equations in Hirsch's numerical computation of internal and external flows - 2nd edit
 

Hi, i am following a book, Hirsch's numerical computation of internal and external flows - 2nd edition, vol 1. I have a task to extend a set of equations from 2d to 3d but i cant understand how Hirsch defines/derives his 2d numerical solution. The equations i refer to are (12.4.27).

I cant understand how he gets the equations can anyone explain?

http://postimg.org/image/3w9v1ko97/http://postimg.org/image/3w9v1ko97/http://postimg.org/image/3w9v1ko97/ can anyone explain how the equations 12.4.27 are formed/derived to me please :)

I know that the scheme is second order central difference but would like to be able to derive the equations from Taylor series expansion.

I do not have the book at this moment, the grid is non-uniform and staggering is used?
I see the use of linear averaging for the mid-section values

yes your right grid is clustered and staggering is applied to connect values at the cell centers with face defined values. weighted averages are applied to obtain the interface values.

Ok, I think that once the grid arrengement is defined you can apply the linear average between connected nodes. It can be somehow tedious to do the manipulation but it is not very complicated to verify the formulas.

can you explain what you mean further please?

you should know from the book the arrangement of the staggered variables to verify the equation

http://postimg.org/image/wsi9o4ood/

is this what you are talking about?

Yes. ;)

ok i still not sure how to get the (12.4.27) equations for u_x,v_x,u_y,v_y etc can you show me? thanks for helping me btw.

ok i think i have understood how the equations for 2d are derived but i have tried to extend the scheme to be three dimensional. can you tell me if i am correct in my 3d formulas please?

http://imageshack.com/a/img923/3116/prEM4i.png

please help fellow cfders.:)