Fractional Step Method interpretation
 

Dear all,

I am using the Fractional Step Method (FSM) for the first time, so I am really just trying to understand how it normally behaves. Despite some effort, I still cannot get it to work as it presumably should.

In accordance with (Perot 1993, 1995) and (Zang, Street & Koseff, 1994), I discretize the equations before performing the FSM factorization. In practice, this means that the boundary conditions chosen for the velocity u are applied to u*; is this right? So if, as in my case, you have no-slip at the bottom and a Dirichlet (e.g. u=u0) at the top, then u* will tend toward zero at the bottom and toward u0 at the top. (Perhaps this is where my interpretation is wrong?)

Then comes the pressure correction. If you already have u* tending toward 0 on the surface, then that would mean grad(p) should also tend toward 0 on the surface to yield u=0, i.e. constant pressure on the surface. As you point out, this does not make sense. How is one then supposed to apply the fractional step method?

By the way, I use a non-staggered, non-orthogonal grid.

Thanks in advance for your help!

Jean-François

Re: Fractional Step Method interpretation
 

>In practice, this means that the boundary conditions chosen for the velocity u are applied to u*

Correct. Both of the B.C.'s you describe are Dirichlet.

>By the way, I use a non-staggered, non-orthogonal grid.

The non-staggered grid is probably the issue. Many of the fraction step/pressure correction methods have issues (like limitation to normal velocity B.C.'s, for example) if you try to use a non-staggered discretization. There are some versions that stagger only some of the flow variables, but I'm not sure if these methods are still in use.

Jason

Re: Fractional Step Method interpretation
 

Jean-Francois,

I have an article that I wrote (currently in press for the Journal of Computational Physics) where I spend some time really explaining the steps one has to follow with the fractional step method using a non-staggered, curvilinear, Finite volume approach. In addition, I discuss conservation issues (that might also be of interest to you).

Therefore, shoot me an email at felten@research.ge.com so that I could email you my paper.

Sincerely,

Frederic