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Boundary conditions for Staggered grid - steady pipe Flow - SIMPLE

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Old   November 3, 2021, 05:39
Post Boundary conditions for Staggered grid - steady pipe Flow - SIMPLE
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Aman Sangal
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Hi everyone,

I'm sorry for yet another thread, but I am getting stuck pretty bad. I promise to upload all my notes, & proper documentation for devising a staggered solver with Steady & Unsteady problems from scratch.

For now, I am having trouble defining the boundary condition on a staggered grid. This is for a SIMPLE solver I am trying to create.
For a Staggered Model with Velocity grid encapsulating the Pressure grid fully, I am using the following boundary condition for pipe flow.
1. Ux = 1.0 West
2. Uy = 0.0 West
3. Ux[East] = Ux[East-1]
4. Uy[East] = Uy[East-1]
5. Uy[North] = 0
6. Uy[South] = 0
7. P[East] = 0
Please have a look at the annotated image too. I've disregarded gravity in the momentum predictor here, & used East column of Pressure = 0 B.C.


Are these minimal necessary boundary conditions implied onto the grid, or some of them can be removed?
Also, I'd appreciate any easy get arounds for implementing these boundary conditions, besides resizing the whole system of equation matrix.

Any documentation you can guide me toward for staggered boundary conditions would be marvellous, as I can't finding anything proper in patankar, Chowdhury, or peric.
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Old   November 4, 2021, 00:29
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Aman Sangal
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https://www.youtube.com/watch?v=hb4R...KB9aqT&index=4

This cleared all of my doubts. I wasn't discretising the diffusion term for boundary cell seperately, just using coefficients from generalised cell, which isn't a problem for the convective terms, but is a problem for diffusion terms.
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boundary conditions, simple solver, singular matrix, staggered grid

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