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projection method for helical pipe(3D)

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Old   August 14, 2010, 21:30
Default projection method for helical pipe(3D)
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I want to simulation the flow in helical pipe.
I have one Continuity equation and three momentum equations in s=>(u),r=>(v),teta=>(w).
I used staggered mesh and descritized all of terms in central(finite difference).
I want to use projection method for solution these navier-stokes equations.

first problem:
What is stability condition for helical coordinates (three dimensional)in projection method?because I don’t know which number of interval in s,r,teta causes convergence!

second problem :
In descritized scheme we have i+2,i-2,j+2,j-2,k+2,k-2 indexes for u,v and w.
what do I have to do for the nodes of near the boundary? It means that two nodes produced out of domain but I don’t know value of them and they are unknowns.

Third problem:
We have to apply boundary s and teta I have to apply periodic
Conditions.what are periodic boundary conditions for u,v and w in s and teta?

Is there any paper or books(references) for programming of projection method(three dimensional)?

Thanks for your guidance and aid
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