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Boundary conditions in the proyection method

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Old   November 1, 2004, 03:55
Default Boundary conditions in the proyection method
  #1
Oscar Salazar
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Hi

Is it possible to apply the projection method in a system with combination of Neuman and Dirichlet boundary conditions for the velocity? sample: flow inside a pipe

Boundary conditions (cylindrical 2D Navier-Stokes):

inflow (z=0): Uz(0,r) = 3 , Ur(0,r) = 0

outflow (z=L): dUz/dz = 0 , Ur(0,r) = 0

center (r=0): dUz/dr = 0 , Ur(z,0) = 0

wall (r=R): Uz(z,R) = 0 , Ur (z,R) = 0

thanks
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Old   November 1, 2004, 05:03
Default Re: Boundary conditions in the proyection method
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Junseok Kim
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I think you can still use the projection method, by the way, you may want to change inflow (z=0): Uz(0,r) = 3 as someting like

Uz(0,r) = 3(R-r)(R+r)/R^2

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Old   November 4, 2004, 01:25
Default Re: Boundary conditions in the proyection method
  #3
J.Deng
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I'm trying program codes for projection method on staggerd grid. When simulate a problem like 'lid-driven cavity flow', the boudary conditions are easy to set, but when a outflow is included, the boudary condition is hard to impose. Most references I have found are concerned about the Dirichlet bondary conditions, who can provide me some more detailed papers on the boudary conditions for projection method? Thanks!
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Old   November 4, 2004, 05:23
Default Re: Boundary conditions in the proyection method
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Halim Choi
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Hi,

Your outflow condition is not right. If you use the velocity boundary condition at the exit (that means you do not use the pressure boundary condition at the exit), the mass conservation must be satisfied at the outlet. Try following way.

(1) First impose at z=L, dUz/dz=0, dUr/dz=0 such that;

Do J=2,JMAX-1

Uz(IMAX,J)=Uz(IMAX-1,J)

Ur(IMAX,J)=Ur(IMAX-1,J)

end do

(2) Calculate mass flow rate at inlet

Flowin=0.

Do J=2,JMAX-1

Flowin=Flowin+density(1,J)*r(J)*delta_r(J)*Uz(1,J)

end do

where delta_r is the size of each control volume in r_direction.

(3) Calculate mass flow rate at exit

Flowout=0.

Do J=2,JMAX-1

Flowout=Flowout+density(1,J)*r(J)*delta_r(J)*Uz(IM AX,J)

end do

(4) Calculate Factor=Flowin/Flowout

(5) Imposed the velocity at exit such that

Do J=2,JMAX-1

Uz(IMAX,J)=Factor*Uz(IMAX,J)

end do

Above method is what SIMPLE people are usually doing.

I hope this helps.

Halim Choi
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Old   November 5, 2004, 10:28
Default Re: Boundary conditions in the proyection method
  #5
Oscar Link
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HI! look at the papers by Philip Gresho & Co.:

(1984) Int. J. Num. Meth. in Fluids, Vol4, 557-598 (1987) Int. J. Num. Meth. in Fluids, Vol7, 1111-1145 (1990) Int. J. Num. Meth. in Fluids, Vol11, 587-620

I found there a lot of usefull tips, but the articles were too much theoretical oriented for me. Anyway, I think that it is a good start!

Greetings,

Oscar.

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