[digger]

Dear Friends,

I have started to play with the implementation of some numerical procedures. I’ve just accomplished my finite volume solver for 2D advection-diffusion equation. I started to think about numerical implementation of steady-state incompressible Navier-Stokes model on a staggered grid. I have no very strong background in numerics, I’ve just read the book of Ferziger and Peric and the one of Moukalled et al., however the 2D staggered grid arrangement, for me is not too well documented therein (or maybe I just don’t understand it).

I would like to ask for your help. I just want to start out with one question but probably I will be refreshing this thread a couple of times during implementation. I would be kindly and sincerely grateful for your help.

This is what I’ve accomplished till now. I started with the derivation of discretized form of the u-momentum equation for some location in the „bulk” of my computational domain. This was not too complicated step (hoping I did it correctly).


As can be already seen for discretization of the viscous stress component (more precisely the derivative du/dy) on left boundary of (i,J) node I am using the velocity value at u(i-1,J+1), indicated by the green circle. But then I encountered the first conceptual problem when I started to think about the u-velocity node indicated by the green circle. Ferziger suggests that the shear stress on “east” face on u-momentum element should be calculated using east face of the v-momentum element. But for the u-velocity element I don’t have a “full” v-momentum element. How should I evaluate the du/dy derivative for this element indicated by the green circle?