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 Jean-FranÃ§ois Corbett February 23, 2006 10:12

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.

Jean-François

 jasond February 27, 2006 18:32

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

 Frederic Felten March 1, 2006 11:38

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

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