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How can I get u,v momentum equation in staggered grid? |
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May 20, 2013, 03:09 |
How can I get u,v momentum equation in staggered grid?
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#1 |
Senior Member
Dongyue Li
Join Date: Jun 2012
Location: Beijing, China
Posts: 838
Rep Power: 17 |
Hi All,
I want to calculate the 16 cells cavity flow manully. I have get the result by OpenFOAM which is so easy to calculate.But I want to know deeply about CFD so I want to calculate it manully. Generally in most books regarding CFD.We have this u momentum equation:IMAGE 1. After integration this u momentum in u control volume.and some arrangement(like the book said..)We have IMAGE 2. 1'The problem is when I do it myself.I cannot integrate it ...Does anyone know how to integrate it?(All of the books have neglect the discretisation precedure.) 2'BTW,in IMAGE 1,there is a v in the equation.Why its gone in the discretisation form? Thanks in advance. |
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May 20, 2013, 03:25 |
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#2 |
Senior Member
Join Date: Dec 2011
Location: Madrid, Spain
Posts: 134
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Hi.
1) Check book "Introduction to computational fluid dynamics, the finite volume method" by Versteeg&Malalasekera, you'll find the discretization thoroughly described there. 2) The equation you showed is the discretized form of the u velocity component equation. The equation for v has the exact same form, but substituting deltax by delta y and the corresponding ai,j coefficients. Again check book. Cheers, Michujo. |
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May 20, 2013, 03:26 |
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#3 |
New Member
Mitesh Vegad
Join Date: Apr 2013
Posts: 18
Rep Power: 13 |
The equation that you have posted is for X direction momentum conservation and the SCALAR unknown there is u. The v that you are talking of is taken care as mass flow through the face. It is similar to treatment of the first u term that is there in the first term i your equation.
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May 20, 2013, 04:33 |
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#4 | |
Senior Member
Dongyue Li
Join Date: Jun 2012
Location: Beijing, China
Posts: 838
Rep Power: 17 |
Quote:
Thanks for your reply. Yeah,I am reading that book ,thats super good.But it neglect the discretisation precedure.I am a newbie. So I have to ask for a favor. I wrote my procedures.I dont know if its rite. could you guys help me to check it out please? Thanks. |
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May 20, 2013, 05:15 |
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#5 | |
Senior Member
Dongyue Li
Join Date: Jun 2012
Location: Beijing, China
Posts: 838
Rep Power: 17 |
Quote:
See the image below... |
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May 20, 2013, 19:37 |
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#6 |
Senior Member
Dongyue Li
Join Date: Jun 2012
Location: Beijing, China
Posts: 838
Rep Power: 17 |
Hi All,
Thanks for your attention.I have done this now.This should be clear. |
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