How can I get u,v momentum equation in staggered grid?

sharonyue · May 20, 2013, 03:09

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.

michujo · May 20, 2013, 03:25

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.

m.vegad · May 20, 2013, 03:26

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.

sharonyue · May 20, 2013, 04:33

Quote:

Originally Posted by m.vegad

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.

Hi michujo and Mitesh,

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.

sharonyue · May 20, 2013, 05:15

Quote:

Originally Posted by sharonyue

I dont know if its rite. could you guys help me to check it out please? Thanks.

Looks its not rite.
See the image below...

sharonyue · May 20, 2013, 19:37

Hi All,

Thanks for your attention.I have done this now.This should be clear.

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May 20, 2013, 03:25		#2
michujo Senior Member Join Date: Dec 2011 Location: Madrid, Spain Posts: 134 Rep Power: 15	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.

May 20, 2013, 03:26		#3
m.vegad 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.