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Pressure boundary conditions in MAC method

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Old   January 20, 2000, 21:00
Default Pressure boundary conditions in MAC method
  #1
Ravi
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Hi,

I am working on a natural convection problem and am using the using the unsteady formulation of the MAC method given in Hoffmann (pg 321-322). Although the book says that pressure boundary conditions are not needed for the staggered mesh, the equation for pressure includes pressure outside the boundary.

Thanks for your help

Ravi
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Old   January 21, 2000, 03:55
Default Re: Pressure boundary conditions in MAC method
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Chetan
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Ravi If you are upto something in MAC you must have defined "ghost cells" which are actully outside the physical domain of interest but are required (and hence defined) for satisfying boundary conditions. These serve the purpose for defining boundary conditions for all variable including pressure. However, if you are trying to find pressure ON THE SURFACE (like for calculating drag and such things),then you have to perform some arithmetic gymnastics which comes after you have finished computing. Chetan
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Old   January 21, 2000, 12:07
Default Re: Pressure boundary conditions in MAC method
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Ravi
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I have defined ghost cells outside the boundary but I do not know the pressure boundary conditions for the problem that I am working on.

Thanks

Ravi
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Old   January 21, 2000, 13:03
Default Re: Pressure boundary conditions in MAC method
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Chetan
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Ravi

As the famous saying goes "there are no boundary conditions for pressure" you can't do much. Pressure is a floating value in the sense that it is relative. That is the essence of this method (others also).

One starts with some initial conditions (for all variables). Then these are updated by solving the momentum equation

U(n+1,i,j,k) = U(n,i,j,k) + DeltaT*Other terms

similar expressions for other variables.

n is time index and i,j,k are spatial indices.

Other terms are known values (if you are on the first (time) iteration the initial conditions constitute these OTs. If you are somewhere in the middle of the computation the results from the last itreration are there).

Then you take these updated values and see if the continuity equation is satisfied. If no, take a fraction of the non-zero value (divergence) and update velocities and pressures (standard expressions) and go back to your momentum equation. Obviously, these steps are performed for the "real" cells only. Meaning if you had IMAX cells in X-direction including two ghost cells, you do DO I=2,IMAX-1.

Now, here is when you ask where are the pressure boundary conditions. The answer is the same old saying (say above). So, what happens is that the pressure is given some initial value (Assume 0.00 for the full field) and it gets updated as per the above steps. It floats about the initial value you gave.

Regards
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Old   January 21, 2000, 14:50
Default Re: Pressure boundary conditions in MAC method
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Ravi
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Thanks

Ravi
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