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

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.
http://www.cfd-online.com/Forums/att...red-grid-1.jpg
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.

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.

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.

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

Hi All,

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