures I cant able to differentiate the methodology between SIMPLE and projection methods except the treatment of convective terms. Can any one explain me the concept behind projection methods? If proj method is superior than SIMPLE, why they are not used in commercial softwares like FLUENT? thanks in advance for your reply..

I think you are comparing apples and oranges here, which explains the confusion.

Projection methods are used to solve incompressible flow problems, where one may start with an initial velocity field (u^n) (which may or may not satisfy the divergence-free condition). When one want to obtain u^(n+1), however, one has to solve the pressure Poisson equation, which "projects" the solution into divergence-free space, meaning the velocity field satisfies the continuity equation. SIMPLE is one such projection method, which finds the solution by iterative method.

thanks agg.. can you comment about fractional step method in this context?

Let us suppose to start with an initial velocity field u^n (which may or maynot satisfy continuity)

Fractional method lets one update the velocity field in 2 steps. In the first step one computes an intermediate velocity field u* based on the convective and diffusive and any other terms (like gravity, eddy viscosity etc.) This velocity field does not satisfy continuity. To obtain the correct velocity field u^(n+1) one solves the Poisson equation which projects the velocity field into a divergence-free space.

For more information, refer to Kim and Moin's 1985 JCP paper on the fractional step method.

thanks agg.. your explanations are very helpful..