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Ventilation Design Handbook on Animal Research Facilities Using Static Microisolators 
the center of each face of the cell so that fluxes flowing through the cell can be calculated 
directly. 
Once the solution domain has been gridded, each governing equation must be integrated over 
each cell. Only when the laws of conservation, as well as the turbulent transport equations, are 
satisfied at each cell (within a tolerable degree) is the solution complete. 
For simplicity of coding, all the governing equations are organized into a similar form. This 
generic form can be written as: 
dpE/,-4> 
a*, 
f 
r 
\ 
= s 
(5.30) 
The first term represents the convection of any variable, <j), by the mean fluid velocity, U l ; the 
second term represents diffusion where T is the diffusion coefficient; and the third term is a 
source or sink term where <(> is either created or destroyed. When integrating over a control 
volume we obtain: 
J p(pU r n6A - Jf^-.ndA = J SdV 
(5.31) 
The calculation of these integrals is the center of the discretization process. Figure 5.05 shows a 
single orthogonal cell and some of its neighbors. With a nonstaggered grid, all variables are 
stored at the center of the cell at point P. Neighboring points include points E, W, WW, and so 
on. In the schemes that follow, a lower case subscript (n, e, s, w) refers to values at the 
appropriate face whereas an upper case subscript (N, E, S, W) refers to values at the appropriate 
cell centers. 
5.2.5. 1 Treatment of the diffusion terms 
The diffusion term is the simplest to integrate. By looking at the diffusive flux at the west face of 
the cell we can write: 
= (5.32) 
J K 
Where h w is the distance between cell centers. The above equation can be rewritten as: 
